Method for creating numerical analysis models for polymer materials

Abstract

This invention provides a method for creating numerical analysis models of polymer materials that can reproduce the spatial distribution of recrosslinking with minimal computational effort. [Solution] A method for creating a numerical analysis model of a polymer material. This method includes: a cutting step of cutting at least one polymer chain model 5 with a bonding model 7; a step of selecting at least one particle model 6A from a pair of particle models 6 that were bonded to the cut bonding model 7; a step of probabilistically calculating a displacement vector ΔV according to a predetermined average value of distances; a search step of searching for the particle model 6 closest to a position moved by the displacement vector ΔV from the position of the selected particle model 6A; and a step of adding a bond between the closest particle model 6 and a particle model 6 adjacent to the closest particle model 6.

Description

Technical Field

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[0005]

[0001] The present invention relates to a method for creating a model for numerical analysis of polymer materials.

Background Art

[0002] The following Patent Document 1 describes a method for creating a model for numerical analysis of polymer chains. This creation method includes a step of inputting a polymer chain model including a plurality of particle models and a bonding model for bonding between adjacent particle models based on the polymer chain, and a cutting step of cutting the bonding of the polymer chain model.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Non-Patent Documents

[0004]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] At the cleavage points of polymer chains, radicals are typically generated, followed by a radical chain reaction. During this process, radicals may move between molecules through reactions such as hydrogen abstraction. Additionally, new bonds, known as recrosslinking, may form between polymer chains. Since such recrosslinking affects the properties of polymer materials, it is crucial to create a numerical analysis model of polymer chains that can reproduce the spatial distribution of recrosslinking in order to accurately estimate the properties of polymer materials through simulation. One known method for reproducing this spatial distribution of recrosslinking is to perform precise molecular dynamics simulations that reproduce the elementary processes of the reaction, as described in Non-Patent Literature 1. However, such precise simulations require a large amount of computation, making them difficult to apply to large-scale models.

[0006] This invention was devised in view of the above-described circumstances, and its main objective is to provide a method for creating a numerical analysis model of polymer materials that can reproduce the spatial distribution of recrosslinking with a small amount of computation. [Means for solving the problem]

[0007] The present invention relates to a method for creating a numerical analysis model of a polymer material, comprising the steps of: inputting one or more polymer chain models, each including a plurality of particle models and a coupling model connecting adjacent pairs of the particle models, into a computer based on the polymer chains constituting the polymer material; arranging the polymer chain models in a cell which is a predetermined three-dimensional virtual space to set up a polymer material model; a cutting step in which the computer cuts at least one of the polymer chain models with the coupling model; a step in which the computer selects at least one of the pair of particle models that were coupled to the cut coupling model; a step in which the computer probabilistically calculates a displacement vector according to a predetermined average value of distances; a search step in which the computer searches for the particle model closest to a position moved by the displacement vector from the position of the selected particle model; and a step in which the computer adds a coupling between the closest particle model and a particle model adjacent to the closest particle model. This is a method for creating numerical analysis models of polymer materials, including [specific details omitted]. [Effects of the Invention]

[0008] The present invention provides a method for creating numerical analysis models of polymer materials. By adopting the above configuration, the average value of a predetermined distance is used as the average radical migration distance from the cleavage site to the recrosslinking site. This makes it possible to create numerical analysis models of polymer materials that can reproduce the spatial distribution of recrosslinking with less computation, without having to perform precise molecular dynamics simulations to reproduce the elementary reaction processes as in the conventional method. [Brief explanation of the drawing]

[0009] [Figure 1] This is a perspective view showing an example of a computer used to perform a method for creating numerical analysis models of polymer materials. [Figure 2] This is the structural formula of polybutadiene. [Figure 3]This flowchart shows an example of the processing procedure for creating a numerical analysis model for polymer materials. [Figure 4] This is a conceptual diagram illustrating an example of a polymer chain model (Kremer-Grest model). [Figure 5] This is a conceptual diagram showing an example of a cell in which polymer chain models are arranged. [Figure 6] This is a conceptual diagram showing an example of a polymer chain model before cleavage. [Figure 7] Figure 6 is a conceptual diagram showing a polymer chain model in a cleaved state. [Figure 8] This flowchart shows an example of the processing procedure for the re-crosslinking step. [Figure 9] This figure shows an example of the coordinates of the center of mass and the displacement vector of a selected particle model. [Figure 10] This graph shows an example of a one-dimensional normal distribution. [Figure 11] This figure shows an example of a particle model with added bonding. [Figure 12] This is a flowchart showing the processing steps for a simulation method of polymer materials. [Modes for carrying out the invention]

[0010] Embodiments of the present invention will be described below with reference to the drawings. It should be understood that the drawings contain exaggerations and representations that differ from the actual dimensional ratios of the structures in order to aid in understanding the content of the invention. Furthermore, the same or common elements are denoted by the same reference numerals throughout each embodiment, and redundant explanations are omitted. Moreover, the specific configurations shown in the embodiments and drawings are for the purpose of understanding the content of the present invention, and the present invention is not limited to the specific configurations shown in the drawings.

[0011] A method for creating a numerical analysis model of a polymer material according to this embodiment (hereinafter sometimes simply referred to as the "creation method") is used to create a numerical analysis model of a polymer material (hereinafter sometimes simply referred to as the "polymer material model") that can reproduce the spatial distribution of re-crosslinking accompanying the cleavage of polymer chains for a polymer material composed of polymer chains. The polymer material model includes one or more numerical analysis models of polymer chains (hereinafter sometimes simply referred to as the "polymer chain models"). The computer 1 is used in the creation method of this embodiment.

[0012] [Computer] FIG. 1 is a perspective view showing an example of the computer 1 for executing the method for creating a numerical analysis model of a polymer material. The computer 1 of this embodiment includes a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. In the main body 1a, for example, an arithmetic processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and a disk drive device are provided. The software for executing the creation method of this embodiment is stored in advance in the storage device.

[0013] [Polymer material] The polymer material is not particularly limited as long as it includes polymer chains. The polymer material of this embodiment is exemplified as being rubber (in this example, cis-1,4 polybutadiene (hereinafter sometimes simply referred to as "polybutadiene")), but is not particularly limited. Further, the polymer material may be composed of, for example, a plurality of types of polymer chains having different chemical structures, or may be one in which a filler (for example, silica or carbon) is blended. Further, the polymer material may have a new structure that does not exist at present.

[0014] [Polymer chain] Figure 2 shows the structural formula of polybutadiene. The polymer chain 2 of this embodiment is composed of a plurality of atoms (in this example, carbon atoms and hydrogen atoms). The polymer chain 2 of this embodiment is composed of {-[CH2-CH=CH-CH2]-} of the monomer 3 composed of a methylene group (-CH2-) and a methine group (-CH-), which are linked with a polymerization degree n. Both ends of this polymer chain 2 are composed of methyl groups (-CH3) instead of methylene groups (-CH2-).

