JP7601135B2 - Method for creating a model for numerical analysis of polymer chains and a simulation method - Google Patents

Description

The present invention relates to a method for creating a model for numerical analysis of polymer chains and a simulation method.

The following Patent Document 1 describes a method for creating a polymer material model. In this method, a polymer material model is created by arranging a filler model having at least one filler particle model and a polymer model including multiple polymer particle models in a predetermined virtual space that corresponds to at least a portion of the volume of the polymer material.

Patent No. 6353290

In order to accurately predict physical quantities such as viscoelasticity using a polymer material model such as the one described above, it is necessary to properly reproduce the molecular weight distribution of the polymer chains. In polymer materials, for example, during kneading, extrusion processes, aging, wear, etc., polymer chains can be broken, causing changes in the molecular weight distribution of the polymer chains and affecting physical quantities such as viscoelasticity. For this reason, it is necessary to create a numerical analysis model in which the polymer chains are broken, based on the molecular weight distribution of the object to be analyzed.

However, for example, in models in which polymer chains are randomly cut by automatic computer processing, fragments with extremely small molecular weights tend to be produced, and there is a problem in that it is not possible to create a numerical analysis model of the polymer chain that approximates the desired molecular weight distribution.

The present invention was devised in consideration of the above-mentioned circumstances, and its main objective is to provide a method that makes it possible to create a numerical analysis model of a polymer chain that approximates a desired molecular weight distribution.

The present invention is a method for creating a model for numerical analysis of a polymer chain, comprising: a step of inputting a polymer chain model including a plurality of particle models and a bond model that bonds adjacent particle models based on the polymer chain into a computer; and a cutting step in which the computer cuts the bonds of the polymer chain model, the cutting step comprising: a step of selecting one bond model to be cut from the bond models that constitute the polymer chain model; a step of predicting whether or not the sizes of fragment models (one or two of the fragment models resulting from the cutting) are all greater than a predetermined threshold value when it is assumed that the selected bond model is cut; and a conditional cutting step of cutting the polymer chain model with the selected bond model when the predicted sizes of the fragment models are all greater than the threshold value.

By adopting the above steps, the method for creating a polymer material model of the present invention makes it possible to create a numerical analysis model of a polymer chain that approximates a desired molecular weight distribution.

FIG. 1 is a perspective view showing a computer for executing a method for creating a model for numerical analysis of a polymer chain. This is the structural formula of polybutadiene. 1 is a flowchart showing a processing procedure of a method for creating a numerical analysis model of a polymer chain. Schematic diagram of a polymer chain model (Kremer-Grest model). FIG. 2 is a conceptual diagram showing a cell in which a polymer chain model is arranged. 10 is a flowchart showing a processing procedure of a cutting process. 13 is a flowchart showing a processing procedure of a threshold setting step. 1 is a graph showing the molecular weight distribution of a polymer material. 1A and 1B are conceptual diagrams showing models of polymer chains to be cut. 13 is a flowchart showing a processing procedure of a prediction step. 11 is a flowchart showing a processing procedure of a first step. 13 is a flowchart showing a processing procedure of an additional determination step. 9( a ) is a conceptual diagram showing a state in which the polymer chain model in FIG. 9( a ) is cut, and FIG. 9( b ) is a conceptual diagram showing a state in which the polymer chain model in FIG. 9( b ) is cut. 1 is a graph showing the molecular weight distribution of a polymer chain model. FIG. 1 is a conceptual diagram showing a polymer chain model in which interactions are defined. 1 is a flowchart showing a processing procedure of a simulation method for a polymer material. 1 is a graph showing molecular weight distributions of Examples and Comparative Examples.

Below, an embodiment of the present invention will be described with reference to the drawings. It should be understood that the drawings contain exaggerated expressions and expressions that differ from the dimensional ratios of the actual structure in order to aid in understanding the contents of the invention. Furthermore, the same reference numerals are used for identical or common elements throughout each embodiment, and duplicate explanations will be omitted. Furthermore, the specific configurations shown in the embodiments and drawings are intended to aid in understanding the contents of the present invention, and the present invention is not limited to the specific configurations shown in the drawings.

The method for creating a model for numerical analysis of a polymer chain according to this embodiment (hereinafter, simply referred to as the "creation method") is used to create a model for numerical analysis of a polymer chain (hereinafter, simply referred to as the "polymer chain model") that approximates a desired molecular weight distribution. A computer 1 is used in the creation method according to this embodiment.

[computer]
1 is a perspective view showing a computer 1 for executing a method for creating a numerical analysis model of a polymer chain. The computer 1 of this embodiment includes 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 for executing the creation method of this embodiment stored therein in advance.

[Polymer chain]
The polymer chains constitute a polymer material. The polymer material of this embodiment is exemplified as rubber (in this example, cis-1,4 polybutadiene (hereinafter, sometimes simply referred to as "polybutadiene")), but is not particularly limited thereto. The polymer material may be composed of, for example, multiple rubbers, may be crosslinked, or may contain a filler (for example, silica or carbon). The polymer material may also have a new structure that does not currently exist.

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

The polymer chains 2 are broken, for example, during kneading, during the extrusion process, when they deteriorate over time, when they are worn, etc. Therefore, in each of these conditions, the molecular weight distribution of the polymer chains shows a certain tendency.

[Method of creating a model for numerical analysis of polymer chains]
Next, a method for creating the present embodiment will be described. In the method for creating the present embodiment, a numerical analysis model in which the polymer chain 2 is cut is created based on the molecular weight distribution of the analysis target (e.g., molecular weight distribution during kneading, extrusion process, aging, wear, etc.). Fig. 3 is a flowchart showing the processing procedure of the method for creating a numerical analysis model of a polymer chain.

[Enter polymer chain model]
In the creation method of this embodiment, first, a polymer chain model is input to a computer 1 (shown in FIG. 1) based on a polymer chain 2 (shown in FIG. 2) (step S1). In this embodiment, a coarse-grained molecular model (in this example, the Kremer-Grest model) is used as the polymer chain model, but is not particularly limited, and may be, for example, an all-atom model or a united atom model. Figure 4 is a conceptual diagram of a polymer chain model 5 (Kremer-Grest model 5B).

