Polymer material simulation method

Abstract

To calculate properties of a high polymer material including a first polymer and a second polymer which are mutually insoluble.SOLUTION: There is provided a simulation method for a high polymer material model. This method includes a process S11 of inputting a high polymer material model including a first polymer model and a second polymer model as a mutual separation structure. Further, a computer executes: a first process S1 of calculating a first concentration distribution of the first polymer model and second polymer model; a second process S2 of virtually sectioning the high polymer material model into a plurality of regions; a third process S3 of calculating a second concentration distribution of the first polymer model and second polymer model in the plurality of regions, respectively; a fourth process S4 of calculating properties of at least one region among the plurality of regions based upon the second concentration distribution; and a fifth process S5 of calculating properties of the whole system of the high polymer material from the properties of the at least one region among the plurality of regions.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a method for simulating a polymer material. [Background technology]

[0002] Methods for calculating the physical properties of polymeric materials (polymer blends) containing two or more types of polymers include molecular dynamics, coarse-grained molecular dynamics, and other methods using various empirical formulas (see, for example, Patent Document 1 listed below). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2020-086835 Summary of the Invention [Problem to be solved by the invention]

[0004] For example, in the case of a polymer blend in which multiple polymers are immiscible with each other, the physical properties of the entire polymer blend system are thought to be significantly affected by the concentration distribution of the multiple polymers. However, all of the above-mentioned methods for calculating physical properties assume that the concentration distribution of the multiple polymers is approximately uniform throughout the entire polymer blend system, making it difficult to predict the physical properties of immiscible polymer blends.

[0005] The present invention was devised in consideration of the above-described circumstances, and its main object is to provide a simulation method capable of calculating the physical properties of a polymeric material containing a first polymer and a second polymer that are incompatible with each other. [Means for solving the problem]

[0006] The present invention is a simulation method for calculating the physical properties of a polymeric material containing a first polymer and a second polymer that are incompatible with each other, the method comprising the steps of: inputting a polymeric material model for numerical calculation, which includes a first polymer model and a second polymer model as a phase-separated structure based on the polymeric material, into a computer; and the computer executes the following steps: a first step of calculating a first concentration distribution, which is the concentration distribution of the first polymer model and the second polymer model in the entire system of the polymeric material model; a second step of virtually dividing the polymeric material model into a plurality of regions; a third step of calculating a second concentration distribution, which is the concentration distribution of the first polymer model and the second polymer model in each of the plurality of regions, based on the first concentration distribution; a fourth step of calculating the physical properties of at least one of the plurality of regions based on the second concentration distribution in each of the plurality of regions; and a fifth step of calculating the physical properties of the entire system of the polymeric material from the physical properties of at least one of the plurality of regions. [Effects of the Invention]

[0007] By employing the above steps, the polymer material simulation method of the present invention makes it possible to calculate the physical properties of a polymer material containing a first polymer and a second polymer that are incompatible with each other. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. 1 is a perspective view showing a computer for executing a simulation method for a polymer material according to an embodiment of the present invention. [Figure 2] 3 is a flowchart showing a processing procedure of a simulation method according to the present embodiment. [Figure 3] 10 is a flowchart showing the processing procedure of the first step. [Figure 4] 10 is a flowchart showing the processing procedure of a polymer material model input step of the present embodiment. [Figure 5] FIG. 1 is a conceptual diagram showing a polymer material model. [Figure 6]FIG. 2 is a conceptual diagram showing a first polymer model and an additive model. [Figure 7] FIG. 1 is a partially enlarged view of a polymer material model. [Figure 8] FIG. 1 is a conceptual diagram showing a polymer material model divided into multiple spatial regions. [Figure 9] The concentration distribution of the first polymer, the second polymer, and the third polymer throughout the polymeric material system. [Figure 10] FIG. 1 is a conceptual diagram showing a polymer material model 10 divided into a plurality of regions 14. [Figure 11] 10 is a flowchart showing the processing procedure of a fifth step. [Figure 12] 1 is a graph showing a histogram of physical properties. [Figure 13] 10 is a flowchart showing the procedure of a first step according to another embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

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

[0010] The polymer material simulation method of this embodiment (hereinafter sometimes simply referred to as the "simulation method") calculates the physical properties of a polymer material containing a first polymer and a second polymer that are incompatible with each other. The simulation method of this embodiment uses a computer.

[0011] 1 is a perspective view showing a computer 1 for executing the simulation method for polymeric materials of this embodiment. The computer 1 of this embodiment is configured to include a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with, for example, a central processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2. The storage device has software and the like stored in advance for executing the simulation method of this embodiment.

[0012] [Polymer materials] The polymeric material is not particularly limited as long as it contains a first polymer (first molecular chain) and a second polymer (second molecular chain) that are incompatible with each other. The first polymer in this embodiment is styrene-butadiene rubber (SBR). The second polymer in this embodiment is butadiene rubber (BR). The first polymer and the second polymer are not limited to these embodiments. The polymeric material may further contain a third polymer or the like that is different from the first polymer and the second polymer. The third polymer or the like may be either incompatible with the first polymer and the second polymer or compatible with them.

[0013] The polymer material of this embodiment further includes an additive that is added together with the first polymer and the second polymer. Examples of the additive include resin and oil. The additive of this embodiment is resin.

[0014] [Physical Properties] In the simulation of this embodiment, the physical properties calculated are not particularly limited and are selected appropriately depending on, for example, the purpose of analyzing the polymer material. The physical properties in this embodiment preferably include at least one of dynamic viscoelasticity, glass transition temperature, tensile properties, viscosity, vulcanization properties (for example, induction time tC(10), 50% vulcanization time tC(50), and 90% vulcanization time tC(90) measured using a vulcanization tester (curelastometer)), and hardness. These physical properties are useful for developing polymer materials, designing production facilities, and the like. In this embodiment, the glass transition temperature is used.

[0015] Incidentally, when the first polymer and the second polymer are incompatible with each other, as in this embodiment, the physical properties of the entire system of the polymer material, which is a blend of these polymers, are thought to be significantly affected by the concentration distribution of the first polymer and the second polymer.

[0016] Furthermore, when an additive is added to a polymeric material as in this embodiment, the physical properties of the entire polymeric material system are thought to be significantly affected by the concentration distribution of the additive (bias toward the first polymer and the second polymer).