[0015] The polymer material may contain a crosslinking agent. Thereby, the polymer chain 2 can be crosslinked (that is, crosslinking is included in the intramolecular and intermolecular of the polymer chain 2). Examples of the crosslinking agent include sulfur that forms monosulfide crosslinking, disulfide crosslinking, or polysulfide crosslinking, and organic peroxides that form peroxide crosslinking.

[0016] [Method for creating a model for numerical analysis of polymer materials (First Embodiment)] Next, the creation method of this embodiment will be described. Figure 3 is a flowchart showing an example of the processing procedure of the method for creating a model for numerical analysis of polymer materials.

[0017] [Inputting a polymer chain model] In the creation method of this embodiment, first, based on the polymer chain 2 (shown in Figure 2) that constitutes the polymer material, one or more polymer chain models are input into the computer 1 (shown in Figure 1) (step S1). The polymer chain model of this embodiment is modeled as a coarse-grained molecular model (in this example, the Kremer-Grest model).

[0018] Figure 4 is a conceptual diagram showing an example of the polymer chain model 5. The polymer chain model 5 of this embodiment includes a plurality of particle models 6 and a bond model 7 that connects a pair of adjacent particle models 6, 6. When the polymer chain model 5 is a coarse-grained molecular model (Kremer-Grest model 5B) as in this embodiment, the polymer chain 2 is represented using a plurality of particle models 6 that are fewer than the plurality of atoms that constitute the polymer chain 2 (shown in Figure 2).

[0019] In this embodiment, particle model 6 is treated as a point mass in the equations of motion in calculations such as structural relaxation based on molecular dynamics, which will be described later. For this reason, parameters such as mass, volume, diameter, or charge are defined for particle model 6.

[0020] Particle model 6 is obtained by substituting monomer 3 or a structural unit that forms part of monomer 3 in polymer chain 2 shown in Figure 2. The total number of particle models 6 that make up one polymer chain model 5 (in this example, Kremer-Grest model 5B) can be set as appropriate, as in the conventional method (for example, from 10 to about 5000 (5000 in this example)).

[0021] The bonding model 7 in this embodiment is defined by a first potential P1 set between particle models 6, 6. The first potential P1 in this embodiment can be defined as the sum of the LJ potential and the FENE potential. Details and constants of the LJ potential and FENE potential are described in Non-Patent Literature 2 (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, pp. 5057-5086).

[0022] Polymer chain model 5 may include a crosslinking point model (not shown) that models the crosslinking points. This crosslinking point model, like the bonding model 7, is bonded to particle models 6, 6 and can be defined by the sum of the LJ potential and the FENE potential. Polymer chain model 5 is input (stored) into computer 1 shown in Figure 1.

[0023] Furthermore, in step S1, in addition to the polymer chain model 5, molecular models (not shown) that model substances (molecules) other than polymer chain 2 shown in Figure 2 may also be set. Examples of substances include fillers, coupling agents, and oils. Such substances can be modeled, for example, as molecular models that include one or more particle models 6 and zero or more bond models 7.

[0024] [Enter cell] Next, the creation method of this embodiment involves inputting a predetermined three-dimensional virtual space, which is a cell, into the computer 1 (shown in Figure 1) (step S2). Figure 5 is a conceptual diagram showing an example of a cell 10 in which polymer chain models 5 are arranged. In Figure 5, two polymer chain models 5, 5 are shown as representative examples.

[0025] Step S2 of this embodiment first defines a cell 10, which is a three-dimensional virtual space corresponding to a part of the polymer material. The cell 10 of this embodiment has at least one pair of faces 11, 11 facing each other (in this embodiment, three pairs of faces 11, 11 facing each other). The cell 10 of this embodiment is defined as a cube, a rectangular prism, or a parallelepiped (in this embodiment, a cube unless otherwise specified).

[0026] Periodic boundary conditions are defined for each face 11, 11 of cell 10. The length L1 of each side of cell 10 is preferably at least twice the radius of inertia (not shown), which is a quantity representing the spread of the polymer chain model 5. This prevents collisions with the cell's own image due to the periodic boundary conditions in structural relaxation calculations based on molecular dynamics, as described later. Cell 10 is stored in computer 1 (shown in Figure 1).

[0027] [Place the polymer chain model inside the cell to set up the polymer material model] Next, in the creation method of this embodiment, computer 1 (shown in Figure 1) sets up the polymer material model 12 by arranging one or more polymer chain models 5 inside the cell 10 (step S3). In this embodiment, one or more polymer chain models 5 are arranged in the cell 10 by computer 1 (shown in Figure 1), but this is not particularly limited, and they may be arranged by, for example, an operator operating computer 1. The number of polymer chain models 5 can be appropriately set (for example, 10 to 100) based on, for example, the computing power of computer 1, the size of the cell 10, and the size of the polymer chain models 5. Also, if molecular models other than polymer chain models 5 (not shown) are input in step S1, those molecular models are also arranged inside the cell 10.

[0028] The procedure for arranging the polymer chain model 5 is not particularly limited. In this embodiment, for example, one or more polymer chain models 5 are randomly arranged inside the cell 10 based on the Monte Carlo method. For such initial arrangement of polymer chain models 5, commercially available software (for example, COGNAC included in the Soft Material Comprehensive Simulator (J-OCTA) manufactured by JSOL Corporation) may be used.

[0029] [Define the interaction] Next, the creation method of this embodiment defines interactions between particle models 6, 6 and between the bonding model 7 included in the polymer material model 12, which includes the polymer chain model 5 (step S4). In this embodiment, a second potential P2 is defined as an interaction in which attractive and repulsive forces act between the particle models 6, 6. Such a second potential P2 can be defined, for example, based on the LJ potential. The procedure for setting the details and constants of the LJ potential is as described in Non-Patent Literature 2 above. The bonding model 7 is defined by the first potential P1 set between the particle models 6, 6, as described above. The polymer material model 12 with defined interactions is input (stored) in the computer 1 shown in Figure 1.

[0030] [Calculate structural relaxation of polymer chain models] Next, in the creation method of this embodiment, computer 1 (shown in Figure 1) calculates the structural relaxation of the polymer material model 12 (in this example, polymer chain model 5, which is the Kremer-Grest model 5B) based on molecular dynamics (step S5). In the structural relaxation calculation of this embodiment, for example, Newton's equations of motion are applied, assuming that the particle model 6 of the polymer material model 12 follows classical mechanics for a predetermined time in cell 10. The movement of the particle model 6 at each time step is then tracked.

[0031] In molecular dynamics calculations, pressure and temperature, or volume and temperature, are kept constant in cell 10. This allows the initial configuration of the polymer material model 12 (in this example, the Kremer-Grest model 5B) to be relaxed in step S5, approximating the molecular motion of an actual polymer material. In this embodiment, this is continued until the initial configuration of the polymer material model 12 is sufficiently relaxed. This creates a polymer material model 12 that models the polymer material. For example, the above-mentioned commercially available software can be used to calculate the structural relaxation. Note that in step S1, when the polymer material model 12 described above is input, if a polymer material model 12 with a configuration after structural relaxation (a structurally relaxed polymer material model 12) is input, and structural relaxation calculation is not necessary, the structural relaxation calculation (step S5) may be omitted. The polymer material model 12 is stored in computer 1 (shown in Figure 1).

