Method for simulating polymer materials

Abstract

To provide a method which can create a mixing-type model of two polymeric material models with an interface formed.SOLUTION: The present invention relates to a method for simulating a polymeric material including: the step S1 of inputting a first polymeric material model and a second polymeric material model which are a modeled first polymeric component and a modeled second polymeric component, respectively; and the step S2 of inputting a mixing-type model in which the first and second polymeric material models are arranged so that an interface is formed between the first and second polymeric material models. The method further includes the step S3 in which a computer performs a molecular kinetics calculation for the mixing-type model and structurally relaxes the mixing-type model. The step S3 of the structural relaxation includes the first step of restraining the first polymeric material model to maintain the interface and structurally relaxing the mixing-type model.SELECTED DRAWING: Figure 2

Description

Technical Field

[0001] The present disclosure relates to a method for simulating polymer materials.

Background Art

[0002] The following Patent Document 1 describes a method for simulating polymer materials. In this method, a molecular structure model is set up in a cell having an arbitrary space, in which a molecular chain model having a three-dimensional structure composed of a finite number of particles representing atoms or aggregates thereof and bond chains that connect between these particles to define the relative positions of the respective particles is arranged. Then, a simulation of structural relaxation for stabilizing the molecular structure model based on molecular dynamics calculation is performed.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] By the way, in polymer materials, a plurality of types of polymer components may be blended. In such polymer materials, it is known that an interface is formed between the polymer components. Therefore, in order to perform a simulation for examining the interaction etc. at the interface, it is important to create a mixed system model of two polymer material models in which the interface is formed.

[0005] The present disclosure has been devised in view of the above actual situation, and the main object thereof is to provide a method capable of creating a mixed system model of two polymer material models in which an interface is formed.

Means for Solving the Problems

[0006] The present disclosure relates to a method for simulating a polymer material, which includes the steps of: inputting into a computer a first polymer material model and a second polymer material model, which are respectively modeled for a first polymer component and a second polymer component based on a classical molecular dynamics method; inputting into the computer a mixed system model in which the first polymer material model and the second polymer material model are arranged so that an interface is formed between the first polymer material model and the second polymer material model; and the computer performing molecular dynamics calculations on the mixed system model to structurally relax the mixed system model. The step of structurally relaxing includes a first step of structurally relaxing the mixed system model by restraining the first polymer material model so that the interface is maintained.

Advantages of the Invention

[0007] By adopting the above steps, the simulation method of the polymer material of the present disclosure can create a mixed system model of two polymer material models with an interface formed therebetween.

Brief Description of the Drawings

[0008]

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Mode for Carrying Out the Invention

[0009] Hereinafter, an embodiment of the present disclosure will be described with reference to the drawings. It should be understood that the drawings include exaggerated expressions and expressions different from the actual structural dimensional ratios in order to assist in understanding the content of the disclosure. Also, throughout each embodiment, the same or common elements are denoted by the same reference numerals, and redundant descriptions are omitted. Furthermore, the specific configurations shown in the embodiments and the drawings are for understanding the content of the present disclosure, and the present disclosure is not limited to the specific configurations shown.

[0010] In the simulation method of the polymer material of the present embodiment (hereinafter, sometimes simply referred to as "simulation method"), a mixed system model of two polymer material models with an interface formed is created. In the simulation method of the present embodiment, the computer 1 is used.

[0011] [Computer] FIG. 1 is a perspective view of a computer for executing the simulation method of the polymer material. The computer 1 of the present embodiment includes a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. In the main body 1a, for example, an arithmetic processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2 are provided. In the storage device, software for executing the simulation method of the present embodiment and the like are stored in advance.

[0012] [Polymer material] The polymer material of this embodiment includes a first polymer component and a second polymer component. In such a polymer material, an interface is formed between the first polymer component and the second polymer component. Examples of the first polymer component and the second polymer component include, but are not limited to, natural rubber, butadiene rubber, polyisoprene rubber, styrene-butadiene rubber, etc.