The polymer chain model 5 of this embodiment is configured to include a plurality of particle models 6 and a bond model 7 that bonds adjacent particle models 6, 6. When the polymer chain model 5 is the Kremer-Grest model 5B as in this embodiment, the polymer chain 2 is represented using a plurality of particle models 6 that is fewer than the number of atoms that constitute the polymer chain 2 (shown in FIG. 2).

The particle model 6 in this embodiment is treated as a mass point in the equation of motion in the calculation of structural relaxation based on molecular dynamics described below. For this reason, parameters such as mass, volume, diameter, and charge are defined for the particle model 6.

The particle models 6 are replacements for the monomers 3 of the polymer chain 2 shown in FIG. 2 or structural units that form part of the monomers 3. The total number of particle models 6 constituting one polymer chain model 5 (in this example, the Kremer-Grest model 5B) can be set appropriately (for example, about 10 to 5,000 (in this example, 5,000)) as in the conventional case. In this embodiment, in the cutting step S4 (shown in FIG. 3) described later, the polymer chain model 5 is cut so as to approximate the desired molecular weight distribution, so the total number of particle models 6 is set so as to have a molecular weight distribution larger than the desired molecular weight distribution.

The bond model 7 in this embodiment is defined by a first potential P1 set between the 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 of the LJ potential and the FENE potential, constants, etc. are as described in Paper 1 (Kurt Kremer & Gary S. Grest, "Dynamics of entangled linear polymer melts: A molecular-dynamics simulation", J. Chem Phys. vol.92, No.8, 15 April 1990, p5057-5086).

In step S1 of this embodiment, only the polymer chain model 5 (in this example, the Kremer-Grest model 5B) is set, but this is not limited to the above. For example, a molecular model (not shown) that models a substance (molecule) other than a polymer chain may be set. Such a molecular model may include, for example, one or more particle models 6 and zero or more bond models 7. The polymer chain model 5 is stored in the computer 1 (shown in FIG. 1).

[Enter cell]
Next, in the creation method of this embodiment, a cell, which is a virtual space corresponding to a part of a polymer material, is input to a computer 1 (shown in FIG. 1) (step S2). Fig. 5 is a conceptual diagram showing a cell 10 in which a polymer chain model 5 is arranged. In Fig. 5, two polymer chain models 5 are shown as representatives.

The cell 10 in 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 in this embodiment is defined as a rectangular parallelepiped or cube (in this embodiment, a cube).

A periodic boundary condition is defined for each face 11, 11 of the cell 10. The length L1 of each side of the cell 10 is preferably, for example, at least twice the radius of gyration (not shown), which is an amount indicating the spread of the polymer chain model 5. This makes it possible to prevent collisions with the self-image due to the periodic boundary condition in the structural relaxation calculation based on molecular dynamics described below. The cell 10 is stored in the computer 1 (shown in FIG. 1).

[Place polymer chain model]
Next, in the simulation method of this embodiment, the computer 1 (shown in FIG. 1) arranges a plurality of polymer chain models 5 inside the cell 10 (step S3). In step S3 of this embodiment, the plurality of polymer chain models 5 are arranged randomly according to the arrangement input in step S1. Note that, when a molecular model (not shown) is input in step S1, the molecular model is also arranged. The number of polymer chain models 5 can be appropriately set (for example, set to 10 to 100) based on, for example, the computing power of the computer 1, the size of the cell 10, the size of the polymer chain model 5, and the like.

The procedure for placing the polymer chain model 5 is not particularly limited. For example, if a molecular model (not shown) is not input, the polymer chain model 5 may be randomly placed inside the cell 10 based on the Monte Carlo method. For example, commercially available software (for example, COGNAC included in Soft Material Integrated Simulator (J-OCTA) manufactured by JSOL Co., Ltd.) may be used for the initial placement of the polymer chain model 5. The cell 10 in which the polymer chain model 5 is placed is stored in the computer 1 (shown in FIG. 1).

[Cutting the polymer chain model (cutting step)]
Next, in the creation method of this embodiment, the computer 1 (shown in FIG. 1 ) cuts bonds of the polymer chain model 5 (cutting step S4). In the cutting step S4 of this embodiment, the polymer chain model 5 is cut based on the molecular weight distribution of the analysis target (e.g., molecular weight distribution during kneading, extrusion, aging, wear, etc.).

Conventionally, there is no established method known for cutting a polymer chain model 5 so that it follows a specific molecular weight distribution. For example, when a polymer chain model 5 is cut randomly by automatic processing using a computer 1 (shown in Figure 1), there is a tendency for a large number of fragments with extremely small molecular weights to be generated, resulting in the problem that a polymer chain model for numerical analysis that approximates a desired molecular weight distribution cannot be created.

The reason why the generation of a large number of small fragments as described above does not occur in actual polymer chains is thought to be because there is less entanglement with surrounding molecular chains near the ends of the polymer chains, which could become small fragments if cut. In other words, it is presumed that near the ends, there is less entanglement, which speeds up the diffusion movement, which in turn promotes stress relaxation of the tension in the molecular chains that occurs during deformation, making it difficult for strong tension to occur in the molecular chains near the ends, and therefore making it difficult for the cutting reaction to proceed.

In this embodiment, similar to the cutting process of an actual polymer chain, a polymer chain model 5 that approximates a desired molecular weight distribution is created by suppressing cutting of small polymer chain models 5 whose size is equal to or smaller than a predetermined threshold. In this embodiment, the size of the polymer chain model 5 is exemplified as the maximum chain length (in this example, the maximum chain length that can be taken within the fragment). Figure 6 is a flowchart showing the processing procedure of the cutting process S4.

[Setting the threshold (threshold setting process)]
In the cutting step S4 of this embodiment, first, a threshold is set (threshold setting step S41). The threshold is used to determine cutting of the polymer chain model 5. The threshold can be defined as appropriate. In this embodiment, in order to create a polymer chain model 5 that approximates the molecular weight distribution of a specific polymer material, the threshold is defined, for example, based on the following procedure. Fig. 7 is a flowchart showing the processing procedure of the threshold setting step S41.

In the threshold setting step S41 of this embodiment, first, the molecular weight distribution of a polymer material (not shown) including polymer chain 2 (shown in FIG. 2) is obtained (step S411). The molecular weight distribution of the polymer material can be obtained as appropriate. In this embodiment, first, a polymer material (test piece) to be analyzed (e.g., during kneading, during an extrusion process, during aging or wear, etc.) is manufactured. Then, the molecular weight distribution of the polymer material is obtained based on the known gel permeation chromatography (GPC).