[0032] [Calculate the deformation of the polymer material model (deformation step)] Next, in the manufacturing method of this embodiment, the computer 1 (shown in Figure 1) calculates the deformation of the polymer material model 12 prior to the next cutting step S7 (deformation step S6). In deformation step S6, deformations such as uniaxial elongation and shear are calculated on the polymer material model 12, thereby calculating the elongation of the polymer chain model 5 located inside the cell 10. The deformation step S6 of this embodiment is performed prior to the next cutting step S7. As a result, in cutting step S7, the cutting of the polymer chain model 5 that has been elongated due to the deformation can be calculated.

[0033] The deformation calculation of the polymer material model 12 can be performed as appropriate once the elongation of the polymer chain model 5 has been calculated. In deformation step S6 of this embodiment, the periodic deformation (shear deformation in this example) of the polymer material model 12 is calculated.

[0034] In this embodiment, the deformation of the polymer material model 12 is calculated based on the time evolution equation of molecular dynamics calculations of shear deformation. For example, the SLLOD method is used for this time evolution equation. Details of the SLLOD method are described, for example, in Non-Patent Literature 3 (Denis J. Evans & GP Morriss, "Nonlinear-response theory for steady planar Couette flow", Phys. Rev. A, 30(3): 1984, pp. 1528-1530). Furthermore, periodic shear calculations can be realized by periodically changing the amount of shear strain γ according to a sine wave γ(t) = A·sin(ωt) (where A is the maximum strain and ω is the frequency). By such periodic shear calculations, deformation simulations corresponding to a dynamic viscoelasticity measurement device (DMA) that applies periodic shear deformation to a polymer material can be performed.

[0035] The deformation calculation of polymer material models is not limited to the application of periodic shear deformation. For example, based on the procedure described in the patent document (Japanese Patent No. 6408856), the deformation of the polymer material model 12 may be calculated such that one end (one side surface 11) and the other end (the other side surface 11) of the polymer material model 12 are separated from each other in the Y-axis direction of Figure 5. For these deformation calculations, commercially available software such as the one mentioned above or the molecular dynamics calculation program LAMMPS may be used.

[0036] In the deformation step S6 of this embodiment, the deformation of the polymer material model 12 is calculated, which in turn calculates the elongation of the polymer chain model 5 arranged inside the cell 10. The deformed polymer material model 12 is input (stored) into the computer 1 shown in Figure 1. Although the generation method of this embodiment is illustrated as an example of how deformation step S6 is performed, it is not limited to this embodiment. In step S1, where the polymer material model 12 is input, if deformation calculation is not necessary, for example, if a polymer material model 12 with a deformed arrangement (including the elongated polymer chain model 5) has already been input, the deformation calculation (deformation step S6) may be omitted.

[0037] [Cutting the polymer chain model with the bonded model (cutting step)] Next, in the manufacturing method of this embodiment, computer 1 (shown in Figure 1) cuts at least one of the polymer chain models 5 with the bonding model 7 (cutting step S7). In this embodiment, cutting step S7 is performed on the deformed polymer material model 12 (extended polymer chain model 5). As a result, in cutting step S7, the polymer chain model 5 that has been extended due to deformation is cut.

[0038] The polymer chain model 5 can be cleaved as appropriate. For example, one of the binding models 7 included in any of the polymer chain models 5 may be randomly selected and cleaved. In the cleavage step S7 of this embodiment, at least one of the polymer chain models 5 is cleaved by a binding model 7 based on the procedure of the cleavage process described in Patent Document 1. Figure 6 is a conceptual diagram showing an example of the polymer chain model 5 after the deformation step S6. Figure 6 is simplified compared to the polymer chain model 5 shown in Figure 4 by reducing the total number of particle models 6 and binding models 7.

[0039] In the severing step S7 of this embodiment, first, one or more bond models 7a to be severed are selected from at least one of the polymer chain models 5. The bond models 7a to be severed may be selected as appropriate. In this embodiment, among the polymer chain models 5 that constitute the polymer material model 12 shown in Figure 5, one or more bond models 7a to be severed are randomly selected from polymer chain models 5 whose end-to-end distance is greater than or equal to a predetermined threshold. The threshold for the end-to-end distance may be set as appropriate, for example, based on the physical properties of the polymer chain 2 shown in Figure 2 (such as the severing stress of the material or the activation energy of the chemical reaction for severing).

[0040] Next, in the cutting step S7 of this embodiment, assuming that the polymer chain model 5 is cut by the selected binding model 7a, as shown in Figure 6, a fragment model 13 is identified, which is a collection of particle models 6 linked by other binding models 7 other than the selected binding model 7a. The fragment model 13 includes a first fragment model 13A positioned on one end 5a side of the polymer chain model 5 with respect to the selected binding model 7a, and a second fragment model 13B positioned on the other end 5b side of the polymer chain model 5 with respect to the selected binding model 7a.

[0041] Next, in the cleavage step S7 of this embodiment, it is predicted whether the fragment model 13 (first fragment model 13A and second fragment model 13B) is greater than a predetermined threshold. The threshold is set, as in Patent Document 1, based on the molecular weight that has the highest frequency in the molecular weight distribution of the polymer material including the polymer chain 2 shown in Figure 2.

[0042] Next, in the cleavage step S7 of this embodiment, if the size of the fragment model 13 (the maximum chain length of the first fragment model 13A and the second fragment model 13B) is determined to be greater than the threshold, the polymer chain model 5 is cleaved by the selected binding model 7a. On the other hand, if at least one of the sizes of the fragment model 13 is determined to be less than the threshold, a new binding model 7a to be cleaved may be selected, or a binding model 7a to be cleaved may be selected from other polymer chain models 5. Figure 7 is a conceptual diagram showing the state in which the polymer chain model 5 of Figure 6 has been cleaved.

[0043] Thus, in the cutting step S7 of this embodiment, the polymer chain model 5 is cut only if the size of the fragment model 13 (the maximum chain length of the first fragment model 13A and the second fragment model 13B) is greater than the threshold. This suppresses the cutting of small polymer chain models 5 whose size after cutting is below the threshold, similar to the cutting process of the actual polymer chain 2 (shown in Figure 2). The cut polymer chain model 5 (fragment model 13) is input (stored) into the computer 1 shown in Figure 1.

[0044] In this embodiment, the cutting step S7 involves cutting the polymer chain model 5 that has been elongated due to deformation. However, the cutting is not necessarily limited to the polymer chain model 5 being elongated. Instead, for example, any of the bonding models 7 of the polymer material model 12 may be randomly selected and cut. Also, in this embodiment, the cutting step S7 involves cutting the fragment model 13 when it is determined that the size of each fragment model 13 is greater than a threshold. However, the cutting is not necessarily limited to such a determination, and the fragments may always be cut. Such random cutting of bonding models 7 can be used to simulate the cutting of polymer chains 2 (shown in Figure 2) due to thermal degradation or aging. In this case, it is not necessary to input the polymer material model 12 with the deformed configuration (i.e., deformed) in step S1, and the deformation step S6 may be omitted.