[0013] For the first polymer component and the second polymer component, for example, different polymer components are selected from the above polymer components. The first polymer component of this embodiment is butadiene rubber. The second polymer component is natural rubber. Note that the first polymer component and the second polymer component are not limited to such a mode.

[0014] [Simulation method of polymer material (First Embodiment)] Next, the simulation method of this embodiment will be described. FIG. 2 is a flowchart showing the processing procedure of the simulation method of the polymer material of this embodiment.

[0015] [Input the first polymer material model and the second polymer material model] In the simulation method of this embodiment, first, a first polymer material model 3 and a second polymer material model 4 are input into the computer 1 (step S1). FIG. 3 is a diagram partially showing the first polymer material model 3 and the second polymer material model 4. FIG. 4 is a diagram showing the second polymer material model 4.

[0016] As shown in FIG. 3, the first polymer material model 3 and the second polymer material model 4 are those obtained by modeling the first polymer component and the second polymer component respectively based on the classical molecular dynamics method. In this embodiment, based on the structures (molecular chains) of the first polymer component and the second polymer component, the first polymer material model 3 and the second polymer material model 4 in which particles (in this example, coarse-grained particles 3a, 4a) composed of a large number of atoms or aggregates thereof are arranged are set.

[0017] [First polymer material model] As shown in FIG. 3, the first polymer material model 3 of the present embodiment is defined as a coarsened molecular model in which a first polymer component (in this example, butadiene rubber) is represented using a plurality of coarsened particles 3a. The coarsened molecular model of the present embodiment is exemplified as a Kremer-Grest model, but is not particularly limited. The first polymer material model 3 of the present embodiment includes a plurality of coarsened particles 3a and a bond chain model 3b that connects adjacent coarsened particles 3a, 3a.

[0018] The coarsened particle 3a is obtained by substituting a monomer (not shown) of the molecular chain of the first polymer component (in this example, butadiene rubber) or a structural unit forming a part of the monomer. Thereby, a plurality (for example, 10 to 5000) of coarsened particles 3a are set in the first polymer material model 3. Such substitution with the coarsened particles 3a is appropriately performed, for example, based on a paper (by 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).

[0019] In the molecular dynamics calculation described later, the coarsened particle 3a is treated as a mass point of the equation of motion. Therefore, parameters such as mass, volume, particle diameter, or charge are defined for the coarsened particle 3a.

[0020] The bonded chain model 3b of the present embodiment is defined by a bonding potential P1 with a set maximum elongation between the coarse-grained particles 3a, 3a. The bonding potential P1 can be defined as appropriate. The bonding potential P1 of the present embodiment is defined as the sum of the LJ potential (Lennard-Jones potential) and the FENE potential. The LJ potential and the FENE potential are as shown in, for example, formulas (1) and (2) of Patent Document (Japanese Patent Application Laid-Open No. 2020-042434). In such a bonded chain model 3b, a restoring force is defined to return the distance between the coarse-grained particles 3a, 3a to a position where the LJ potential and the FENE potential balance each other.

[0021] The interaction parameters ε of the LJ potential and the FENE potential, the maximum elongation R 0 , and the unit length of the coarse-grained particle (a parameter corresponding to the diameter of the coarse-grained particle) σ can be set as appropriate. These constants can be set as appropriate, for example, based on the above-mentioned paper. Thereby, the first polymer material model 3 is defined.

[0022] [Second Polymer Material Model] As shown in FIGS. 3 and 4, the second polymer material model 4 of the present embodiment is defined as a coarse-grained molecular model (in this example, the Kremer-Grest model) that represents the second polymer component (natural rubber in this embodiment) using a plurality of coarse-grained particles 4a. The second polymer material model 4 of the present embodiment, similar to the first polymer material model 3, includes a plurality of coarse-grained particles 4a and a bonded chain model 4b that bonds adjacent coarse-grained particles 4a, 4a.

[0023] The coarse-grained particle 4a is a substitution of a monomer (not shown) of the molecular chain of the second polymer component (butadiene rubber in this example) or a structural unit forming a part of the monomer. Thereby, a plurality (for example, 10 to 5000) of coarse-grained particles 4a are set in the second polymer material model 4.