Figure 8 is a graph showing the molecular weight distribution (differential molecular weight distribution) of a polymer material. This is a graph of the logarithm of the molecular weight, and has a shape close to a log-normal distribution with a single peak. This shape characteristic is not only during manufacturing, but also after the polymer chain is cut due to processing or aging, and the shape itself tends not to change much, although the peak molecular weight shifts overall to become smaller. On the other hand, if it is assumed that the polymer chain is cut randomly, the molecular weight distribution approaches a Poisson distribution, and a large peak is expected to appear at an extremely small molecular weight. However, such a small molecular weight peak is not seen in an actual polymer chain. Therefore, in reality, it is difficult to generate random cuts that generate polymer chains 2 with extremely small molecular weights, and instead, it is suggested that polymer chains 2 with large molecular weights are preferentially cut. The molecular weight distribution is stored in a computer 1 (shown in Figure 1).

Next, in the threshold setting step S41 of this embodiment, a threshold is set based on the molecular weight distribution (shown in FIG. 8) (step S412). The threshold is appropriately set based on the molecular weight distribution. It is considered that the physical properties of the polymer material are most affected by the polymer chain 2 having a molecular weight W1 that is the peak of the differential molecular weight distribution (i.e., the molecular weight that is most frequent) in the molecular weight distribution. From this perspective, the threshold is set based on the molecular weight W1 that is most frequent in the molecular weight distribution.

In this embodiment, the threshold is appropriately set with the goal of creating the most polymer chain models 5 corresponding to the molecular weight W1 with the highest frequency in the molecular weight distribution. For this reason, a molecular weight W2 slightly smaller than the molecular weight W1 (for example, 85% to 99% of the molecular weight W1) may be set as the threshold. Alternatively, various thresholds may be set to create the polymer chain models 5, and among these thresholds, the threshold with the molecular weight with the highest frequency of the polymer chain models 5 closest to the above-mentioned molecular weight W1 may be selected.

The size of the polymer chain model 5 may be specified not as the molecular weight, but as the maximum chain length, that is, the maximum of the chain lengths that can be taken within the fragment model. Here, the chain length may be defined as an amount related to the length of the polymer chain, and may be defined as an amount related to the length of the path that passes through the bond model 7 and the particle model 6 between the two particle models 6, 6 selected as both ends. The unit of the chain length may also be defined as appropriate using the length, number of particles, mass, etc. The chain length in this embodiment is defined as the number of particle models 6 included in the shortest path (i.e., the path that has the smallest number of bond models 7) among the possible paths. The relationship between the maximum chain length of the polymer chain model 5 and the corresponding molecular weight may change depending on the number of branches of the polymer chain of the generated fragment. For this reason, the threshold value in this embodiment is set as the value obtained by dividing the molecular weight by the product of the molecular weight of the particle model 6 and a constant related to branching. In addition, the constant related to branching may be defined as an appropriate real value of 1 or more. In this embodiment, the constant related to branching is set to 1. The threshold value is stored in computer 1 (shown in Figure 1).

[Set upper limit for number of disconnections]
Next, in the cutting step S4 of this embodiment, an upper limit value of the total number of cuts of the polymer chain model 5 is set (step S42). The upper limit value can be appropriately set if the molecular weight distribution of the polymer chain model 5 after the cutting step S4 (shown in FIG. 14) and the molecular weight distribution of the polymer material (shown in FIG. 8) can be approximated. In this embodiment, when the threshold is a molecular weight, the upper limit value of the total number of cuts is set by further subtracting 1 from the value obtained by dividing the total molecular weight of the polymer chain model 5 by the threshold. On the other hand, when the threshold is a maximum chain length, the upper limit value of the total number of cuts is set by further subtracting 1 from the value obtained by dividing the total number of particles of the polymer chain model 5 by the product of the threshold and a constant related to branching. Here, the total molecular weight of the polymer chain model 5 is obtained by multiplying the total number of particles of the polymer chain model 5 by the molecular weight per particle model 6. By setting such an upper limit value, excessive cutting of the polymer chain model 5 is suppressed, and it is possible to approximate the molecular weight distribution of the polymer material (shown in FIG. 8). The upper limit value is input to the computer 1 (shown in FIG. 1).

[Select a binding model]
Next, in the cutting step S4 of this embodiment, one bond model 7 to be cut is selected from the bond models 7 (shown in FIG. 4) constituting the polymer chain model 5 (step S43). Figures 9(a) and (b) are conceptual diagrams showing the polymer chain model 5 to be cut. In Figures 9(a) and (b), the polymer chain model 5 is shown in a simplified form compared to Figures 4 and 5. Also, Figure 9(b) shows the polymer chain model 5 bonded by the bond model 7 at the crosslinking point 14.

When multiple polymer chain models 5 (shown in FIG. 5) are input as in this embodiment, one polymer chain model 5 is selected from the polymer chain models 5. This polymer chain model 5 may be selected randomly or based on a predetermined criterion (e.g., the bond energy of the bond model 7). Then, as shown in FIGS. 9(a) and (b), one bond model 7a to be cut is randomly selected from the multiple bond models 7 constituting the selected polymer chain model 5. The bond model 7a to be cut is stored in the computer 1 (shown in FIG. 1).

[Predicting the size of the fragment model after cutting (prediction step)]
Next, in the cutting step S4 of this embodiment, when it is assumed that the polymer chain model 5 is cut by the selected bond model 7a, it is predicted whether the size of each of the fragment models 13 (one or two fragment models 13 generated by cutting), which is a collection of particle models 6 connected by other bond models 7 except the selected bond model 7a, is larger than a predetermined threshold (prediction step S44). As described above, the fragment model 13 is defined as a collection of particle models 6 connected by other bond models 7 except the selected bond model 7a. These fragment models 13 can be determined appropriately. For example, starting from one and the other of the two particle models 6 connected by the selected bond model 7a, and searching all the particle models 6 via the bond models 7 other than the selected bond model 7a, the two fragment models 13 can be determined. However, it should be noted that when two particle models 6 bound by the selected bond model 7a are linked from one to the other via a bond other than the selected bond model 7a, these two fragment models 13 become equal to each other, and the total number of fragment models 13 to be determined becomes one (rather than two). Fig. 10 is a flowchart showing the processing procedure of the prediction step S44.