[0017] On the other hand, conventional calculation methods (e.g., molecular dynamics) assume that the concentration distribution of the first polymer and the second polymer (including the additive in this example) is almost uniform throughout the polymer material system, making it difficult to predict the physical properties of polymer blends.

[0018] [Simulation method for polymer materials (first embodiment)] In the simulation method of this embodiment, the physical properties of the polymer material are calculated taking into account the concentration distribution of the first polymer and the second polymer (including the additive in this example). Fig. 2 is a flowchart showing the processing procedure of the simulation method of this embodiment.

[0019] [Calculate the first concentration distribution (first step)] In the simulation method of this embodiment, first, a computer 1 (shown in FIG. 1) calculates a first concentration distribution, which is the concentration distribution of a first polymer model and a second polymer model in the entire system of a polymer material model (first step S1). In this embodiment, the first concentration distribution is calculated based on a coarse-grained molecular dynamics (CGMD) method. Figure 3 is a flowchart showing the processing procedure of the first step S1 of this embodiment.

[0020] [Enter polymer material model] In the first step S1 of this embodiment, first, a polymer material model for numerical calculation is input into a computer 1 (shown in FIG. 1) based on the polymer material (polymer material model input step S11). The polymer material model of this embodiment is set to include a first polymer model and a second polymer model as a phase separation structure. FIG. 4 is a flowchart showing the processing procedure of the polymer material model input step S11 of this embodiment. FIG. 5 is a conceptual diagram showing a polymer material model 10. FIG. 6 is a conceptual diagram showing a first polymer model 2A and an additive model 3.

[0021] [Enter the first polymer model] In the polymer material model input step S11 of this embodiment, first, a first polymer model 2A modeling a first polymer (in this example, styrene-butadiene rubber) is input to a computer 1 (shown in FIG. 1) (step S111).

[0022] 5 and 6, the first polymer model 2A of this embodiment is defined as a coarse-grained model (in this embodiment, the Kremer-Grest model). Note that the first polymer model 2A is not limited to a coarse-grained model and may be, for example, an all-atom model or a united-atom model.

[0023] The first polymer model 2A of this embodiment is configured to include a plurality of particle models 5 and a bond chain model 6 that bonds adjacent particle models 5, 5. The particle models 5 of the first polymer model 2A of this embodiment are formed by substituting a structural unit that constitutes a monomer or a part of a monomer of the first polymer (molecular chain). As a result, the first polymer model 2A is configured to include a plurality of particle models 5 (for example, 10 to 5,000). Such substitution can be performed appropriately based on a conventional method.

[0024] 6, the particle model 5 of this embodiment is treated as a mass point in the equation of motion in molecular dynamics calculations. That is, parameters such as mass, volume, particle diameter D1, or charge are defined for the particle model 5.

[0025] The bonded chain model 6 of this embodiment is defined by a potential P1 with an extended length set between the particle models 5, 5. The potential P1 of this embodiment is an anharmonic potential U ch (r) is the anharmonic potential U ch For (r), the same formula as that in formula (2) described in Patent Document 1 is used.

[0026] Anharmonic potential U ch The constants and variables in (r) can be set appropriately depending on the structure of the first polymer (in this example, styrene-butadiene rubber). In this embodiment, the constants and variables are set based on, for example, Paper 1 (Kurt Kremer & Gary S. Grest, "Dynamics of Entangled Linear Polymer Melts: A Molecular-Dynamics Simulation," J. Chem Phys., Vol. 92, No. 8, April 15, 1990). This allows the definition of a linear first polymer model 2A in which the particle model 5 is constrained to be flexible. The first polymer model 2A is stored in a computer 1 (shown in FIG. 1).

[0027] [Enter the second polymer model] Next, in the polymer material model input step S11 of this embodiment, a second polymer model 2B (shown in FIG. 5) modeling a second polymer (butadiene rubber in this example) is input to the computer 1 (shown in FIG. 1) (step S112).

[0028] 5 and 6, in step S112 of this embodiment, a second polymer model 2B is set based on the same procedure as in step S111 of inputting a first polymer model 2A. Therefore, like the first polymer model 2A, the second polymer model 2B of this embodiment is configured to include a plurality of particle models 5 and a bond chain model 6 that bonds adjacent particle models 5, 5.

[0029] The particle model 5 of the second polymer model 2B of this embodiment is a replacement of a monomer or a structural unit that forms a part of a monomer of the second polymer (molecular chain). The bonded chain model 6 of the second polymer model 2B of this embodiment is defined by a potential P2 (not shown) with an extended length set between the particle models 5, 5. The potential P2 is an anharmonic potential U ch (r) is the anharmonic potential U ch Each constant and variable in (r) can be set appropriately based on the structure of the second polymer (butadiene in this example) and the above-mentioned paper 1. This allows defining a linear second polymer model 2B in which the particle model 5 is constrained to be flexible. The second polymer model 2B is stored in a computer 1 (shown in FIG. 1).

[0030] [Enter additive model] Next, in the polymer material model input step S11 of this embodiment, an additive model 3 that models an additive material (resin in this example) is input to the computer 1 (shown in FIG. 1) (step S113).

[0031] As shown in Figures 5 and 6, the additive model 3 of this embodiment is set as one independent particle model. Note that the additive model 3 may be composed of a plurality of particle models, such as a first polymer model 2A and a second polymer model 2B. As shown in Figure 6, the additive model 3 is treated as a mass point in the equation of motion in the molecular dynamics calculation. That is, parameters such as mass, volume, particle diameter D2, or charge are defined for the additive model 3.

[0032] The particle diameter D2 of the additive model 3 can be set appropriately. In this embodiment, the particle diameter D2 is set to be the same as the particle diameter D1 of the particle model 5. The additive model 3 is stored in the computer 1 (shown in FIG. 1).

[0033] Cell Input Next, in the polymer material model input step S11 of this embodiment, a cell 7 (shown in FIG. 5) which is a virtual space corresponding to a part of the polymer material to be analyzed is input to the computer 1 (shown in FIG. 1) (step S114).