[0024] The coarsened particle 4a is treated as a mass point of the equation of motion in the molecular dynamics calculation described later. Therefore, parameters similar to those of the coarsened particle 3a of the first polymer material model 3 are defined for the coarsened particle 4a.

[0025] As shown in FIG. 3, the bond chain model 4b of the present embodiment is defined by a bond potential P2 with a set maximum elongation length between the coarsened particles 4a, 4a. The bond potential P2 can be defined as appropriate. The bond potential P2 of the present embodiment is defined as the sum of the LJ potential and the FENE potential, similar to the bond potential P1 of the first polymer material model 3.

[0026] The interaction parameters ε and the maximum elongation length R of the LJ potential and the FENE potential 0 , and the unit length of the coarsened particle (parameter corresponding to the diameter of the coarsened particle) σ can be set as appropriate, for example, based on the above-mentioned paper. Thereby, the second polymer material model 4 is defined.

[0027] [Mixed System Model Input Step] Next, in the simulation method of the present embodiment, a mixed system model in which the first polymer material model 3 and the second polymer material model 4 are arranged is input to the computer 1 (shown in FIG. 1) (mixed system model input step S2). FIG. 5 is a diagram showing the mixed system model 2.

[0028] In the mixed system model 2 of the present embodiment, the first polymer material model 3 and the second polymer material model 4 are arranged so that an interface 5 is formed between the first polymer material model 3 and the second polymer material model 4. FIG. 6 is a flowchart showing the processing procedure of the mixed system model input step S2.

[0029] In the mixed system model input step S2 of the present embodiment, first, a cell 6 which is a virtual space is input to the computer 1 (shown in FIG. 1) (step S21). FIG. 7 is a perspective view showing the cell 6.

[0030] The cell 6 of this embodiment corresponds to a part of a polymer material (in this example, rubber in which a first polymer component and a second polymer component are blended). The cell 6 of this embodiment has at least a pair of opposing surfaces 7, 7 (in this embodiment, three pairs of opposing surfaces 7, 7). The cell 6 of this embodiment is defined as a rectangular parallelepiped or a cube (in this embodiment, a rectangular parallelepiped).

[0031] Periodic boundary conditions are defined for each of the surfaces 7, 7 of the cell 6. Thereby, in the molecular dynamics calculation described later, for example, a part of the first polymer material model 3 and the second polymer material model 4 (shown in FIG. 5) that go out from one surface 7a can be calculated to enter from the other surface 7b. Note that the size of the cell 6 can be appropriately set according to, for example, the total number of the first polymer material models 3 and the second polymer material models 4 arranged inside the cell 6. The cell 6 is stored in the computer 1 (shown in FIG. 1).

[0032] [Arranging the First Polymer Material Model and the Second Polymer Material Model] Next, in the mixed system model input step S2 of this embodiment, the first polymer material model 3 and the second polymer material model 4 (shown in FIG. 3) are arranged inside the cell 6 shown in FIG. 7 (step S22). As shown in FIG. 5, in the step S22 of this embodiment, the first polymer material model 3 and the second polymer material model 4 are arranged so that an interface 5 is formed between the first polymer material model 3 and the second polymer material model 4.

[0033] In the step S22 of this embodiment, first, the first polymer material model 3 shown in FIG. 3 is arranged inside the cell 6 shown in FIG. 7. As shown in FIG. 5, in this embodiment, a plurality of first polymer material models 3 are randomly arranged so as to be unevenly distributed on one side in the first direction (in this example, the z-axis direction) selected from the x-axis direction, the y-axis direction, and the z-axis direction inside the cell 6.

[0034] Next, in step S22 of the present embodiment, the second polymer material model 4 (shown in FIGS. 3 and 4) is disposed inside the cell 6. As shown in FIG. 5, in the present embodiment, a plurality of second polymer material models 4 are randomly disposed inside the cell 6 so as to be unevenly distributed on the other side in the first direction (in this example, the z-axis direction). Thereby, in step S22, the first polymer material model 3 and the second polymer material model 4 are disposed such that an interface 5 is formed between the first polymer material model 3 and the second polymer material model 4.