[Predicting whether the size of the first fragment model is greater than a threshold (first step)]
In the prediction step S44 of this embodiment, first, as shown in Figures 9(a) and 9(b), it is predicted whether or not the size of the first fragment model 13A, which is the fragment model 13 on one side of the selected binding model 7a, will be larger than a threshold value (first step S441). In Figures 9(a) and 9(b), the first fragment model 13A is shown in color.

In order to calculate whether the size of the first fragment model 13A will be larger than the threshold value, a simple method of calculating the size of the first fragment model 13A is conceivable. However, with this method, when calculating the size of the fragment, it is possible that all particle models 6 constituting the polymer chain model 5 will be searched at most, which requires a very large amount of calculation (proportional to or greater than the total number of particle models 6 and bond models 7 in the entire system), and this can be very inefficient. For this reason, it is desirable to discontinue further searches when it becomes clear that the size of the first fragment model 13A will be larger than the threshold value. Figure 11 is a flowchart showing the processing procedure of the first step S441.

[Search for the size of the set of particle models that make up the first fragment model]
As described above, in the first step S441 of this embodiment, first, the particle models 6 of the first fragment model 13A are searched for within a range in which the size of the set of particle models 6 constituting the first fragment model 13A does not exceed a threshold value (step S51).

In step S51 of this embodiment, when the size of the fragment model 13 is the molecular weight, starting from one particle model 6e bound to the selected bond model 7a, the particle models 6 constituting the first fragment model 13A are searched one after another via bond models 7 other than the selected bond model 7a. Then, the value obtained by multiplying the number of newly found (searched) particle models 6 by the molecular weight per particle model 6 is calculated as the molecular weight of the first fragment model 13A, and when it becomes clear that this molecular weight is greater than the threshold, it is determined that the size of the first fragment model 13A has become greater than the threshold, and further search is terminated. On the other hand, if the molecular weight of the first fragment model 13A is not greater than the threshold (below the threshold), all searches are completed while the calculated molecular weight is below the threshold. The search algorithm is appropriately selected. For example, depth-first search, breadth-first search, random search, etc. can be used. In this embodiment, breadth-first search is used.

In step S51 of this embodiment, when the size of the fragment model 13 is the maximum chain length, starting from one particle model 6e bound to the selected bond model 7a, the particle models 6 constituting the first fragment model 13A are searched one after another using a breadth-first search via bond models 7 other than the selected bond model 7a. Then, the depth of the search (i.e., the value obtained by adding 1 to the number of bond models 7 passed through) is set as the lower limit of the maximum chain length, and when it becomes clear that the depth of the search, which is the lower limit of this maximum chain length, is greater than the threshold, that is, when it becomes clear that the maximum chain length is greater than the threshold, the search of the particle model 6 is terminated. On the other hand, when the maximum chain length that can be taken within the first fragment model 13A is not greater than the threshold (below the threshold), all searches are completed while the calculated lower limit of the maximum chain length is below the threshold (i.e., the set of particle models 6 constituting the first fragment model 13A is determined). Note that, unlike the case where the threshold is molecular weight, even if the lower limit of the maximum chain length calculated by the above-mentioned method is below the threshold, the actual maximum chain length may be greater than the threshold. For this reason, in cases where the lower limit of the maximum chain length calculated by the above method is equal to or less than the threshold, it is preferable to add a judgment step (an additional judgment step S55 described below) for more accurately estimating the maximum chain length. Depending on whether the (approximate value of) the maximum chain length obtained in the additional judgment step S55 is greater than the threshold, it is possible to (approximately) calculate whether the size of the first fragment model 13A is greater than the threshold.

In step S51 of this embodiment, when the size of the fragment model 13 is the maximum chain length, another search algorithm may be adopted instead of the breadth-first search. However, when another search algorithm is adopted, even if further search is terminated when it becomes clear that the size of the first fragment model 13A will be larger than the threshold value, it is difficult to satisfy the termination condition compared to a breadth-first search, which is guaranteed to search from the side with the smaller maximum chain length, and there is a tendency to perform more searches, which may be inefficient. Therefore, it is preferable to use a breadth-first search.

In step S51 of this embodiment, the size of the set of particle models 6 that make up the searched first fragment model 13A is finally stored in the computer 1 (shown in FIG. 1).

[Determine whether the size of the particle model set of the first fragment model is greater than a threshold value]
Next, in the first step S441 of this embodiment, it is determined whether or not the size of the set of particle models 6 that constitute the found first fragment model 13A is greater than a threshold value (step S52).

If it is determined in step S52 that the size of the set of particle models 6 that make up the first fragment model 13A is greater than the threshold value (Yes in step S52), it is finally determined that the size of the first fragment model 13A is greater than the threshold value (step S53). This is then stored in the computer 1 (shown in FIG. 1) as the final determination result of the first step S441 (i.e., the size of the first fragment model 13A is greater than the threshold value), and the series of processes in the first step S441 ends.

On the other hand, if it is determined in step S52 that the size of the first fragment model 13A is equal to or smaller than the threshold value (step S52: No), the set of particle models 6 constituting the first fragment model 13A is determined without exception as the object to be determined in the additional determination step S55 described above (step S54). In step S54, the set of particle models 6 constituting the first fragment model 13A is stored in the computer 1 (shown in FIG. 1). Then, based on this set of particle models 6, an additional determination step S55 is performed to more accurately estimate the maximum chain length.

[Additional Judgment Step]
For example, the Floyd-Warshall method can be used in the additional determination step S55. By using this method, the maximum chain length can always be calculated accurately. However, since the amount of calculation in this method is proportional to the cube of the total number of particle models 6 included in the first fragment model 13A, there is a problem that it is not practical, especially when a large threshold value is used for a large-scale molecular model.