[0034] As shown in FIG. 5, the cell 7 of this embodiment is defined as a rectangular parallelepiped having three pairs of mutually facing planes 7a, 7b. A periodic boundary condition is defined for each of the planes 7a, 7b. In such a cell 7, for example, it is possible to calculate that a portion of the first polymer model 2A and the second polymer model 2B (including the additive model 3 in this example) that exits one plane 7a enters from the opposite plane 7b. Therefore, one plane 7a and the opposite plane 7b can be treated as being continuous (connected).

[0035] The lengths L1a, L1b, and L1c of each side of the cell 7 can be set appropriately. In this embodiment, the lengths L1a, L1b, and L1c are preferably at least twice the radius of gyration (not shown), which is an amount indicating the extent of the first polymer model 2A and the second polymer model 2B. This prevents the cell 7 from colliding with its own image due to the periodic boundary condition in the molecular dynamics calculation, allowing for appropriate calculation of the spatial extent of the first polymer model 2A and the second polymer model 2B. Furthermore, the size of the cell 7 is set to a stable volume at, for example, 1 atmosphere. This allows the cell 7 to define the volume of at least a portion of the polymer material to be analyzed. The cell 7 is stored in the computer 1 (shown in FIG. 1).

[0036] [Place a polymer model in a cell] Next, in the polymer material model input step S11 of this embodiment, the computer 1 (shown in FIG. 1) arranges the first polymer model 2A and the second polymer model 2B in the cell 7 (step S115). In this embodiment, the first polymer model 2A and the second polymer model 2B (including the additive model 3 in this example) are arranged in the cell 7 so as to include the first polymer model 2A and the second polymer model 2B as a phase-separated structure.

[0037] In step S115 of the present embodiment, the procedure for arranging the first polymer model 2A, the second polymer model 2B, and the additive model 3 is not limited as long as the first polymer model 2A and the second polymer model 2B can be contained in the cell 7 as a phase-separated structure. In step S115 of the present embodiment, a plurality of first polymer models 2A, a plurality of second polymer models 2B, and a plurality of additive models 3 are arranged in the cell 7 using a DBMC (Density Biased Monte Carlo) method. The DBMC method can be used for calculation using, for example, COGNAC included in the above-mentioned J-OCTA.

[0038] [Define interaction potential] Next, in the polymer material model input step S11 of this embodiment, an interaction potential P3 is defined for the first polymer model 2A, the second polymer model 2B, and the additive model 3 (step S116), as shown in Fig. 5. The interaction potential P3 includes a first potential P3a to a sixth potential P3f.

[0039] A first potential P3a (not shown) is defined between a pair of particle models 5, 5 of adjacent first polymer models 2A, 2A. A second potential P3b (not shown) is defined between a pair of particle models 5, 5 of adjacent second polymer models 2B, 2B. A third potential P3c (shown in FIG. 5) is defined between a pair of adjacent additive models 3, 3.

[0040] A fourth potential P3d (shown in FIG. 5) is defined between the particle model 5 of the first polymer model 2A and the particle model 5 of the second polymer model 2B. A fifth potential P3e (shown in FIG. 5) is defined between the particle model 5 of the first polymer model 2A and the additive model 3. A sixth potential P3f (shown in FIG. 5) is defined between the particle model 5 of the second polymer model 2B and the additive model 3.

[0041] The interaction potential P3 (the first potential P3a to the sixth potential P3f) is, for example, an LJ potential U LJ (r) can be used to define the LJ potential U LJ The same formula as in the formula (1) described in the above Patent Document 1 is used for (r). The LJ potential U LJ Each constant in (r) can be set appropriately based on, for example, paper 2 (SL Mayo, BD Olafson & WA Goddard III, "DREIDING: A Generic Force Field for Molecular Simulations", J. Phys. Chem. 1990, 94, 8897). The interaction potential P3 (first potential P3a to sixth potential P3f) is stored in computer 1 (shown in FIG. 1).

[0042] Next, in the polymer material model input step S11 of this embodiment, the computer 1 (shown in FIG. 1) calculates the structural relaxation of the first polymer model 2A and the second polymer model 2B (step S117). In step S117 of this embodiment, the structural relaxation is calculated for the first polymer model 2A, the second polymer model 2B, and the additive model 3.

[0043] In the molecular dynamics calculation, for example, the pressure (for example, 1 atm) and temperature (for example, 290 K to 305 K) are kept constant (NPT constant) in cell 7. Furthermore, in the molecular dynamics calculation, Newton's equations of motion are applied to cell 7 for a predetermined time, assuming that the first polymer model 2A, the second polymer model 2B, and the additive model 3 follow classical mechanics. The movements of the particle models 5 of the first polymer model 2A and the second polymer model 2B, and the additive model 3 are tracked for each unit time step. The calculation of structural relaxation can be processed using, for example, COGNAC included in the above-mentioned J-OCTA.

[0044] A polymer material model 10 having an interface structure (phase-separated structure) between the first polymer model 2A and the second polymer model 2B can be created by calculating the structural relaxation of the first polymer model 2A and the second polymer model 2B. FIG. 7 is a partially enlarged view of the polymer material model. In FIG. 7, the additive model 3 and the bond chain model 6 shown in FIGS. 5 and 6 are omitted, and the particle model 5 of the first polymer model 2A is colored. This polymer material model 10 for numerical calculations, which includes the first polymer model 2A and the second polymer model 2B as a phase-separated structure, is stored in a computer 1 (shown in FIG. 1).

[0045] [Divide into multiple spatial regions] Next, in the first step S1 of this embodiment, the polymer material model 10 is divided into a plurality of spatial regions (step S12). Fig. 8 is a conceptual diagram showing the polymer material model 10 divided into a plurality of spatial regions 11. In Fig. 8, the first polymer model 2A, the second polymer model 2B, and the additive model 3 shown in Figs. 5 and 7 are omitted.

[0046] In step S12 of this embodiment, as shown in Fig. 8, the cell 7 constituting the polymer material model 10 is divided into a plurality of spatial regions 11 along a direction (in this example, the X-axis direction) intersecting with the interface 12 (shown in Fig. 7) between the first polymer model 2A and the second polymer model 2B. Each spatial region 11 is specified by coordinate values ​​of the X-axis, Y-axis, and Z-axis in the polymer material model 10. The plurality of spatial regions 11 are stored in a computer 1 (shown in Fig. 1).