[0045] In the cutting step S7 of this embodiment, after cutting the polymer chain model 5, structural relaxation and deformation calculations similar to those in the deformation step S6 may be performed for a predetermined simulation time prior to the next re-crosslinking step S8. This allows for the reproduction of the waiting time between the occurrence of cutting and the occurrence of re-crosslinking.

[0046] [Add a bonding model to the polymer chain model (recrosslinking step)] Next, in the manufacturing method of this embodiment, computer 1 (shown in Figure 1) adds a binding model 7 to particle models 6, 6 that are not bound to each other by a binding model 7, either within the same polymer chain model 5 or between different polymer chain models 5, 5 (re-crosslinking step S8). Figure 8 is a flowchart showing an example of the processing procedure for re-crosslinking step S8.

[0047] In the recrosslinking step S8 of this embodiment, a predetermined average value of distances is used to reproduce the spatial distribution of recrosslinking. The method for determining (selecting) this average value of distances is not particularly limited. In order for this average value of distances to be selected to represent the average radical migration distance from the site of cleavage to the site of recrosslinking, for example, a precise molecular dynamics simulation that reproduces the elementary processes of the reaction may be performed on a small scale, as in the conventional method, and the obtained average migration distance may be used. Alternatively, the average radical migration distance may be measured experimentally, or a predetermined average value of distances may be selected so that the physical properties such as viscoelasticity of the polymer material model 12 created by the method of this embodiment reproduce those of an experiment (physical properties such as viscoelasticity of an actual polymer material).

[0048] [Select at least one particle model that was coupled to the disconnected bond model] In the recrosslinking step S8 of this embodiment, first, the computer 1 (shown in Figure 1) selects at least one of the pair of particle models 6A and 6B that were bonded to each of the bond models 7a that were cut in the cutting step S7, as shown in Figure 7 (step S81). In this embodiment, the particle model 6 is selected by the computer 1 (shown in Figure 1), but this is not particularly limited, and it may be selected by an operator, for example.

[0049] The selected particle model 6 is not particularly limited, as long as it is the pair of particle models 6A and 6B that were bonded to the broken bond model 7a. In this embodiment, particle model 6 is selected based on the radicals generated at the broken portion of the polymer chain 2 shown in Figure 2. For example, if radicals are generated at only one of the two newly formed ends resulting from one break in the polymer chain 2, then only one of the pair of particle models 6A and 6B shown in Figure 7 is randomly selected. If radicals are generated at both of the two newly formed ends resulting from one break in the polymer chain 2 shown in Figure 2, then the pair of particle models 6A and 6B shown in Figure 7 are selected. The selected particle model 6A or / or particle model 6B is input (stored) in the computer 1 shown in Figure 1.

[0050] [Select one particle model from the selected particle models] Next, in the re-crosslinking step S8 of this embodiment, the computer 1 (shown in Figure 1) selects one particle model 6 from among the particle models 6 selected in step S81 (step S82). The order of selection is not particularly limited, and for example, they may be selected in a random order. In this embodiment, the order selected in step S81 is used as is. Step S82 of this embodiment is repeated in step S89, described later, until there are no unselected particle models 6, so that the particle models 6 selected in step S81 are selected without omission or duplication. The selected particle models 6 are input (stored) in the computer 1 shown in Figure 1.

[0051] [Calculate displacement vector] Next, in the re-crosslinking step S8 of this embodiment, the computer 1 (shown in Figure 1) probabilistically calculates the displacement vector according to a predetermined average value of distances (step S83). This displacement vector is used to determine the approximate position of the radicals after they have moved by a radical chain reaction, which were generated in the particle model 6 selected in step S82. Figure 9 shows an example of the coordinates of the center of gravity 6c of the particle model 6 selected in step S82 and the displacement vector ΔV.

[0052] The coordinates of the displacement vector ΔV are calculated as relative coordinates from the coordinates of the center of mass 6c of the particle model 6 selected in step S82. Here, the three-dimensional coordinate axis components of the x, y, and z axes of the center of mass 6c of the particle model 6 selected in step S82 are represented, for example, by (a,b,c).

[0053] The displacement vector ΔV has three-dimensional coordinate axis components (Δx, Δy, Δz). Therefore, for the particle model 6 selected in step S82, the approximate position C1 of the radical after movement by the radical chain reaction is equal to the vector sum of the centroid 6c of the particle model 6 selected in step S82 and the displacement vector ΔV, and the three-dimensional coordinate axis components are represented as (a+Δx, b+Δy, c+Δz).

[0054] The probability distribution function in three-dimensional space can be appropriately set such that the three-dimensional coordinate axis components (Δx, Δy, Δz) of the displacement vector ΔV follow the average value of predetermined distances selected based on the average radical migration distance from the point of cleavage to the point of re-bridgement. The probability distribution function in this embodiment is a three-dimensional normal distribution. For each of the three-dimensional coordinate components of such a probability distribution function (i.e., the x-axis component, y-axis component, and z-axis component), a one-dimensional normal distribution is used such that the mean is 0 and the standard deviation σ is the value obtained by dividing the predetermined average value of the distances by the square root of 3. This assumes that radical migration is approximated by Brownian diffusion, and holds true, for example, when the hydrogen abstraction reaction occurs sufficiently fast (i.e., is dominant).

[0055] Figure 10 is a graph showing an example of a one-dimensional normal distribution 15. In Figure 10, the horizontal axis of the normal distribution 15 represents one-dimensional coordinates, and the vertical axis represents the probability density.

[0056] In this embodiment, a normally distributed random number based on a normal distribution 15 is generated for each of the three coordinate axis components "Δx", "Δy", and "Δz" that constitute each of the three coordinate axis components of the displacement vector ΔV. The algorithm for generating the normally distributed random numbers is not particularly limited. In this embodiment, the Box-Muller method is used. This allows the three coordinate axis components (Δx, Δy, Δz) of the displacement vector ΔV to be defined, as shown in Figure 9. That is, the three coordinate axis components of the displacement vector ΔV are generated based on a normally distributed random number whose mean is 0 and whose standard deviation σ is the value obtained by dividing the mean of a predetermined distance by the square root of 3. The displacement vector ΔV is input (stored) in the computer 1 shown in Figure 1.