In the additional judgment step S55 of this embodiment, instead of the Warshall-Floyd method, a method of performing a breadth-first search twice is used, which will be described later. This method is known as a method of calculating the maximum chain length (diameter of a graph) when there is no loop (a tree-structured graph in graph theory), and since the amount of calculation is directly proportional (i.e., proportional to the first power) to the total number of bond models 7 included in the first fragment model 13A, it is much faster than the Warshall-Floyd method, in which the amount of calculation is proportional to the cube of the total number of particle models 6. This method has the advantage that the maximum chain length is calculated quickly and accurately when there is no loop, but has the disadvantage that when the first fragment model 13A contains a loop, although it is fast, only an approximation of the maximum chain length is obtained, not an accurate maximum chain length. However, even when such a loop is included, the approximation obtained is the lower limit of the maximum chain length, and the size of the first fragment model 13A having a maximum chain length below the threshold is not erroneously determined to be larger than the threshold, so that the occurrence of a first fragment model 13A having a size below the threshold can be reliably prevented. It should be noted that although the selected bond model 7a may not be cleaved even though it is actually cleavable, the probability of this occurring is very low, so it is considered to pose little practical problem. Figure 12 is a flowchart showing the processing procedure of the additional determination step S55.

[Specify the first particle model]
In the additional determination step S55 of this embodiment, taking into consideration the above-mentioned procedure, first, in the first fragment model 13A (shown in FIGS. 9A and 9B), a first particle model 6a that is one of the particle models 6 farthest from the particle model 6e bound to the selected bond model 7a is searched for (step S61). More specifically, this first particle model 6a is one of the particle models 6 that are farthest (i.e., the number of minimum bond models 7 to be passed through is the largest) among the particle models 6 that can be reached from the starting particle model 6e by starting from one particle model 6e of the two particle models 6 bound by the selected bond model 7a and passing through a bond model 7 other than the selected bond model 7a.

When there are multiple first particle models 6a that are the furthest, one of them is appropriately selected as the first particle model 6a. In this embodiment, the first particle model 6 that is found to be the furthest is selected as the first particle model 6a.

The first particle model 6a can be specified as appropriate. In this embodiment, the first particle model 6a is specified based on a predetermined algorithm. The algorithm can be selected as appropriate, but it is preferable to use a breadth-first search from the viewpoint of the amount of calculation. Similarly, in the second step S442 described later in this embodiment, it is preferable to use a breadth-first search for the additional determination.
The first particle model 6a is stored in the computer 1 (shown in FIG. 1).

[Specify the second particle model]
Next, in the additional determination step S55 of this embodiment, in consideration of the above-mentioned procedure, starting from the first particle model 6a, the second particle model 6b, which is one of the particle models 6 farthest from the first particle model 6a, is searched for in the first fragment model 13A (step S62). More specifically, starting from the first particle model 6a, the second particle model 6b is one of the particle models 6 farthest (i.e., the number of minimum bond models 7 to be passed through is the largest) among the particle models 6 that can be reached from the starting first particle model 6a via bond models 7 other than the selected bond model 7a. This second particle model 6b can be appropriately specified. In this embodiment, the second particle model 6b is specified based on a predetermined algorithm (e.g., breadth-first search). Note that, if there are multiple farthest particle models 6, any one of them is selected as the second particle model 6b. The second particle model 6b is stored in the computer 1 (shown in FIG. 1).

[Specifying the chain length between the first and second particle models]
Next, in the additional judgment step S55 of this embodiment, the chain length between the first particle model 6a and the second particle model 6b is specified as the size of the first fragment model 13A (the maximum chain length of the first fragment model 13A) (step S63). In step S63 of this embodiment, the size of the first fragment model 13A is specified based on the above-mentioned procedure. In this embodiment, when the first fragment model 13A includes a loop, an approximation value of the size of the first fragment model 13A can be approximately specified as the size of the first fragment model 13A. The specified chain length is (approximately) specified as the size of the first fragment model 13A and input to the computer 1 (shown in FIG. 1).

[Determine whether the size of the first fragment model is greater than the threshold value]
Next, in the additional determination step S55 of this embodiment, it is determined whether the size of the first fragment model 13A is greater than a threshold value (step S64). The determination result is stored in the computer 1 (shown in FIG. 1).

[Finally determine whether the size of the first fragment model is greater than the threshold value based on the additional determination result]
Next, in the first step S441 of this embodiment, it is finally determined whether the size of the first fragment model 13A is larger than the threshold value based on the determination result of the additional determination step S55 (step S56). If it is determined in step S56 that the size of the first fragment model 13A is larger than the threshold value ("Yes" in step S56), this is stored in the computer 1 (shown in FIG. 1) as the final determination result of the first step S441 (i.e., the size of the first fragment model 13A is larger than the threshold value) (step S53). On the other hand, if it is determined in step S56 that the size of the first fragment model 13A is equal to or smaller than the threshold value ("No" in step S56), this is stored in the computer 1 (shown in FIG. 1) as the final determination result of the first step S441 (i.e., the size of the first fragment model 13A is equal to or smaller than the threshold value) (step S57).

[Calculating the size of the second fragment model (second step)]
Next, as shown in Fig. 10, in the prediction step S44 of this embodiment, it is predicted whether the size of the second fragment model 13B, which is the fragment model 13 on the other side with respect to the selected binding model 7a, will be greater than a threshold value (second step S442). In the second step S422, the calculation of the size of the second fragment model 13B can be performed in the same procedure as the first step S441. That is, in the second step S442, first, in the second fragment model 13B (shown in Figs. 9(a) and 9(b)), the third particle model 6c that is farthest from the other particle model 6f different from the one particle model 6e bound to the selected binding model 7a is specified.

Next, similarly to the first step S441, in the second fragment model 13B, starting from the third particle model 6c, the fourth particle model 6d, which is one of the particle models 6 furthest from the third particle model 6c, is identified. Then, the chain length between the third particle model 6c and the fourth particle model 6d is identified as the size of the second fragment model 13B (the maximum chain length of the second fragment model 13B). In this embodiment, when the second fragment model 13B includes a loop, an approximation value of the size of the second fragment model 13B can be approximately identified as the size of the second fragment model 13B. Then, it is determined whether the size of the second fragment model 13B is greater than a threshold value. The determination result is stored in the computer 1.