[0035] The numbers of the first polymer material model 3 and the second polymer material model 4 are not particularly limited. For example, based on the volume fraction of the first polymer component and the volume fraction of the second polymer component included in the polymer material to be analyzed, the numbers (ratios inside the cell 6) of the first polymer material model 3 and the second polymer material model 4 may be set respectively.

[0036] [Define the LJ interaction potential (first polymer material model - second polymer material model)] Next, in the mixed system model input step S2 of the present embodiment, as shown in FIG. 3, an LJ interaction potential Q1 is defined between the coarse-grained particles 3a of the first polymer material model 3 and the coarse-grained particles 4a of the second polymer material model 4 (step S23). The LJ interaction potential Q1 is defined by the following formula (1).

[0037]

Equation

[0038] In the above formula (1), the distance r ij , the cutoff distance r c , and the parameter (corresponding to the diameter of the coarse-grained particle) σ are defined based on the coordinates of the centers of the coarse-grained particles 3a and 4a. Each constant can be appropriately set, for example, based on the paper (by S. L. Mayo, B. D. Olafson & W. A. Goddard III, "DREIDING: A Generic Force Field for Molecular Simulations", J. Phys. Chem. 1990, 94, 8897).

[0039] The LJ interaction potential Q1 of the present embodiment is such that when the distance r ij between the coarse-grained particle 3a of the first polymer material model 3 and the coarse-grained particle 4a of the second polymer material model 4 is less than the cutoff distance r c , a repulsive force acts. Therefore, in the present embodiment, for example, the interaction parameter ε is set to 1.0, the parameter (corresponding to the diameter of the coarse-grained particle) σ is set to 1.0, and the cutoff distance r c is set to 2 1 / 6 . The LJ interaction potential Q1 is stored in the computer 1.

[0040] [Define the LJ interaction potential (between adjacent first polymer material models)] Next, in the mixed system model input step S2 of the present embodiment, an LJ interaction potential Q2 is defined between the coarse-grained particles 3a and 3a of the adjacent first polymer material models 3 and 3 (step S24). The LJ interaction potential Q2 is defined by the above formula (1).

[0041] In the LJ interaction potential Q2 of the present embodiment, an attractive force and a repulsive force are set to act between the coarse-grained particles 3a, 3a of the adjacent first polymer material models 3, 3. Therefore, in the present embodiment, for example, 1.0 is set for the interaction parameter ε, 1.0 is set for the parameter σ (corresponding to the diameter of the coarse-grained particle), and the cut-off distance r c is set to 2.5. The LJ interaction potential Q2 is stored in the computer 1.

[0042] [Define the LJ interaction potential (between adjacent second polymer material models)] Next, in the mixed system model input step S2 of the present embodiment, an LJ interaction potential Q3 is defined between the coarse-grained particles 4a, 4a of the adjacent second polymer material models 4, 4 (step S25). The LJ interaction potential Q3 is defined by the above formula (1).

[0043] In the LJ interaction potential Q3 of the present embodiment, an attractive force and a repulsive force are set to act between the coarse-grained particles 4a, 4a of the adjacent second polymer material models 4, 4. Therefore, in the present embodiment, for example, 1.0 for the interaction parameter ε, 1.0 for the parameter σ (corresponding to the diameter of the coarse-grained particle), and the cut-off distance r c is set to 2.5. The LJ interaction potential Q3 is stored in the computer 1.

[0044] In the mixed system model input step S2 of the present embodiment, by performing the series of processes shown in FIG. 6, a mixed system model 2 (shown in FIG. 5) in which an interface 5 is formed between the first polymer material model 3 and the second polymer material model 4 is set. The mixed system model 2 is input into the computer 1 (shown in FIG. 1).