[0047] [Calculate the first concentration distribution] Next, in a first step S1 of this embodiment, a first concentration distribution, which is the concentration distribution of the first polymer model 2A and the second polymer model 2B in the entire system of the polymer material model 10, is obtained based on the concentrations of the first polymer model 2A and the second polymer model 2B in the plurality of spatial regions 11 (step S13). The first concentration distribution of this embodiment is obtained as the concentration distribution of the first polymer model 2A, the second polymer model 2B, and the additive model 3.

[0048] In step S13 of this embodiment, first, the number of particle models 5 of the first polymer model 2A, the number of particle models 5 of the second polymer model 2B, and the number of additive models 3 are tallied in each spatial region 11. The ratio (volume fraction) of these numbers is found as the concentration distribution of the first polymer model 2A, the second polymer model 2B, and the additive model 3 in each spatial region 11. Then, the concentration distributions of the first polymer model 2A, the second polymer model 2B, and the additive model 3 in each spatial region 11 are arranged (plotted) in the order of arrangement in the spatial region 11 (spatial position of the polymer material), thereby finding a first concentration distribution of the entire system of the polymer material model 10.

[0049] Fig. 9 is a graph showing a first concentration distribution 21, which is the concentration distribution of the first polymer model 2A, the second polymer model 2B, and the additive model 3 in the entire system of the polymer material model 10. In the graph of Fig. 9, the vertical axis of the graph represents the concentrations (volume fractions) of the first polymer model 2A, the second polymer model 2B, and the additive model 3. Meanwhile, the horizontal axis represents the spatial position in the polymer material model 10 in a predetermined direction (in this example, the X-axis direction of the polymer material model 10).

[0050] In the first step S1 of this embodiment, the first concentration distribution 21 is calculated based on a coarse-grained molecular dynamics method, but the present invention is not limited to this. For example, the first concentration distribution 21 may be calculated based on a dissipative particle dynamics (DPD) method. In this case, a soft-core potential Usoftcore is defined as the interaction potential P3. The first concentration distribution 21 is stored in a computer 1 (shown in FIG. 1).

[0051] [Virtual division into multiple regions (second step)] Next, in the simulation method of this embodiment, the polymer material model 10 is virtually divided into a plurality of regions (second step S2). The division of the regions may be performed by a computer 1 (shown in FIG. 1) or by an operator. FIG. 10 is a conceptual diagram showing the polymer material model 10 divided into a plurality of regions 14.

[0052] In this embodiment, the multiple regions 14 are configured as partial models (partial systems of the entire system) obtained by dividing the polymer material model 10, unlike the spatial regions 11 (shown in FIG. 8) that separate the cells 7 of the polymer material model 10. In this embodiment, the polymer material model 10 is virtually divided into multiple regions 14 along a direction (in this example, the X-axis direction) that intersects with the interface 12 (shown in FIG. 7) between the first polymer model 2A and the second polymer model 2B. Note that the regions 14 are not limited to this embodiment, and may be virtually divided along the Y-axis or Z-axis, or along the X-axis, Y-axis, and Z-axis. The multiple regions 14 are stored in the computer 1 (shown in FIG. 1).

[0053] [Calculate the second concentration distribution (third step)] Next, in the simulation method of this embodiment, the computer 1 (shown in FIG. 1) calculates second concentration distributions, which are concentration distributions of the first polymer model 2A and the second polymer model 2B in each of the multiple regions 14, based on the first concentration distributions 21 (third step S3). The second concentration distributions of this embodiment are calculated as concentration distributions of the first polymer model 2A, the second polymer model 2B, and the additive model 3.

[0054] The second concentration distribution is calculated as appropriate. In the third step S3 of this embodiment, first, in the first concentration distribution 21 shown in Fig. 9, the portions 13 corresponding to each region 14 (shown in Fig. 10) are identified. The horizontal axis of the first concentration distribution 21 corresponds to the coordinate value in the X-axis direction of the cell 7 shown in Fig. 10. Therefore, the portions 13 corresponding to each region 14 can be easily identified based on the X-axis coordinate value (position in the X-axis direction) of each region 14.

[0055] Next, in a third step S3 of this embodiment, the concentration distributions (volume fractions) of the first polymer model 2A, the second polymer model 2B, and the additive model 3 are identified in each of the identified portions 13. As a result, second concentration distributions 22, which are the concentration distributions of the first polymer model 2A, the second polymer model 2B, and the additive model 3 in each of the multiple regions 14, are identified (calculated).

[0056] In the second concentration distribution 22 of each of the multiple regions 14 (portions 13), the concentration (volume fraction) of at least one of the first polymer model 2A, the second polymer model 2B, and the additive model 3 may vary along the horizontal axis (X-axis direction). In such regions 14, the average value of the concentration (volume fraction) of the first polymer model 2A, the average value of the concentration (volume fraction) of the second polymer model 2B, and the average value of the concentration (volume fraction) of the additive model 3 may be calculated. This allows the concentrations of the first polymer model 2A, the second polymer model 2B, and the additive model 3 to be uniquely identified. The second concentration distribution 22 is input into the computer 1 (shown in FIG. 1).

[0057] [Calculate physical properties of multiple regions (Step 4)] Next, in the simulation method of this embodiment, the computer 1 (shown in FIG. 1) calculates the physical properties of at least one of the multiple regions 14 based on the second concentration distribution 22 (shown in FIG. 9) of each of the multiple regions 14 shown in FIG. 10 (fourth step S4). The physical properties of the region 14 are calculated appropriately based on the second concentration distribution 22. The fourth step S4 of this embodiment preferably includes a step of calculating the physical properties of the region 14 based on at least one of a molecular dynamics method, a coarse-grained molecular dynamics method, and a predetermined empirical formula.

[0058] [4th step (molecular dynamics method)] In the process of calculating the physical properties of region 14 based on the molecular dynamics method, an all-atom model (or united atom model) that models the first polymer, the second polymer, and the additive is used. The all-atom model is defined based on a conventional procedure (for example, the procedure described in a patent document (JP 2020-135375 A)).