[0057] Furthermore, if slower diffusion than Brownian diffusion (such as diffusion originating from Routh motion or leptation motion of polymer chain 2 shown in Figure 2) is dominant, the movement of radicals cannot be approximated by Brownian diffusion, and the probability distribution function cannot be approximated by a three-dimensional normal distribution. In this case, the probability distribution function can be obtained, for example, by performing a precise molecular dynamics simulation that reproduces the elementary processes of the reaction on a small scale, as in the conventional method. Also, the algorithm for calculating the displacement vector ΔV is not limited to the method in which random numbers following a one-dimensional probability distribution are generated for each of the three-dimensional coordinate components as described above. As an example of another algorithm, the following method can be used. First, random direction vectors (Δex, Δey, Δez) are probabilistically determined using random numbers for direction. Next, the distance Δr is probabilistically determined using random numbers for distance (random numbers following the radial distribution function of the probability distribution function). Then, the product of the random direction vectors (Δex, Δey, Δez) and the distance Δr, (Δr·Δex, Δr·Δey, Δr·Δez), is defined as the displacement vector ΔV. Here, "x·y" in the formula represents the product of x and y.

[0058] As an algorithm for generating random numbers for direction, to calculate a random direction vector (Δex, Δey, Δez), first, Δez may be calculated as a uniform random number between -1 and 1. Next, by calculating ψ as a uniform random number between 0 and 2π, Δex may be calculated as sqrt(1-z^2)·cos(ψ) and Δey may be calculated as sqrt(1-z^2)·sin(ψ). Here, "x^y" in the formula represents "x to the power of y". Furthermore, as an algorithm for generating random numbers for distance, to calculate the distance Δr, first, the radial distribution function, which is the integral of the probability distribution function with respect to the radial direction, may be calculated, and then, based on this radial distribution function, Walker's Alias ​​Method may be used.

[0059] [Search for the particle model closest to the position after moving by the displacement vector (search step)] Next, in the re-crosslinking step S8 of this embodiment, the computer 1 (shown in Figure 1) searches for the particle model 6 that is closest to a position moved by a displacement vector ΔV from the position of the particle model 6 selected in step S82 (search step S84).

[0060] In the search step S84 of this embodiment, first, as shown in Figure 9, the position of the particle model 6 selected in step S82 is identified. The coordinates (a,b,c) of the centroid 6c of the particle model 6 are identified as the position of this particle model 6. Next, the coordinates (a+Δx,b+Δy,c+Δz) of the approximate position C1, which is moved by a displacement vector ΔV (i.e., relative coordinates (Δx,Δy,Δz)) from the position of the particle model 6 selected in step S82 (i.e., the coordinates (a,b,c) of the centroid 6c), are identified. Then, among the multiple particle models 6 that constitute each of the polymer chain models 5, the particle model 6 closest to the moved position is searched for.

[0061] The particle model 6 can be searched as appropriate. In this embodiment, the particle model 6 is searched using either the cell list method or the nearest neighbor search method as the search algorithm.

[0062] In this embodiment, when the cell list method is used as the search algorithm in search step S84, the search starts from the subregion containing the estimated position C1 of the radical after movement, in a grid of subdivided subregions (not shown) of the cell 10 shown in Figure 5, and proceeds to the most distant subregions in order of proximity to the subregion. For each subregion, the distance D between the coordinates of the centroid 6c of each particle model 6 and the coordinates of the estimated position C1 of the radical after movement is calculated for all particle models 6 contained within it. The minimum value of the distance D of the particle models 6 explored so far is updated as a candidate for the shortest distance D1. Furthermore, the particle model 6 that has such a shortest distance D1 is updated as the candidate for the particle model 6 closest to the estimated position C1 of the radical. Based on this candidate for the shortest distance D1, subregions whose distance D from the estimated position C1 of the radical after movement is always greater than the candidate for the shortest distance D1 are excluded from the subregions to be explored. This series of processes continues until there are no more subregions to explore. Then, the candidate particle model 6 obtained in step S82 is identified as the particle model 6 closest to the position (approximate value C1 of the radical position) that is moved by a displacement vector ΔV from the position of the particle model 6 selected in step S82. Furthermore, the candidate for the shortest distance D1 obtained in the end is identified as the shortest distance D1.

[0063] If the nearest neighbor search method is used in the search algorithm of search step S84 of this embodiment, the search method based on a kd tree in Euclidean space, as shown in Non-Patent Literature 4 (JL Bentley, Communications of the ACM, 18(9), 509-517 (1975)), is applied to three-dimensional space to identify the particle model 6 closest to the moved position and the shortest distance D1. If no periodic boundary conditions are set in cell 10 as shown in Figure 5, the coordinate values ​​of all particle models 6 in three-dimensional space included in the polymer chain model 5 are registered directly in the kd tree. However, if periodic boundary conditions are set in cell 10, instead, the coordinate values ​​of all particle models 6 in three-dimensional space, including mirror images in the x, y, and z directions, expanded by ±0.5 times the period length, are registered for each particle model 6 included in the polymer chain model 5. In this embodiment, the total number of registered coordinate values ​​is 8 times the total number of particle models 6 included in the polymer chain model 5. This allows for the search of the nearest particle model 6, including particle models 6 that cross peripheral boundary conditions.

[0064] This embodiment, similar to the recrosslinking of actual polymer chains 2 (shown in Figure 2), does not limit itself to the polymer chain model 5 that constitutes the particle model 6 selected in step S82, but also includes particle models 6 of other polymer chain models 5 to search for the particle model 6 closest to the position moved by the displacement vector ΔV. Note that since recrosslinking occurs between polymer chains 2 shown in Figure 2, particle models constituting molecular models such as fillers (not shown) are not searched.

[0065] In the search step S84, if the estimated position C1 of the radical that moved corresponding to the cleavage of polymer chain model 5 is inside a region constituting a molecular model other than polymer chain model 5, such as a filler, the displacement vector ΔV may be recalculated (modified). For example, if the estimated position C1 of the radical that moved is closer to the center of mass of any of the primary particles of the filler than the radius of the primary particle of the filler, the displacement vector ΔV may be repeatedly modified until the estimated position C1 is no longer closer than that radius. This can reduce the computational cost required to search for particle model 6.

[0066] In the search step S84, only particle models 6 whose shortest distance D1 from the estimated position C1(a+Δx,b+Δy,c+Δz) where the radical moved to the nearest particle model 6 is less than or equal to a predetermined threshold may be searched. This prevents particle models 6 that are far from the estimated position C1 where the radical moved from being searched for as targets for recrosslinking. As a result, the average distance between cleavage and recrosslinking associated with the cleavage of the polymer chain 2 shown in Figure 2 can be accurately reproduced. The threshold for the shortest distance D1 is appropriately set, for example, based on the recrosslinking that occurs in the polymer chain 2, and is set to 1 to 5 times (2 times in this example) the diameter of the particle model 6. Furthermore, the shortest distance D1 is determined based on the centroid 6c of the particle model 6.

[0067] In the search step S84, if only particle models 6 whose shortest distance D1 is less than or equal to a predetermined threshold are searched for as described above, it is possible that no particle model 6 that meets this condition may be found. In such cases, steps S83 onward are repeated until a particle model 6 that meets the condition is detected, thereby changing the displacement vector ΔV and allowing the particle model 6 to be searched for again. This increases the probability of detecting a particle model 6 that meets the condition.