[0045] [Structure relaxation process] Next, in the simulation method of the present embodiment, the computer 1 (shown in FIG. 1) performs molecular dynamics calculations on the mixed system model 2 (shown in FIG. 5) to relax the structure of the mixed system model 2 (structural relaxation step S3). In the structural relaxation step S3 of the present embodiment, molecular dynamics calculations are performed on the first polymer material model 3 and the second polymer material model 4 (shown in FIG. 5) arranged in the cell 6. FIG. 8 is a flowchart showing the processing procedure of the structural relaxation step S3 of the present embodiment.

[0046] [First step] In the structural relaxation step S3 of the present embodiment, first, the first polymer material model 3 is constrained so that the interface 5 is maintained, and the mixed system model 2 is structurally relaxed (first step S31). Here, "the interface 5 is maintained" means that the second polymer material model 4 does not enter the region where the first polymer material model 3 is arranged, and the first polymer material model 3 does not enter the region where the second polymer material model 4 is arranged.

[0047] In the first step S31 of the present embodiment, first, the first polymer material model 3 is constrained. The constraint of the first polymer material model 3 is carried out as appropriate. In the present embodiment, inside the cell 6, the coordinates of the coarse-grained particles 3a of the first polymer material model 3 are fixed. Thereby, the first polymer material model 3 is constrained to be immobile in the molecular dynamics calculation. Note that the bond potential P1 and the LJ interaction potentials Q1 to Q3 (shown in FIG. 3) defined for the first polymer material model 3 are not invalidated.

[0048] Next, in the first step S31 of the present embodiment, molecular dynamics calculations are performed on the first polymer material model 3 and the second polymer material model 4. FIG. 9 is a diagram showing the mixed system model 2 in which the first polymer material model 3 is constrained and structurally relaxed.

[0049] In the molecular dynamics calculation of this embodiment, in cell 6, the pressure (e.g., 1 atm) and temperature (e.g., 290 K to 305 K) are kept constant (NPT constant). Also, in the molecular dynamics calculation, for example, for cell 6 for a predetermined time, assuming that the first polymer material model 3 and the second polymer material model 4 follow classical mechanics, Newton's equations of motion are applied. Then, the movement of the coarse-grained particles 3a and 4a at each moment is tracked for each unit time step of the molecular dynamics calculation. Such a calculation of structural relaxation can be processed using, for example, COGNAC included in the Soft Material Comprehensive Simulator (J-OCTA) manufactured by JSOL Corporation.

[0050] In the first step S31 of this embodiment, the first polymer material model 3 is constrained. Therefore, in the first step S31, even if a molecular dynamics calculation is performed on the first polymer material model 3, as shown in FIG. 9, the initial arrangement (the arrangement state in the mixed system model input step S2) of the first polymer material model 3 is maintained.

[0051] On the other hand, in the first step S31 of this embodiment, the second polymer material model 4 is not constrained. As a result, in the first step S31, the initial arrangement (the arrangement state in the mixed system model input step S2) of the second polymer material model 4 before the structural relaxation step S3 shown in FIG. 5 is relaxed as shown in FIG. 9.

[0052] Incidentally, for the second polymer material model 4, when the distance r ij between adjacent coarse-grained particles 4a and 4a is small, a large repulsive force acts between those coarse-grained particles 4a and 4a, and it may move significantly toward the first polymer material model 3 side. Such a second polymer material model 4 tries to enter (intrude) into the region where the first polymer material model 3 is arranged while pushing back the first polymer material model 3. If the entry of this second polymer material model 4 is allowed, the interface 5 between the first polymer material model 3 and the second polymer material model 4 will not be maintained.

[0053] In the first step S31 of this embodiment, due to the restraint of the first polymer material model 3, the first polymer material model 3 can be prevented from being pushed back by the second polymer material model 4 that moves largely toward the first polymer material model 3 side, and the entry of the second polymer material model 4 can be prevented. As a result, in the simulation method of this embodiment, since the interface 5 is maintained between the first polymer material model 3 and the second polymer material model 4, it becomes possible to create the mixed system model 2 in which the interface 5 is formed.