[0059] In the step of calculating physical properties based on molecular dynamics, first, all-atom models (not shown) that model the first polymer, the second polymer, and the additive are placed in cells (not shown) that are virtual spaces corresponding to each region 14 (shown in FIG. 10). The all-atom models are placed in each cell based on the second concentration distributions 22 (shown in FIG. 9) of each of the multiple regions 14. In this way, regional models (not shown) that model each of the multiple regions 14 are set.

[0060] Next, in each region model (not shown), structural relaxation is calculated based on molecular dynamics for the all-atom model. This allows the physical properties (in this example, the glass transition temperature) of each region 14 (shown in FIG. 10) to be calculated. The physical properties (glass transition temperature) are calculated as appropriate based on conventional procedures (for example, the procedures described in patent document (JP 2016-070889 A)).

[0061] In this way, in the molecular dynamics method, the physical properties of each region model (not shown) are calculated using an all-atom model (not shown), and therefore, compared to, for example, the coarse-grained molecular dynamics method, it is possible to calculate the physical properties of each of the multiple regions 14 (shown in Figure 10) with high accuracy.

[0062] [4th step (coarse-grained molecular dynamics method)] In the process of calculating the physical properties of region 14 based on the coarse-grained molecular dynamics method, a first polymer model 2A, a second polymer model 2B, and an additive model 3 (shown in FIG. 4) defined as coarse-grained models are used.

[0063] In the step of calculating physical properties based on the coarse-grained molecular dynamics method, first, a first polymer model 2A, a second polymer model 2B, and an additive model 3 are arranged in a predetermined cell (not shown) based on the second concentration distribution 22 (shown in FIG. 9) of each of the plurality of regions 14. As a result, a region model (not shown) is set that models each of the plurality of regions 14 (shown in FIG. 10).

[0064] Next, in each region model (not shown), structural relaxation is calculated based on molecular dynamics for the first polymer model 2A, the second polymer model 2B, and the additive model 3. As a result, the physical properties (in this example, the glass transition temperature) of each region 14 shown in FIG.

[0065] In this way, in the coarse-grained molecular dynamics method, the physical properties of each region model (not shown) are calculated using a coarse-grained model, and therefore, compared to when an all-atom model is used (molecular dynamics method), for example, the physical properties of multiple regions 14 (shown in Figure 10) can be calculated in a shorter time.

[0066] When calculating the physical properties of the region 14 based on the coarse-grained molecular dynamics method, the physical properties may be calculated using the region 14 configured as a partial model (a part of the entire system) obtained by dividing the polymer material model 10. This can omit the setting of the above-mentioned region model (not shown).

[0067] [Step 4 (empirical formula)] The empirical formula is used to calculate the physical properties of each of the multiple regions 14 shown in Fig. 10 based on the second concentration distribution 22 shown in Fig. 9. The empirical formula is not particularly limited as long as it can calculate the physical properties of the multiple regions 14. The empirical formula of this embodiment employs at least one of the FOX formula, the KWEI formula, and the GORDON-TAYLOR formula.

[0068] The FOX formula is shown in the following formula (1): The glass transition temperature Tg can be determined by the FOX formula (1) below.

[0069]

number

[0070] The glass transition temperatures of the first polymer, the second polymer, and the additive are substituted into Tg1 to Tg3 in the above formula (1), respectively. These glass transition temperatures can be easily calculated, for example, by inputting the chemical structures of the first polymer, the second polymer, and the additive based on the QSPR (quantitative structural property relationship) described below.

[0071] The second concentration distribution 22 (the concentration of the first polymer model 2A, the concentration of the second polymer model 2B, and the concentration of the additive model 3) shown in FIG. 9 is substituted into Φ1 to Φ3 in the above formula (1) for each of the multiple regions 14 (shown in FIG. 10).

[0072] In this way, in the step of calculating the physical properties based on the empirical formula (in this example, the FOX formula), the concentrations Φ1 to Φ3 and the glass transition temperatures Tg1 to Tg3 identified from the second concentration distribution 22 shown in Fig. 9 are substituted for each of the plurality of regions 14 (shown in Fig. 10), thereby calculating the physical properties (in this example, the glass transition temperatures) of each of the plurality of regions 14.

[0073] When calculating the physical properties of the region 14 using the KWEI equation and the GORDON-TAYLOR equation, the variables of the FOX equation in the above equation (1) are used, thereby allowing the physical properties of the region 14 to be calculated.

[0074] In the fourth step S4, if it is determined that the properties of one of the multiple regions 14 are dominant over the properties of the entire polymeric material system, the properties of only that one region 14 may be calculated. This reduces the calculation time for the properties. This determination can be made as appropriate. For example, if there is a large difference between the properties (glass transition temperature) of the first polymer and the properties (glass transition temperature) of the second polymer, the region 14 in which the polymer (polymer model) that exhibits the properties at a predetermined temperature is primarily distributed (highest concentration) is determined to be dominant over the properties of the entire polymeric material system. The predetermined temperature is specified, for example, as the operating temperature of a product (e.g., a tire) using the polymeric material. The properties of region 14 are stored in computer 1 (shown in FIG. 1).

[0075] [Calculate the physical properties of the entire polymer material system (step 5)] Next, in the simulation method of this embodiment, the computer 1 (shown in FIG. 1) calculates the physical properties of the entire polymer material system from the physical properties of at least one region 14 out of the multiple regions 14 (shown in FIG. 10) (fifth step S5). The physical properties of the entire polymer material system can be calculated appropriately from the physical properties of the regions 14. Note that, if the physical properties of one region 14 out of the multiple regions 14 dominate the physical properties of the entire polymer material system, that physical property may be determined as the physical properties of the entire polymer material system.

[0076] In the fifth step S5 of this embodiment, the physical properties of the entire polymer material system are calculated based on the transfer sum of the physical properties of each of the multiple regions 14. Fig. 11 is a flowchart showing the processing procedure of the fifth step S5.

[0077] [Create a histogram of physical properties] In the fifth step S5 of this embodiment, the computer 1 (shown in FIG. 1) creates a histogram of the physical properties using the physical properties of each of the multiple regions 14 (shown in FIG. 10) (step S51). In step S51 of this embodiment, the physical properties of each of the multiple regions 14 are counted for each physical property value. This creates a histogram of the physical properties.

[0078] 12 is a graph showing a histogram of physical properties. The histogram of physical properties shows the relationship between the physical property and the number (frequency) of regions for which the physical property was calculated. The histogram of physical properties is stored in computer 1 (shown in FIG. 1).