[0068] The identified particle model 6 is input (stored) into computer 1 shown in Figure 1.

[0069] [Determine whether the explored particle model is suitable for adding bindings.] Next, in the re-crosslinking step S8 of this embodiment, the computer 1 (shown in Figure 1) determines whether the particle model 6 explored in the exploration step S84 is suitable for adding bonds (step S85). In step S85 of this embodiment, whether or not it is suitable for adding bonds (bonding model 7) is determined as appropriate. In this embodiment, if the total number of bonding models 7 already bonded to the explored particle model 6 is 2 or less, it is determined that it is suitable for adding bonding model 7. On the other hand, if the total number of bonding models 7 already bonded to the explored particle model 6 is 3 or more, it is determined that it is not suitable for adding bonding model 7. In the Kremer-Grest model, if the total number of bonding models 7 bonded to the particle model 6 of the polymer chain model 5 is 2 or less, the polymer chain 2 (shown in Figure 2) corresponding to the polymer chain model 5 corresponds to an uncrosslinked state. On the other hand, if the total number of bonding models 7 bonded to the particle model 6 of the polymer chain model 5 is 3 or more, the polymer chain 2 corresponding to the polymer chain model 5 corresponds to a crosslinked state. Therefore, the determination in this embodiment indicates that the total number of times a bonding model 7 can be added (i.e., the total number of times a crosslink can be added) is limited to at most once. Such determination depends on the molecular structure of the polymer chain 2 used. For example, the threshold for the total number may be set to a value greater than 2.

[0070] If the determination in step S85 is positive (i.e., particle model 6 is suitable for adding a bond ("Yes" in step S85)), the next step S86 is performed. On the other hand, if the determination in step S85 is negative (i.e., particle model 6 is not suitable for adding a bond ("No" in step S85)), steps S83 onwards are performed again, changing (updating) the displacement vector ΔV, and particle model 6 is searched for again.

[0071] In this embodiment, the re-crosslinking step S8 is exemplified by the case where, as described above, there is no particle model suitable for adding bonds ("No" in step S85), and step S83, which updates the displacement vector ΔV, is executed. However, this is not particularly limited. For example, if there is no particle model suitable for adding bonds ("No" in step S85), steps S86 (i.e., searching for particle model 6) to S88 (i.e., adding bonds) described later may be omitted, and step S89 (i.e., determining whether or not there is an unselected particle model 6) described later may be executed.

[0072] [Search for particle models adjacent to the previously explored particle models] Next, in the re-crosslinking step S8 of this embodiment, computer 1 (shown in Figure 1) searches for particle model 6 adjacent to the particle model 6 found in the search step S84 (step S86). Particle model 6 can be searched as appropriate. In this embodiment, the cell list method, which is the search algorithm, is used to search for particle model 6. Furthermore, all particle model 6 are searched within a range in which the distance from the particle model 6 found in the search step S84 is less than the maximum bond length (1.5σ in the Kremer-Grest model of this example).

[0073] In step S86 of this embodiment, based on the cell list method of the search algorithm, cell 10 is divided into grid-like subdivided subregions with spatial steps wider than the maximum bond length. Next, starting from the subregion containing the estimated position C1 of the radical after movement, only that subregion and a total of 27 subregions adjacent to it (including front, back, left, right, up, down, and diagonally) are selected. For each subregion, the search calculates the coordinates of the centroid 6c of each particle model 6 contained within it, excluding the particle model 6 itself identified in search step S84 and the particle model 6 directly bonded to the particle model 6 identified in search step S84, and the distance between that particle model 6 and the particle model 6 identified in search step S84. If the distance is shorter than the maximum bond length, that particle model 6 is identified as one of the particle models 6 whose distance from the particle model 6 identified in search step S84 is less than the maximum bond length. If, even after completing the search of all sub-regions, no particle matching the conditions is found (i.e., not identified), the process proceeds to the next step S87 (where "No" is selected), and steps S83 onwards are repeated. This changes the displacement vector ΔV, and the particle model 6 is searched for again. This ensures that the particle model 6 that matches the conditions is reliably identified.

[0074] [Determine whether the adjacent particle model is suitable for adding a bond.] Next, in the re-crosslinking step S8 of this embodiment, the computer 1 (shown in Figure 1) determines whether it is appropriate to add a bond between the particle model 6 (adjacent particle model 6) explored in step S86 and the particle model 6 explored in the exploration step S84 (step S87). In step S87 of this embodiment, whether it is appropriate to add a bond (bonding model 7) is determined as appropriate. In this embodiment, similar to step S85, it is determined to be appropriate when the total number of bonding models 7 bonded to particle model 6 is 2 or less, and not appropriate when the total number is 3 or more.

[0075] If the determination in step S87 is positive (i.e., particle model 6 is suitable for adding a bond ("Yes" in step S87)), the next step S88 is performed. On the other hand, if the determination in step S87 is negative (i.e., particle model 6 is not suitable for adding a bond ("No" in step S87)), steps S83 onwards are performed again, the displacement vector ΔV is changed, and particle model 6 is searched for again.

[0076] [Add a join] Next, in the re-crosslinking step S8 of this embodiment, the computer 1 (shown in Figure 1) adds a bond between the particle model 6 closest to a position moved by a displacement vector ΔV from the particle model 6 selected in step S82 (i.e., the particle model 6 identified in the search step S84) and the adjacent particle model 6 (i.e., the particle model 6 identified in step S87) (step S88). Figure 11 shows an example of a pair of particle models 6,6 to which the bond has been added.

[0077] In step S88 of this embodiment, bonds are added as appropriate. In this embodiment, a bonding model 7b is defined (added) between the particle model 6 identified in the exploration step S84 and the particle model 6 identified in step S87. This makes it possible to reproduce the re-crosslinking that accompanies the cleavage of the polymer chain 2 shown in Figure 2. The bonding model 7b is stored in the computer 1 shown in Figure 1.

[0078] In the re-crosslinking step S8 of this embodiment, if the number of updates of the displacement vector ΔV in step S83 exceeds a predetermined threshold, the next step S89 may be performed assuming that no re-crosslinking occurs with respect to the selected particle model 6. This can prevent the re-crosslinking step S8 from falling into an infinite loop.

[0079] In the recrosslinking step S8 of this embodiment, if the total number of bonds (total number of crosslinks) exceeds a predetermined upper limit, the next step S89 may be performed assuming that no recrosslinking occurs with respect to the selected particle model 6.

[0080] The upper limit can be set appropriately depending on the probability of recrosslinking occurring after the cleavage of the polymer material. In this embodiment, the upper limit can be set to 1% to 100% of the total number of polymer chain models 5 arranged in step S2, which sets the polymer material model 12. In this embodiment, setting the upper limit is omitted. Note that if the setting of the upper limit is omitted, it will be equivalent to setting the upper limit to 100%.