[0054] Furthermore, in the simulation method of this embodiment, an LJ interaction potential Q1 (shown in FIG. 3) is defined between the coarse-grained particles 3a of the first polymer material model 3 and the coarse-grained particles 4a of the second polymer material model 4. Thereby, in the first step S31, the second polymer material model 4 that has moved (approached) toward the first polymer material model 3 side can be effectively repelled by the repulsive force of the LJ interaction potential Q1. Therefore, in the first step S31, since the entry of the second polymer material model into the region where the first polymer material model 3 is arranged can be prevented, the interface 5 between the first polymer material model 3 and the second polymer material model 4 can be more reliably maintained.

[0055] In the first step S31 of this embodiment, molecular dynamics calculation is performed on the mixed system model 2 until the initial arrangement of the second polymer material model 4 is sufficiently relaxed. Thereby, in the first step S31, while maintaining the interface 5 between the first polymer material model 3 and the second polymer material model 4, the structure of the second polymer material model 4 can be relaxed (a stable arrangement is sought).

[0056] [Release the restraint of the first polymer material model] Next, in the structure relaxation step S3 of this embodiment, after the first step S31, the restraint of the first polymer material model 3 is released (step S32). In the step S32 of this embodiment, the fixing of the coordinates of the coarse-grained particles 3a of the first polymer material model 3 is released. As a result, the first polymer material model 3 can freely move inside the cell 6 in the molecular dynamics calculation.

[0057] [Second Step] Next, in the structural relaxation step S3 of the present embodiment, the second polymer material model 4 is constrained so that the interface 5 is maintained, and the mixed system model 2 is structurally relaxed (second step S33).

[0058] In the second step S33 of the present embodiment, first, the second polymer material model 4 is constrained. The constraint of the second polymer material model 4 is appropriately implemented. In the present embodiment, inside the cell 6, the coordinates of the macroscopic particles 4a of the second polymer material model 4 are fixed. Thereby, the second polymer material model 4 is constrained to be immovable in the molecular dynamics calculation. Note that the bond potential P2 and the LJ interaction potentials Q1 to Q3 (shown in FIG. 3) defined for the second polymer material model 4 are not invalidated.

[0059] Next, in the second step S33 of the present embodiment, molecular dynamics calculation is performed on the first polymer material model 3 and the second polymer material model 4. The molecular dynamics calculation is performed in the same procedure as in the first step S31.

[0060] In the second step S33 of the present embodiment, the second polymer material model 4 is constrained. Therefore, in the second step S33, even if molecular dynamics calculation is performed on the second polymer material model 4, the arrangement state of the second polymer material model 4 shown in FIG. 9 (the state structurally relaxed in the first step S31) is maintained.

[0061] On the other hand, in the second step S33 of the present embodiment, the first polymer material model 3 is not constrained. Thereby, in the second step S33, the initial arrangement of the first polymer material model 3 before the structural relaxation step S3 (the arrangement state in the mixed system model input step S2) is relaxed.

[0062] In the second step S33 of the present embodiment, due to the restraint of the second polymer material model 4, the entry of the first polymer material model 3 that moves largely toward the second polymer material model 4 can be prevented. Thereby, in the simulation method of the present embodiment, since the interface 5 is maintained between the first polymer material model 3 and the second polymer material model 4, it becomes possible to create the mixed system model 2 in which the interface 5 is formed.

[0063] Furthermore, in the second step S33 of the present embodiment, the first polymer material model 3 that has moved (approached) toward the second polymer material model 4 can be effectively repelled by the repulsive force of the LJ interaction potential Q1 (shown in FIG. 3). Therefore, in the second step S33, the interface 5 between the first polymer material model 3 and the second polymer material model 4 can be more reliably maintained.

[0064] In the second step S33 of the present embodiment, molecular dynamics calculation is performed on the mixed system model 2 until the initial arrangement of the first polymer material model 3 is sufficiently relaxed. Thereby, in the second step S33, while maintaining the interface 5 between the first polymer material model 3 and the second polymer material model 4, the structure of the first polymer material model 3 can be relaxed (to obtain a stable arrangement).