[0079] [Calculate the moving average of physical properties] Next, in the fifth step S5 of this embodiment, the computer 1 (shown in FIG. 1) smooths the histogram (step S52). In step S52 of this embodiment, the sum of the physical properties (i.e., the moving sum) is calculated based on predetermined physical property intervals while shifting the intervals. This results in a curve 23 in which the histogram is smoothed. Note that the curve (smoothed histogram) 23 may be a weighted moving sum calculated by multiplying the physical property of each region 14 by a weight w(n) calculated from the following formula (2) based on a Gaussian function, for example.

[0080]

number

[0081] In Figure 12, the curve 23 is shown by a dashed line. The curve 23 is stored in the computer 1 (shown in Figure 1).

[0082] Identify the maximum value of a property in a smoothed histogram Next, in the fifth step S5 of this embodiment, the computer 1 (shown in FIG. 1) identifies the physical properties of the entire polymeric material system using the maximum value of the physical properties of the smoothed histogram (curve 23) (step S53). In this embodiment, the physical properties of the entire polymeric material system are identified based on curve 23, so that the physical properties of the entire polymeric material system can be identified by removing the variations in the physical properties of each region 14. Furthermore, by identifying the physical properties of the entire polymeric material system based on a weighted moving sum as in this embodiment, it becomes possible to easily take into account the different physical properties of each region 14.

[0083] The physical properties of the entire polymeric material system are appropriately identified based on a curve 23 (shown in FIG. 10) obtained by smoothing a histogram of the physical properties. It is believed that the physical properties of peak 24, which has the largest number of regions (frequency) in the physical property curve 23, have a large influence on the physical properties of the entire polymeric material system. Therefore, in this embodiment, the physical properties of peak 24 of the physical property curve 23 are identified as the physical properties of the entire polymeric material system. The physical properties of the entire polymeric material system are stored in a computer 1 (shown in FIG. 1).

[0084] As described above, in this embodiment, the polymer material model 10 including the first polymer model 2A and the second polymer model 2B as a phase-separated structure is divided into a plurality of regions 14 (shown in FIG. 10), and the physical properties of the entire polymer material system are calculated based on the physical properties of each of the plurality of regions 14. Therefore, unlike conventional methods that assume that the first polymer and the second polymer are compatible (have uniform concentration distributions), the simulation method of this embodiment makes it possible to calculate the physical properties of a polymer material including a first polymer and a second polymer that are incompatible with each other.

[0085] The number of the multiple regions 14 (shown in FIG. 10) into which the polymer material model 10 is virtually divided is preferably 40 to 120. By setting the number of the multiple regions 14 to 40 or more, the polymer material model 10 is virtually divided into small sections and the second concentration distribution 22 (shown in FIG. 9) and physical properties of each of the multiple regions 14 are calculated, thereby improving the calculation accuracy of the physical properties of the entire polymer material system. On the other hand, by setting the number of the multiple regions 14 to 120 or less, the number of regions 14 that are the targets for calculating the second concentration distribution 22 and physical properties is prevented from becoming larger than necessary, thereby preventing an increase in calculation time.

[0086] [Evaluating the physical properties of the entire polymer material system] Next, in the simulation method of this embodiment, whether the physical properties of the entire polymeric material system are good or not is evaluated (step S6). In step S6 of this embodiment, the evaluation may be performed by computer 1 (shown in FIG. 1) or an operator, based on the physical properties of the entire polymeric material system calculated in the fifth step S5.

[0087] In step S6 of the present embodiment, whether the physical properties of the entire polymeric material system are good or not is determined by comparing the physical properties with predetermined threshold values ​​of the physical properties. The threshold value is appropriately set depending on the performance (e.g., fracture resistance) required of the polymeric material.

[0088] If it is determined in step S6 that the physical properties of the entire polymer material system are good ("Yes" in step S6), a product (e.g., a tire, etc.) is manufactured using the polymer material (step S7). On the other hand, if it is determined in step S7 that the physical properties of the entire polymer material system are not good ("No" in step S6), the blending of the first polymer, second polymer, and additives is changed (step S8), and the first step S1 to step S6 are performed again.

[0089] In this way, in the simulation method of this embodiment, the blending ratio of the first polymer, the second polymer, and the additives is changed until the physical properties of the entire polymer material system are improved. As a result, in the simulation method of this embodiment, it becomes possible to reliably manufacture products such as tires using polymer materials with desired performance, for example.

[0090] [Simulation method for polymer materials (second embodiment)] In the simulation methods of the above embodiments, the first concentration distribution 21 is calculated based on the coarse-grained molecular dynamics method or the dissipative particle dynamics method in the first step S1, but is not limited to this. For example, the first concentration distribution 21 may be calculated based on at least one of the self-consistent field method, the polymer density functional method, and the generalized random phase approximation method.

[0091] [First step (self-consistent landing field method)] The Self-Consistent Field Method (SCF method) takes into account the entropy of the configuration of the first polymer, the second polymer, and the additive. The Self-Consistent Field Method can be calculated using, for example, SUSHI included in the Soft Material Integrated Simulator (J-OCTA) manufactured by JSOL Corporation. Figure 13 is a flowchart showing the processing procedure of the first step S1 in another embodiment of the present invention.

[0092] In the polymer material model input step S11 of this embodiment, parameters of the self-consistent field method are input. The parameters include the molecular weight of the first polymer, the molecular weight of the second polymer, and the molecular weight of the additive. Furthermore, the input values ​​of the self-consistent field method include χ parameters. The χ parameters include the first χ parameter to the sixth χ parameter.

[0093] The first χ parameter is the χ parameter between the first polymer. The second χ parameter is the χ parameter between the second polymer. The third χ parameter is the χ parameter between the additive. The fourth χ parameter is the χ parameter between the first polymer and the second polymer. The fifth χ parameter is the χ parameter between the first polymer and the additive. The sixth χ parameter is the χ parameter between the second polymer and the additive.