[0081] [Determine whether or not an unselected particle model exists] Next, in the re-crosslinking step S8 of this embodiment, the computer 1 (shown in Figure 1) determines whether or not there are any unselected particle models 6 in step S82 (step S89). If the determination in step S89 is positive (i.e., there are any unselected particle models 6 in step S82 ("Yes" in step S89)), then steps S82 onward are repeated. On the other hand, if the determination in step S89 is negative (i.e., there are no unselected particle models 6 in step S82 ("No" in step S89)), then the re-crosslinking step S8 is completed, and the polymer material model 12 is stored in the computer 1 (shown in Figure 1). In other words, the entire method of creation of this embodiment is completed.

[0082] In the creation method of this embodiment, the displacement vector ΔV is calculated probabilistically according to the average value of a predetermined distance, and the particle model 6 closest to the position moved by the displacement vector ΔV from the particle model 6 that was bonded to the severed bond model 7 is searched for, and bonds are added to these particle models 6, 6. With this displacement vector ΔV, the average value of a predetermined distance can be used as the average radical travel distance from the location of the break to the location of recrosslinking. As a result, in the creation method of this embodiment, it is possible to create a numerical analysis model of polymer materials that reproduces the spatial distribution of recrosslinking with less computational effort, without having to perform precise molecular dynamics simulations that reproduce the elementary processes of the reaction as in the conventional method.

[0083] In this embodiment, the displacement vector ΔV is generated based on normally distributed random numbers whose mean is 0 and whose standard deviation σ is the value obtained by dividing the average of predetermined distances by the square root of 3, with each of the three-dimensional coordinate axis components being generated. If the movement of radicals can be approximated by Brownian diffusion using such a displacement vector ΔV, the spatial distribution of re-bridgement can be reproduced with high accuracy.

[0084] [Simulation methods for polymer materials] The polymer chain numerical analysis model (polymer chain model 5) created by the method of the previous embodiment is used for simulating polymer materials. Next, the simulation method for polymer materials will be described. Figure 12 is a flowchart showing the processing procedure for the simulation method for polymer materials.

[0085] [Create polymer material models that include recrosslinked polymer chain models] The simulation method of this embodiment first involves a computer 1 (shown in Figure 1) creating a polymer material model 12 that includes a recrosslinked polymer chain model 5 (step S9). In step S9 of this embodiment, the first step is to create the recrosslinked polymer chain model 5 based on the procedure from steps S1 to recrosslinking step S8 of the creation method of previous embodiments (shown in Figure 3). Then, in step S9, a polymer material model 12 including the polymer chain model 5 is created. The polymer material model 12 is stored in the computer 1.

[0086] [Calculate the deformation of polymer material models, including models of recrosslinked polymer chains.] Next, in the simulation method of this embodiment, computer 1 (shown in Figure 1) calculates the deformation of the polymer material model 12, which includes the recrosslinked polymer chain model 5 (step S10). The deformation calculation can be performed as appropriate, and for example, a procedure similar to the deformation step S6 of the creation method of previous embodiments may be adopted. In step S10 of this embodiment, calculations may be performed under mechanically harsh conditions (such as deformation with expansion or strain large enough for the breakage of the polymer chain model 5 to occur mechanically), but it is not necessarily required to perform calculations under such mechanically harsh conditions. For example, the deformation calculation may be omitted, or deformation calculations with minute strains may be performed, in order to simulate degradation over a period of time ranging from short to long, based on conditions sufficient for the breakage and recrosslinking of the polymer chain model 5 to occur chemically (such as high temperature, ultraviolet light, ozone, oxygen, etc.).

[0087] In step S10 of this embodiment, the deformation calculation of the polymer material model 12 allows for the calculation of physical quantities of the polymer material model 12, such as stress and energy loss. In this embodiment, since the deformation of the recrosslinked polymer material model 12 is calculated, the physical quantities of the recrosslinked polymer material can be calculated with high accuracy. The deformation calculation results are input (stored) to the computer 1 shown in Figure 1. The simulation method of this embodiment may also include a step in which the computer 1 outputs the deformation calculation results. The deformation calculation results can be output to, for example, the display device 1d shown in Figure 1. This allows the operator to understand the deformation calculation results.

[0088] [Determine whether the calculation result of the transformation meets the criteria] Next, in the simulation method of this embodiment, computer 1 (shown in Figure 1) evaluates whether the deformation calculation result (in this example, the physical quantity of the polymer material model 12) satisfies predetermined criteria (step S11). The criteria can be set as appropriate according to the performance (e.g., durability) required of the polymer material or the product using the polymer material (e.g., tire, etc.).

[0089] In this embodiment, if the deformation calculation result is determined to meet the criteria (Yes in step S11), the performance of the recrosslinked polymer material model 12 is evaluated as good. In this case, the polymer material is manufactured according to the structure of the polymer chain 2 shown in Figure 2 and the various conditions set in the polymer material model, including the recrosslinking conditions (step S12).

[0090] On the other hand, if the deformation calculation results are determined not to meet the criteria ("No" in step S11), the performance of the recrosslinked polymer material model 12 is evaluated as not being good. In this case, the structure of polymer chain 2 shown in Figure 2, and the various conditions set for the polymer material model, including the recrosslinking conditions, are changed (step S13), and steps S9 to S11 are performed again.

[0091] In the simulation method of this embodiment, the structure of the polymer chain 2 shown in Figure 2, as well as various conditions set in the polymer material model, including the recrosslinking conditions, are changed until the performance of the recrosslinked polymer material model 12 is satisfactory. Therefore, polymer materials with good performance can be manufactured efficiently.

[0092] Although particularly preferred embodiments of the present invention have been described in detail above, the present invention is not limited to the illustrated embodiments and can be implemented in various modified forms. [Examples]

[0093] Based on the processing procedure shown in Figure 3, the spatial distribution of recrosslinking associated with the cleavage of polymer chain 2 shown in Figure 2 was reproduced (Examples 1 and 2). In Examples 1 and 2, first, the polymer chain model (Kremer-Grest model) and the filler model were placed in a cell, which is a three-dimensional virtual space, to set up the polymer material model. Next, in Examples 1 and 2, after the deformation of the polymer material model was calculated, the polymer chain model was cleaved based on the procedure of Patent Document 1 described above.

[0094] For each disconnected coupled model, one of the two particle models that were coupled in the coupled model was randomly selected, and a displacement vector was defined for that selected particle model. The displacement vector was generated based on a normally distributed random number whose mean is 0 and whose standard deviation σ is the value obtained by dividing the mean of the predetermined distance by the square root of 3, with each 3-dimensional coordinate axis component being generated. Then, in Examples 1 and 2, the particle model closest to a position moved by the displacement vector from the position of the particle model was searched for, and a coupling was added between the identified closest particle model and the particle models adjacent to it.

[0095] In Example 1, the average value of the predetermined distance was set to 1 nm, and in Example 2, the average value of the predetermined distance was set to 10 nm. Note that the average values ​​of the predetermined distances set in Example 1 and Example 2 are not based on experiments or other evidence, but are hypothetical values. Then, in Example 1 and Example 2, a probabilistically selected displacement vector was calculated according to these average values ​​of distance.