[0065] [Third step] Next, in the structure relaxation step S3 of the present embodiment, after the second step S33, the restraint of the second polymer material model 4 is released, and the mixed system model 2 is structure-relaxed (third step S34). FIG. 10 is a diagram showing the mixed system model 2 in which the restraint of the second polymer material model 4 is released and structure-relaxed.

[0066] In the third step S34 of the present embodiment, first, the fixing of the coordinates of the coarse-grained particles 4a of the second polymer material model 4 is released. Thereby, the second polymer material model 4 can freely move inside the cell 6 in the molecular dynamics calculation together with the first polymer material model 3.

[0067] Next, in the third step S34 of the present embodiment, molecular dynamics calculations are performed on the first polymer material model 3 and the second polymer material model 4. The molecular dynamics calculations are performed in the same procedure as in the first step S31.

[0068] In the first polymer material model 3, the initial arrangement is relaxed in the second step S33. Therefore, in the third step S34, since a large repulsive force acting between the coarse-grained particles 3a, 3a of the first polymer material model 3 is suppressed, the first polymer material model 3 is prevented from moving largely and entering the second polymer material model 4.

[0069] On the other hand, in the first step S31, the initial arrangement of the second polymer material model 4 is relaxed. Therefore, in the third step S34, since a large repulsive force acting between the coarse-grained particles 4a, 4a of the second polymer material model 4 is suppressed, the second polymer material model 4 is prevented from moving largely and entering the first polymer material model 3.

[0070] Thus, in the third step S34 of the present embodiment, large movements of the first polymer material model 3 and the second polymer material model 4 are suppressed. Therefore, in the third step S34 of the present embodiment, even if the constraints on the first polymer material model 3 and the second polymer material model 4 are released, the first polymer material model 3 and the second polymer material model 4 can be relaxed into a more natural structure while maintaining the interface 5. Thereby, in the simulation method of the present embodiment, a mixed system model 2 of two polymer material models (in this example, the first polymer material model 3 and the second polymer material model 4) having the interface 5 formed therebetween can be created. The mixed system model 2 is stored in the computer 1.

[0071] [Simulation Step] As shown in FIG. 2, in the simulation method of the present embodiment, the computer 1 (shown in FIG. 1) calculates physical quantities, interactions, etc. (hereinafter sometimes simply referred to as "physical quantities, etc.") at the interface 5 (shown in FIG. 10) of the hybrid system model 2 (simulation step S4). The physical quantities, etc. at the interface 5 are calculated as appropriate. In the simulation step S4 of the present embodiment, for example, the deformation of the hybrid system model 2 is calculated, and the physical quantities, etc. at the deformed interface 5 are calculated. The deformation of the hybrid system model 2 can be appropriately carried out, such as tensile deformation or compressive deformation. The deformation calculation of the hybrid system model 2 can be carried out, for example, based on the conventional method described in the patent document (Japanese Patent Laid-Open No. 2016-81297).

[0072] In the simulation method of the present embodiment, a hybrid system model 2 of two polymer material models (in this example, the first polymer material model 3 and the second polymer material model 4) with the interface 5 formed can be created. Thereby, in the simulation method of the present embodiment, it is possible to calculate physical quantities, etc. at the interface 5 that are difficult to measure in an experiment using an actual polymer material. The calculation results are stored in the computer 1 (shown in FIG. 1).

[0073] [Evaluate physical quantities, etc.] Next, in the simulation method of the present embodiment, it is evaluated whether the physical quantities, etc. at the interface 5 are good or not (step S5). In step S5 of the present embodiment, based on the physical quantities, etc. calculated in the simulation step S4, the computer 1 (shown in FIG. 1) may evaluate, or an operator or the like may evaluate.

[0074] In step S5 of the present embodiment, it is determined whether the physical quantities, etc. at the interface 5 are equal to or greater than a predetermined threshold value. The threshold value is appropriately set according to the performance required for the polymer material (for example, fracture resistance performance, etc.).