In this way, in the prediction step S44 of this embodiment, it is possible to predict whether the sizes of the first fragment model 13A and the second fragment model 13B are larger than the threshold value not only in the linear polymer chain model 5 shown in FIG. 9(a) but also in the polymer chain model 5 connected at the cross-linking point 14 shown in FIG. 9(b). Similarly, it is possible to predict whether the sizes of the first fragment model 13A and the second fragment model 13B are larger than the threshold value for the polymer chain model 5 including branches. Note that the second fragment model 13B may be identical to the first fragment model 13A. In such a case, although there may be a waste of calculation in that the same fragment model is inspected twice, in the same way as when they are not identical, in the prediction step S44 of this embodiment, it is possible to correctly predict whether their sizes are both larger than the threshold value.

[Determine whether the size of the fragment model is greater than the threshold value]
Next, in the cutting step S4 of this embodiment, it is determined whether the predicted sizes of the fragment models 13 after cutting (in this example, the first fragment model 13A and the second fragment model 13B) are both larger than a threshold value (step S45). In step S45, the above determination is made based on the prediction result in the prediction step S44.

When it is determined that the sizes of the fragment models 13 (the chain lengths of the first fragment model 13A and the second fragment model 13B) are both greater than the threshold ("Yes" in step S45), the polymer chain model 5 is cut by the selected bond model 7a (conditional cutting step S46). Figure 13(a) is a conceptual diagram showing the state in which the polymer chain model 5 in Figure 9(a) is cut. Figure 13(b) is a conceptual diagram showing the state in which the polymer chain model 5 in Figure 9(b) is cut.

[Conditional cutting process]
In the conditional cutting step S46, for example, the selected bond model 7a is deleted or invalidated. This cuts the polymer chain model 5. In the conditional cutting step S46, when the polymer chain model 5 is cut by the bond model 7a, as shown in FIG. 13(a), if a path connecting one particle model 6e and the other particle model 6f of the two particle models 6 connected by the selected bond model 7a via the bond model 7 is lost, the two fragments are separated into new polymer chain models 5, 5 composed of the fragment models 13 (first fragment model 13A and second fragment model 13B). On the other hand, if this is not the case (if a path remains connecting all particle models 6 included in the fragment model 13 via other bond models 7 even if the selected bond model 7a is cut), the first fragment model 13A and the second fragment model 13B become the same (i.e., all particle models 6 and bond models 7 constituting the first fragment model 13A and the second fragment model 13B are configured as one fragment model 13 that is the same as each other), and no new fragments are generated. The cut polymer chain model 5 (if separated into two fragments, the first fragment model 13A and the second fragment model 13B) is input to the computer 1 (shown in FIG. 1).

On the other hand, if it is determined that either the size of the fragment model 13 (the chain length of each of the first fragment model 13A and the second fragment model 13B) is equal to or less than the threshold value ("No" in step S45), the polymer chain model 5 is not cut by the selected bond model 7a. Then, steps S43 to S45 are performed again. In step S43, which is performed again, a new bond model 7a to be cut may be selected from the bond models 7 of the previously selected polymer chain model 5 (shown in Figures 9(a) and (b)). Also, in step S43, a new polymer chain model 5 different from the previously selected polymer chain model 5 may be selected, and a bond model 7a to be cut may be selected from the selected polymer chain model 5.

In this way, in the creation method of this embodiment, the polymer chain model 5 is cut only when the size of the fragment model 13 (the molecular weight or maximum chain length of each of the first fragment model 13A and the second fragment model 13B) is greater than the threshold value. This suppresses the cutting of small polymer chain models 5 whose size after cutting is equal to or smaller than the threshold value, similar to the cutting process of an actual polymer chain. Therefore, in the creation method of this embodiment, it is possible to create a numerical analysis model (polymer chain model 5) of the polymer chain 2 that approximates the desired molecular weight distribution.

[Determine whether the number of disconnections has reached the upper limit]
Next, in the cutting step S4 of this embodiment, it is determined whether the total number of cuts in the polymer chain model 5 is equal to or greater than the upper limit (step S47). If it is determined that the total number of cuts is equal to or greater than the upper limit ("Yes" in step S47), the series of processes in the cutting step S4 is terminated. On the other hand, if it is determined that the total number of cuts is less than the upper limit ("No" in step S47), steps S43 to S47 are performed again. In the step S43 that is performed again, for example, a new polymer chain model 5 different from the polymer chain model 5 selected last time may be selected, and a bond model 7a to be cut may be selected from the selected polymer chain model 5.

In this way, in the cutting step S4 of this embodiment, the polymer chain model 5 is cut so that the size of the fragment model 13 after cutting becomes larger than the threshold value until the total number of cuts of the polymer chain model 5 reaches the upper limit value. As a result, in the cutting step S4 of this embodiment, it is possible to approximate the molecular weight distribution of the polymer chain model 5 to the molecular weight distribution of the polymer material (shown in FIG. 8) while suppressing excessive cutting of the polymer chain model 5.

Figure 14 is a graph showing the molecular weight distribution (differential molecular weight distribution) of the polymer chain model 5. In this differential molecular weight distribution, the molecular weight W1 where the frequency is greatest, i.e., the peak, corresponds to the molecular weight W1 in the molecular weight distribution of the polymer material shown in Figure 8. In this embodiment, the polymer chain models 5 having the molecular weight W1 that has the greatest effect on the physical properties of the polymer material are created most frequently. Therefore, in this embodiment, it has been shown that the molecular weight distribution of the polymer chain model 5 can be approximated to the molecular weight distribution of the polymer material (shown in Figure 8).

Define Interaction
Next, as shown in Fig. 3, in the creation method of this embodiment, interactions are defined between particle models 6, 6 of the polymer chain model 5 (step S5). Note that if it is not necessary to define the interactions, step S5 may be omitted. Fig. 15 is a conceptual diagram showing the polymer chain model 5 in which interactions are defined.

The interaction in this embodiment is defined as a second potential P2 defined between particle models 6, 6 of a pair of polymer chain models 5, 5. The second potential P2 can be set appropriately, and is defined as one in which attractive and repulsive forces act, for example. The second potential P2 in this embodiment can be defined as an LJ potential, for example. The details of the LJ potential and the procedure for setting constants, etc. are as described in the above-mentioned paper 1. The second potential P2 is stored in a computer 1 (shown in FIG. 1).

[Calculate structural relaxation]
Next, in the creation method of this embodiment, the computer 1 (shown in FIG. 1) calculates the structural relaxation of the polymer chain model 5 based on molecular dynamics (step S6). If the structural relaxation calculation is not necessary, step S6 may be omitted. In the structural relaxation calculation of this embodiment, for example, Newton's equation of motion is applied in the cell 10 for a predetermined time, assuming that the particle model 6 of the polymer chain model 5 follows classical mechanics. Then, the movement of the particle model 6 at each time is tracked for each unit time step.