[0096] For comparison, after the polymer chain model was severed, the bonds between the severed polymer chain model and the other polymer chain model were randomly set without defining a displacement vector for one of the severed particle models (comparative example). The common specifications are as follows: Polymer material model (filler-polymer composite): Polymer chain model (equivalent to styrene-butadiene rubber): Number of polymer chain models: 1,500 Total number of particle models in one polymer chain model: 5000 Number of bridge points: 56,250 Filler model (equivalent to silica): Particle size of filler primary particles: 15 nm Addition amount: 50phr Number of bond models between filler and polymer (equivalent to chemical adsorption of coupling agents): 78,300 Cell side length (periodic boundary length): 125 nm Deformation (periodic shear): Temperature: 0.45 Distortion amplitude: 1.0 Shear period: 100,000τ Simulation time: 200,000τ Number of disconnected combined models: 312 Re-crosslinking: Number of re-crosslinked coupling models: 312

[0097] The test results showed that in Examples 1 and 2, similar to actual polymer chains where radicals are generated upon cleavage, a bond was added between the particle model closest to the position where the polymer chain model was cleaved, moved by a displacement vector from the position of the cleaved particle model, and between the particle models adjacent to the closest particle model. The average distance between the cleaved particle model and the corresponding re-crosslinked nearest particle model was 0.9 nm in Example 1 and 9.9 nm in Example 2, both of which approximated the average values ​​of the above distances (Example 1: 1 nm, Example 2: 10 nm) set to be sufficiently close to the periodic boundary length.

[0098] On the other hand, in the comparative example, unlike Examples 1 and 2, no bond was added to one of the particle models from which the polymer chain model was cut. Instead, one particle model suitable for adding a bond was randomly selected from all the particle models constituting either polymer chain model, and a bond was added to the selected particle model. The average distance between the cut particle model and the nearest corresponding re-crosslinked particle model was 58.2 nm. This value is similar to the expected distance between two random points in a cubic cell satisfying periodic boundary conditions, which is approximately 0.48 times the length of one side of the cell (i.e., 60 nm). Unlike the examples, it was confirmed that the distance could not be controlled to be sufficiently close to the periodic boundary length.

[0099] Thus, in Examples 1 and 2, the average distance between the break and re-crosslinking of polymer chains was set to be sufficiently shorter than the periodic boundary length. In other words, in Examples 1 and 2, the average radical migration distance from the break point to the re-crosslinking point was used as the average value of a predetermined distance. This confirmed that it is possible to create a polymer material model that can reproduce the spatial distribution of actual polymer chain break-related re-crosslinking (the average distance between the break and re-crosslinking) with a small amount of computation, without having to perform precise molecular dynamics simulations to reproduce the elementary processes of the reaction as in the conventional method.

[0100] [Note] The present invention includes the following embodiments.

[0101] [Invention 1] A method for creating a numerical analysis model for polymer materials, The steps include inputting one or more polymer chain models, each including a plurality of particle models and a coupling model that connects adjacent pairs of the particle models, into a computer based on the polymer chains constituting the polymer material, The steps include: arranging the polymer chain model in a cell, which is a predetermined three-dimensional virtual space, to set up the polymer material model; The computer performs a cutting step in which it cuts at least one of the polymer chain models with the bonding model, The computer selects at least one of the pair of particle models that were coupled to the disconnected combined model, The computer probabilistically calculates the displacement vector according to a predetermined average value of distances, The computer performs a search step in which it searches for the particle model closest to a position moved by the displacement vector from the position of the selected particle model, The computer adds a coupling between the nearest particle model and a particle model adjacent to the nearest particle model, including, Method for creating numerical analysis models for polymer materials. [2nd Invention] A method for creating a numerical analysis model of a polymer material according to Invention 1, wherein, in the search step, if no particle model suitable for adding the bond exists in the vicinity of a position moved by the displacement vector from the position of the selected particle model, the computer performs a step of updating the displacement vector to another displacement vector and searches again for the nearest particle model. [Invention 3] A method for creating a numerical analysis model for a polymer material according to invention 1 or 2, wherein the displacement vector is generated based on a normally distributed random number whose mean is 0 and whose standard deviation σ is the value obtained by dividing the mean of the predetermined distance by the square root of 3, and each of the three-dimensional coordinate axis components is generated based on this random number. [4th Invention] A method for creating a numerical analysis model of a polymer material according to any one of inventions 1 to 3, further comprising the step of calculating the structural relaxation and / or deformation of the polymer material model prior to the cutting step. [5th ​​Invention] Based on the method for creating a numerical analysis model of a polymer chain described in claim 1, a computer creates the polymer chain model; The computer creates a polymer material model including the polymer chain model, The computer performs the steps of calculating the deformation of the polymer material model, The computer includes the step of outputting the calculation result of the transformation, Simulation methods for polymer materials. [Explanation of symbols]

[0102] 5 Polymer Chain Models 6 Particle Model 7. Combined Models ΔV displacement vector

Claims

1. A method for creating a numerical analysis model for polymer materials, The steps include inputting one or more polymer chain models, each including a plurality of particle models and a coupling model that connects adjacent pairs of the particle models, into a computer based on the polymer chains constituting the polymer material, The steps include: arranging the polymer chain model in a predetermined three-dimensional virtual space called a cell to set up the polymer material model; The computer performs a cutting step in which it cuts at least one of the polymer chain models with the bonding model, The computer selects at least one of the pair of particle models that were coupled to the disconnected combined model, The average radical migration distance from the point of breakage of the polymer chain to the point of re-crosslinking is predetermined, and the computer calculates a displacement vector by randomization following an isotropic probability distribution function having the average radical migration distance. The computer performs a search step in which it searches for the particle model closest to a position moved by the displacement vector from the position of the selected particle model, The computer adds a coupling between the nearest particle model and a particle model adjacent to the nearest particle model, including, Method for creating numerical analysis models for polymer materials.

2. A method for creating a numerical analysis model of a polymer material according to claim 1, wherein, in the search step, if there is no particle model suitable for adding the bond in the vicinity of a position moved by the displacement vector from the position of the selected particle model, the computer performs a step of updating the displacement vector and searches again for the nearest particle model.

3. A method for creating a numerical analysis model for a polymer material according to claim 1, wherein the displacement vector is generated based on a normally distributed random number whose mean is 0 and whose standard deviation σ is the value obtained by dividing the average radical migration distance by the square root of 3, and the components of each three-dimensional coordinate axis are generated based on this random number.

4. A method for creating a numerical analysis model of a polymer material according to any one of claims 1 to 3, further comprising the step of calculating the structural relaxation and / or deformation of the polymer material model prior to the cutting step.

5. Based on the method for creating a numerical analysis model of a polymer chain described in claim 1, a computer creates the polymer chain model; The computer creates a polymer material model including the polymer chain model, The computer performs the steps of calculating the deformation of the polymer material model, The computer includes the step of outputting the calculation result of the transformation, Simulation methods for polymer materials.

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