[0094] The χ parameter can be calculated based on the group contribution method, Monte Carlo method, molecular dynamics method, or QSPR (Quantitative Structure-Property Relationship). In this embodiment, QSPR is used. In QSPR, an SP value (solubility parameter) is determined based on the chemical structures of the first polymer, the second polymer, and the additive, and the χ parameter can be calculated from this SP value. SUSHI, included in the above-mentioned J-OCTA, is used to calculate the χ parameter.

[0095] In the polymer material model input step S11 of this embodiment, the above parameters are input to define a polymer material model (not shown). The polymer material model is stored in a computer 1 (shown in FIG. 1).

[0096] Next, in the first step S1 of this embodiment, a first concentration distribution 21 is obtained by a balancing calculation of the polymer material model (step S14). In step S14 of this embodiment, a balancing calculation using the χ parameter is performed, and the first concentration distribution 21 (shown in FIG. 9) of the first polymer, the second polymer, and the additive is obtained.

[0097] In this way, in the self-consistent field method, the first concentration distribution 21 can be calculated by setting the above-mentioned parameters, and therefore, compared to, for example, the coarse-grained molecular dynamics method and the dissipative particle dynamics method of the previous embodiments, the first concentration distribution 21 can be calculated more easily and with higher accuracy. The first concentration distribution 21 is stored in a computer 1 (shown in FIG. 1).

[0098] [Step 1 (density functional theory and generalized random phase approximation)] The density functional theory (DFT) is a method for describing the free energy of a system as a functional of the segment density field. On the other hand, the generalized random phase approximation (GRPA) method introduces ideality statistics using the random phase approximation into the Ginzburg-Landau free energy model. These density functional and generalized random phase approximation methods can calculate the first concentration distribution 21 (shown in Figure 9) using a procedure similar to the self-consistent field method (shown in Figure 13). The density functional and generalized random phase approximation methods can be calculated using SUSHI, which is included in the above-mentioned J-OCTA.

[0099] [Polymer material simulation method (third embodiment)] In the above-described embodiments, in the fifth step S5, the histogram is smoothed to identify the physical properties of the entire polymer material system, as shown in Fig. 12, but the present invention is not limited to this. For example, the physical properties of the entire polymer material system may be identified by performing an analysis based on the finite element method.

[0100] In the fifth step S5 of this embodiment, first, input conditions required for analysis by the finite element method are set using the physical properties of each of the plurality of regions 14. The input conditions include, for example, the elastic modulus and Poisson's ratio. These input conditions are identified from the physical properties of each of the plurality of regions 14.

[0101] Next, in the fifth step S5 of this embodiment, a finite element method analysis based on the input conditions is performed to identify the physical properties of the entire polymer material system. In this step, a finite element model (not shown) of the polymer material is first created. This finite element model is obtained by discretizing the polymer material into a finite number of elements. The elastic modulus, Poisson's ratio, etc. are input into each element of this finite element model based on the input conditions. Such a finite element model can be created, for example, based on the description in a patent document (JP 2020-135375 A).

[0102] Next, in this embodiment, the deformation of the finite element model is calculated. This deformation calculation is performed, as in the conventional case, using, for example, commercially available finite element analysis application software (for example, "Abaqus" manufactured by Dassault Systems). This allows the physical properties of the entire polymer material system to be calculated.

[0103] [Simulation method for polymeric materials (fourth embodiment)] In the simulation methods of the previous embodiments, the polymer material model 10 includes the additive model 3, but the present invention is not limited to this. For example, when the polymer material does not include an additive or when the additive has only a small effect on the physical properties, the additive model 3 may be omitted. In this case, the concentration (volume fraction) of the additive model 3 is omitted from the first concentration distribution 21 and the second concentration distribution 22 shown in FIG. 9. As a result, the simulation method of this embodiment, like the previous embodiments, can calculate the physical properties of a polymer material including a first polymer and a second polymer that are incompatible with each other, while shortening the calculation time.

[0104] Although a particularly preferred embodiment of the present invention has been described in detail above, the present invention is not limited to the illustrated embodiment and can be modified and implemented in various ways. [Example]

[0105] The physical properties of a polymer material containing a first polymer and a second polymer that are incompatible with each other and an additive were calculated (Example) based on the procedure shown in Fig. 2. In the first step of the Example, a polymer material model for numerical calculations containing a first polymer model and a second polymer model as a phase-separated structure was input into a computer according to the processing procedure shown in Fig. 3 and Fig. 4, as shown in Fig. 5 and Fig. 6.

[0106] Next, in the first step of the example, a first concentration distribution, which is the concentration distribution of the first polymer model and the second polymer model in the entire system of the polymer material model, was calculated based on the self-consistent field method, as shown in Figure 9. Next, in the example, the polymer material model was virtually divided into a plurality of regions (second step), as shown in Figure 10. Next, in the example, a second concentration distribution, which is the concentration distribution of the first polymer model, the second polymer model, and the additive model in each of the plurality of regions, was calculated based on the first concentration distribution (third step), as shown in Figure 9.

[0107] Next, in the example, the physical properties of each of the plurality of regions were calculated based on the second concentration distribution (fourth step). In the fourth step, the physical properties (glass transition temperatures) of each of the plurality of regions were calculated based on the FOX formula (1) above.

[0108] Next, in the example, the physical properties of the entire polymer material system were calculated from the physical properties of each of the multiple regions based on the processing procedure shown in Figure 11 (step 5). In step 5, first, a histogram of the physical properties was created using the physical properties of each of the multiple regions, as shown in Figure 12. Next, in step 5, the histogram was smoothed (a moving sum was calculated) and the physical properties of the entire polymer material system were identified. In the example, the physical properties of the peak with the largest number of regions (frequency) in the moving sum were identified as the physical properties of the entire polymer material system. The specifications of the example are as follows. First polymer model: First polymer: styrene-butadiene rubber Chain length: 822 Concentration (volume fraction) of the polymer material model (polymer material) in the entire system: 0.72 Second Polymer Model: Second polymer: butadiene rubber Chain length: 561 Concentration (volume fraction) of the polymer material model (polymer material) in the entire system: 0.24 Additive Model: Additive: Resin Chain length: 3 Concentration (volume fraction) of the polymer material model (polymer material) in the entire system: 0.04 Multiple Areas: 80 Moving average of physical properties: Weighted moving average (variance σ=10K)

[0109] As a result of the test, in the examples, a polymer material model including a first polymer model and a second polymer model as a phase-separated structure was divided into multiple regions, and the physical properties of the entire polymer material system could be calculated based on the physical properties of each of the multiple regions. Therefore, in the examples, unlike conventional calculation methods that assume a state in which the concentration distributions of the first polymer and the second polymer are approximately uniform throughout the entire polymer material system, it was possible to calculate the physical properties of a polymer material including a first polymer and a second polymer that are incompatible with each other.