In the molecular dynamics calculation, the pressure and temperature are kept constant, or the volume and temperature are kept constant, in the cell 10. As a result, in step S6, the initial configuration of the polymer chain model 5 is relaxed to approximate the molecular motion of the actual polymer material. In this embodiment, this is continued until the initial configuration of the polymer chain model 5 is sufficiently relaxed. As a result, a polymer material model 12 that models the polymer material is created. For example, the above-mentioned commercially available software can be used to calculate the structural relaxation.

In this embodiment, if there is no need to perform a structural relaxation calculation of the polymer chain model 5, the definition of the interaction (step S5) and the structural relaxation calculation (step S6) may be omitted. Furthermore, inside the cell 10, for example, a filler model (not shown) that models a filler to be mixed into the polymer material may be placed, or a coupling material model (not shown) that models a coupling agent may be placed. The polymer material model 12 is stored in the computer 1 (shown in FIG. 1).

[Simulation method for polymer materials]
The polymer chain numerical analysis model (polymer chain model 5) created by the creation method of the above embodiment is used for simulating a polymer material. Next, a method for simulating a polymer material will be described. Fig. 16 is a flowchart showing the processing procedure of the method for simulating a polymer material.

[Create a polymer chain model]
In the simulation method of this embodiment, first, computer 1 (shown in FIG. 1) creates polymer chain model 5 (step S7). In step S7 of this embodiment, based on the procedure of steps S1 to Scission step S4 of the creation method of the previous embodiment (shown in FIG. 3), polymer chain model 5 (shown in FIG. 15) that approximates a desired molecular weight distribution is created. Polymer chain model 5 is stored in computer 1.

[Create a polymer material model]
Next, in the simulation method of this embodiment, the computer 1 (shown in FIG. 1) creates a polymer material model 12 (shown in FIG. 15) including a polymer chain model 5 (step S8). In step S8 of this embodiment, based on the procedures of steps S5 and S6 (shown in FIG. 3) of the previous embodiment, interactions are defined between the particle models 6, 6 of the polymer material model 12 arranged in the cell 10, and the structural relaxation of the polymer chain model 5 is calculated. This creates a polymer material model 12 (shown in FIG. 15) that models the polymer material. The polymer chain model 5 and the polymer material model 12 are stored in the computer 1.

[Calculate deformation of polymer material model]
Next, in the simulation method of this embodiment, the computer 1 (shown in FIG. 1) calculates the deformation of the polymer material model 12 (shown in FIG. 15) (step S9). The deformation calculation of the polymer material model 12 can be performed appropriately. For example, based on the procedure described in Japanese Patent No. 6408856, the extension of the polymer material model 12 may be calculated so that one end (one side surface 11a) and the other end (the other side surface 11b) of the polymer material model 12 are separated from each other. In addition, a periodic strain may be applied to the polymer material model 12. The above-mentioned commercially available software may be used for such deformation calculation.

In step S9 of this embodiment, the physical quantities (stress, energy loss, etc.) of the polymer material model 12 can be calculated by calculating the deformation of the polymer material model 12. In this embodiment, a polymer chain model 5 that approximates the desired molecular weight distribution (in this example, the molecular weight distribution of the analysis target shown in Figure 8) is used, so that physical quantities (stress, energy loss, etc.) that greatly affect the molecular weight distribution can be calculated with high accuracy. The deformation calculation results are stored in computer 1 (shown in Figure 1).

[Output the deformation calculation results]
Next, in the simulation method of this embodiment, the computer 1 (shown in FIG. 1) outputs the calculation results of the deformation (step S10). The calculation results can 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 inform an operator or the like of the calculation results of the deformation of the polymer material model 12.

[Evaluate the deformation calculation results]
Next, in the simulation method of this embodiment, the calculation result of the deformation is evaluated (step S11). The calculation result may be evaluated by the computer 1 (shown in FIG. 1) or by an operator.

In step S11 of this embodiment, the calculation result of the deformation (in this example, the physical quantity of the polymer material model 12) is evaluated as to whether it satisfies a predetermined criterion. The criterion can be set appropriately depending on the performance required for the polymer material and the product using the polymer material (e.g., a tire, etc.).

In this embodiment, if it is determined that the deformation calculation result meets the criteria ("Yes" in step S11), the performance of the polymer material model 12 is determined to be good. In this case, the polymer material is manufactured based on the structure of the polymer chain 2 and the various conditions set in the polymer material model 12 (step S12).

On the other hand, if it is determined that the deformation calculation results do not meet the criteria ("No" in step S11), the performance of the polymer material model 12 is evaluated as not being good. In this case, the structure of the polymer chain 2 and the various conditions set in the polymer material model 12 are changed (step S13), and steps S7 to S11 are performed again.

In this way, in the simulation method of this embodiment, the structure of the polymer chain 2 and the various conditions set in the polymer material model are changed until the performance of the polymer material is improved, so that a polymer material with good performance can be efficiently manufactured.

The above describes in detail a particularly preferred embodiment of the present invention, but the present invention is not limited to the illustrated embodiment and can be modified and implemented in various ways.

A polymer chain model (coarse-grained molecular model) that models a polymer chain was input, and a model for numerical analysis of the polymer chain was created by cutting the polymer chain model (Examples and Comparative Examples).

In the embodiment, a cutting step for cutting a polymer chain model was performed based on the procedure shown in FIG. 6. In the embodiment, one bond model to be cut was selected from the bond models constituting the polymer chain model, and a prediction step was performed for predicting whether the size of the fragment model after cutting when the polymer chain model is cut with the selected bond model is larger than a predetermined threshold value.

In the prediction process of the embodiment, based on the procedures shown in Figures 10 and 11, it was predicted whether the size of the first fragment model on one side and the size of the second fragment model on the other side of the selected bond model were larger than a threshold value. Then, when the sizes of the first fragment model and the second fragment model were both predicted to be larger than the threshold value, the polymer chain model was cut in the selected bond model.