[0110] [Note] The present invention includes the following aspects.

[0111] [Invention 1] 1. A simulation method for calculating physical properties of a polymeric material comprising a first polymer and a second polymer that are incompatible with each other, comprising: inputting a polymer material model for numerical calculation, which includes a first polymer model and a second polymer model as a phase-separated structure, into a computer based on the polymer material; The computer a first step of calculating a first concentration distribution, which is a concentration distribution of the first polymer model and the second polymer model in the entire system of the polymer material model; a second step of virtually dividing the polymer material model into a plurality of regions; a third step of calculating a second concentration distribution, which is a concentration distribution of the first polymer model and the second polymer model in each of the plurality of regions, based on the first concentration distribution; a fourth step of calculating a physical property of at least one of the plurality of regions based on the second concentration distribution of each of the plurality of regions; and a fifth step of calculating physical properties of the entire system of the polymer material from the physical properties of at least one of the plurality of regions. Simulation methods for polymeric materials. [Invention 2] The simulation method for a polymer material described in present invention 1, wherein the first step includes a step of calculating the first concentration distribution based on at least one of a self-consistent field method for the polymer material, a density functional method for polymers, a generalized random phase approximation method, a coarse-grained molecular dynamics method, and a dissipative particle dynamics method. [Invention 3] The fourth step is a method for simulating a polymeric material according to the first or second aspect of the present invention, which comprises calculating the physical properties of the region based on at least one of a molecular dynamics method, a coarse-grained molecular dynamics method, and a predetermined empirical formula. [Invention 4] 4. A method for simulating a polymer material according to claim 3, wherein the empirical formula includes at least one of the FOX formula, the KWEI formula, and the GORDON-TAYLOR formula. [Invention 5] the fifth step is a step of creating a histogram of the physical properties using the physical properties of each of the plurality of regions; smoothing the histogram; 5. A method for simulating a polymer material according to any one of aspects 1 to 4, comprising a step of specifying the maximum value of the physical property of the smoothed histogram as a physical property of the entire system of the polymer material. [Invention 6] the fifth step is a step of setting input conditions necessary for analysis by the finite element method using the physical properties of each of the plurality of regions; A method for simulating a polymer material according to any one of aspects 1 to 4, comprising a step of executing the finite element analysis based on the input conditions to identify the physical properties of the entire system of the polymer material. [Invention 7] the polymeric material further comprises an additive added together with the first polymer and the second polymer; The polymer material model further includes an additive model; the first concentration distribution is a concentration distribution of the first polymer model, the second polymer model, and the additive model in the entire system of the polymer material model, A method for simulating a polymer material according to any one of the first to sixth aspects of the present invention, wherein the second concentration distribution is a concentration distribution of the first polymer model, the second polymer model and the additive model in each of the plurality of regions. [Invention 8] 8. The method for simulating a polymer material according to any one of claims 1 to 7, wherein the physical properties include at least one of dynamic viscoelasticity, glass transition temperature, tensile properties, viscosity, and hardness. [Explanation of symbols]

[0112] S1 1st process S2 2nd process S3 3rd process S4 4th process S5 5th process

Claims

1. 1. A simulation method for calculating physical properties of a polymeric material comprising a first polymer and a second polymer that are incompatible with each other, comprising: inputting a polymer material model for numerical calculation, which includes a first polymer model and a second polymer model as a phase-separated structure, into a computer based on the polymer material; The computer a first step of calculating a first concentration distribution, which is a concentration distribution of the first polymer model and the second polymer model in the entire system of the polymer material model; a second step of virtually dividing the polymer material model into a plurality of regions; a third step of calculating second concentration distributions, which are concentration distributions of the first polymer model and the second polymer model in each of the plurality of regions, based on the first concentration distributions; a fourth step of calculating a physical property of at least one of the plurality of regions based on the second concentration distribution of each of the plurality of regions; and a fifth step of calculating physical properties of the entire system of the polymer material from the physical properties of at least one of the plurality of regions. Simulation methods for polymeric materials.

2. 2. The method for simulating a polymer material according to claim 1, wherein the first step includes a step of calculating the first concentration distribution based on at least one of a self-consistent field method for the polymer material, a density functional method for polymers, a generalized random phase approximation method, a coarse-grained molecular dynamics method, and a dissipative particle dynamics method.

3. 3. The method for simulating a polymer material according to claim 1, wherein the fourth step includes a step of calculating physical properties of the region based on at least one of a molecular dynamics method, a coarse-grained molecular dynamics method, and a predetermined empirical formula.

4. 4. The method for simulating a polymer material according to claim 3, wherein the empirical formula includes at least one of the FOX formula, the KWEI formula, and the GORDON-TAYLOR formula.

5. the fifth step is a step of creating a histogram of the physical properties using the physical properties of each of the plurality of regions; smoothing the histogram; 3. The method for simulating a polymer material according to claim 1, further comprising the step of specifying a maximum value of the physical property of the smoothed histogram as a physical property of the entire system of the polymer material.

6. the fifth step is a step of setting input conditions necessary for analysis by a finite element method using the physical properties of each of the plurality of regions; 3. The polymer material simulation method according to claim 1, further comprising the step of: executing the finite element analysis based on the input conditions to identify physical properties of the entire polymer material system.

7. the polymeric material further includes an additive added together with the first polymer and the second polymer; The polymer material model further includes an additive model; the first concentration distribution is a concentration distribution of the first polymer model, the second polymer model, and the additive model in the entire system of the polymer material model, The method for simulating a polymer material according to claim 1 , wherein the second concentration distribution is a concentration distribution of the first polymer model, the second polymer model, and the additive model in each of the plurality of regions.

8. The method for simulating a polymer material according to claim 1 or 2, wherein the physical properties include at least one of dynamic viscoelasticity, glass transition temperature, tensile properties, viscosity, vulcanization properties, and hardness.

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