On the other hand, in the comparative example, the polymer chain model was randomly cut by automatic processing by a computer. Then, in the examples and the comparative example, the molecular weight distribution of the polymer chain model was obtained. The common specifications are as follows.
Number of polymer chain models: 30 Total number of particle models in one polymer chain model: 5,000 Number of cross-linking points: 70
Size of the fragment model: Maximum chain length (the maximum chain length that can be taken within the fragment. The chain length is the number of particle models on the shortest path between the two selected particle models via the bond model)
Threshold (maximum chain length) W2: 100

Figure 17 is a graph showing the molecular weight distribution of the examples and comparative examples. In the examples, the polymer chain model was prevented from being cut to a size below the threshold value W2, and the molecular weight W1 with the highest frequency could be made to correspond to the molecular weight W1 of the molecular weight distribution of the polymer material shown in Figure 8. On the other hand, in the comparative examples, the polymer chain model was cut to a size below the threshold value W2, and the molecular weight W3 with the highest frequency could not be made to correspond to the molecular weight W1 shown in Figure 8. Therefore, the examples were able to create a numerical analysis model of the polymer chain that approximated the desired molecular weight distribution compared to the comparative examples.

[Additional Notes]
The present invention includes the following aspects.

[Invention 1]
1. A method for creating a model for numerical analysis of a polymer chain, comprising the steps of:
inputting a polymer chain model including a plurality of particle models and a bond model that bonds adjacent particle models to each other based on the polymer chain into a computer;
a cutting step in which the computer cuts bonds of the polymer chain model,
The cutting step includes:
selecting one bond model to be cleaved from the bond models constituting the polymer chain model;
A step of predicting whether or not the sizes of fragment models (one or two of the fragment models resulting from the cleavage) which are a collection of particle models linked by other bond models excluding the selected bond model, are all larger than a predetermined threshold value when the selected bond model is assumed to be cleaved;
and a conditional cleavage step of cleaving the polymer chain model with the selected binding model when the sizes of the predicted fragment models are all larger than the threshold value.
How to create models for numerical analysis of polymer chains.
[Invention 2]
Prior to the predicting step, a step of setting the threshold value is included;
The step of setting the threshold value includes a step of acquiring a molecular weight distribution of a polymer material including the polymer chain;
and setting the threshold value based on the molecular weight having the highest frequency in the molecular weight distribution.
[The present invention 3]
The predicting step includes a step of searching for a particle model constituting the fragment model starting from one of two particle models bound to the selected binding model, via a binding model other than the selected binding model,
The method for creating a model for numerical analysis of a polymer chain according to the first or second aspect of the present invention, wherein the searching step includes a step of terminating the search for the particle model when it becomes clear that the size of the fragment model is larger than the threshold value.
[Invention 4]
The method for creating a model for numerical analysis of a polymer chain according to any one of Inventions 1 to 3, wherein the size of the fragment model is a molecular weight [Invention 5]
5. The method for creating a model for numerical analysis of a polymer chain according to any one of claims 1 to 4, wherein the size of the fragment model is the maximum chain length.
[Invention 6]
The predicting step includes a step of starting from one of the two particle models bound by the selected binding model, and searching for a first particle model that is one of the particle models farthest from the starting particle model via a binding model other than the selected binding model;
Starting from the first particle model, searching for a second particle model which is one of the particle models farthest from the first particle model via the bond models other than the selected bond model;
and predicting the maximum chain length based on the chain length between the first particle model and the second particle model.
[Invention 7]
A step of creating the polymer chain model by a computer based on the method for creating a polymer chain model for numerical analysis according to any one of the first to seventh aspects of the present invention;
A step of generating a polymer material model including the polymer chain model by the computer;
said computer calculating deformation of said polymeric material model;
and outputting a calculation result of the deformation by the computer.
Simulation methods for polymeric materials.

S43: A step of selecting one binding model to be cut; S44: A step of predicting whether the size of the fragment model after cutting is larger than a threshold value; S46: A conditional cutting step of cutting the polymer chain model with the selected binding model.

Claims (6)

1. A method for creating a model for numerical analysis of a polymer chain, comprising the steps of:
inputting a polymer chain model including a plurality of particle models and a bond model that bonds adjacent particle models to each other based on the polymer chain into a computer;
a cutting step in which the computer cuts bonds of the polymer chain model,
The cutting step includes:
selecting one bond model to be cleaved from the bond models constituting the polymer chain model;
setting a threshold value;
A step of predicting whether or not the sizes of fragment models (one or two of the fragment models resulting from the cleavage) which are a collection of particle models linked by other bond models excluding the selected bond model, are all larger than the threshold value when the selected bond model is cleaved;
and a conditional cleavage step of cleaving the polymer chain model with the selected binding model when the sizes of the predicted fragment models are all larger than the threshold value,
The step of setting the threshold value includes a step of acquiring a molecular weight distribution of a polymer material including the polymer chain;
and setting the threshold value based on the molecular weight that is most frequently found in the molecular weight distribution.
How to create models for numerical analysis of polymer chains. The predicting step includes a step of searching for a particle model constituting the fragment model starting from one of two particle models bound to the selected binding model, via a binding model other than the selected binding model,
2. The method for creating a model for numerical analysis of a polymer chain according to claim 1, wherein the searching step includes a step of terminating the search for the particle model when it becomes clear that the size of the fragment model is larger than the threshold value. 2. The method for creating a model for numerical analysis of a polymer chain according to claim 1, wherein the size of the fragment model is a molecular weight . 2. The method for creating a polymer chain model for numerical analysis according to claim 1, wherein the size of the fragment model is a maximum chain length . The predicting step includes a step of starting from one of the two particle models bound by the selected binding model, and searching for a first particle model that is one of the particle models farthest from the starting particle model via a binding model other than the selected binding model;
searching for a second particle model, which is one of the particle models farthest from the first particle model, starting from the first particle model and passing through the bond models other than the selected bond model;
5. The method for creating a model for numerical analysis of a polymer chain according to claim 4, further comprising: predicting the maximum chain length based on a chain length between the first particle model and the second particle model . A step of creating the polymer chain model by a computer based on the method for creating a polymer chain model for numerical analysis according to claim 1;
A step of generating a polymer material model including the polymer chain model by the computer;
said computer calculating deformation of said polymeric material model;
and outputting a calculation result of the deformation by the computer.
Simulation methods for polymeric materials.

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