[0075] In step S5, when the physical quantity or the like at interface 5 is equal to or greater than the threshold value ( "Yes" in step S5), a product made of a polymer material (for example, a tire or the like) is manufactured (step S6). On the other hand, in step S5, when the physical quantity or the like at interface 5 is less than the threshold value ( "No" in step S5), the blending ratio of the first polymer component and the second polymer component is changed (step S7), and steps S1 to S5 are performed again.

[0076] As described above, in the simulation method of the present embodiment, the blending ratio of the first polymer component and the second polymer component is changed until the physical quantity or the like at interface 5 (shown in FIG. 10) of the mixed system model 2 becomes equal to or greater than the threshold value. Thereby, in the simulation method of the present embodiment, for example, it becomes possible to reliably manufacture a product such as a tire using a polymer material having desired performance.

[0077] [Simulation Method of Polymer Material (Second Embodiment)] In the previous embodiments, the LJ interaction potential Q1 (shown in FIG. 3) defined between the coarse-grained particles 3a of the first polymer material model 3 and the coarse-grained particles 4a of the second polymer material model 4 was defined as it was even after the structural relaxation step S3. However, the present invention is not limited to such a mode. For example, instead of the LJ interaction potential Q1, an interaction potential based on the dissipative particle dynamics method may be defined. FIG. 11 is a flowchart showing the processing procedure of the simulation method of the polymer material according to another embodiment of the present disclosure. The same components as those in the previous embodiments may be denoted by the same reference numerals, and the description thereof may be omitted.

[0078] [Define Interaction Potential Based on Dissipative Particle Dynamics Method] In the simulation method of this embodiment, after the structural relaxation step S3, an interaction potential based on the dissipative particle dynamics method (hereinafter sometimes simply referred to as "DPD potential") is defined instead of the LJ interaction potential Q1 shown in FIG. 3 (step S8). The DPD potential (soft-core potential) is defined by the following formula (2).

[0079] [Number] Here, U nonbond (r ij ): DPD potential r ij : Distance between coarse-grained particles a ij : Constant corresponding to the strength of the repulsive force defined between coarse-grained particles r c : Cutoff distance

[0080] The constant in the above formula (2) can be appropriately set according to, for example, the structure of the polymer component. In this embodiment, 25 is set for the constant a ij and 1.0 is set for the cutoff distance r c , but it is not particularly limited and can be appropriately set according to, for example, the structure of the polymer component, etc.

[0081] Unlike the LJ interaction potential Q1 (shown in FIG. 3), the DPD potential of this embodiment can have a finite value without divergence even when the distance r ij between the coarse-grained particles 3a and 4a becomes zero. Therefore, in the simulation method of this embodiment, in the subsequent simulation step S4, calculation crashes (divergence of potential energy) can be reliably prevented, and stable calculations can be performed.

[0082] Also, in the simulation method of this embodiment, similar to the previous embodiments, the LJ interaction potential Q1 (shown in FIG. 3) is defined prior to the structure relaxation step S3. Therefore, in the simulation method of this embodiment, a mixed system model 2 in which an interface 5 (shown in FIG. 10) is formed between the first polymer material model 3 and the second polymer material model 4 can be reliably created.

[0083] In step S8 of this embodiment, instead of the LJ interaction potential Q2 (shown in FIG. 3) defined between the coarse-grained particles 3a, 3a of the adjacent first polymer material models 3, 3, a DPD potential may be defined. Further, in step S8, instead of the LJ interaction potential Q3 (shown in FIG. 4) defined between the coarse-grained particles 4a, 4a of the adjacent second polymer material models 4, 4, a DPD potential may be defined. Thereby, in the simulation method of this embodiment, more stable calculations can be performed in the subsequent simulation step S4.

[0084] As described above, the particularly preferred embodiments of the present disclosure have been described in detail. However, the present disclosure is not limited to the illustrated embodiments and can be implemented in various forms.

Examples

[0085] A mixed system model of two polymer material models was input into the computer (Examples 1, 2, and Comparative Example). In Examples 1, 2, and the Comparative Example, a mixed system model in which the first polymer material model and the second polymer material model were arranged so that an interface was formed was input based on the processing procedure shown in FIG. 6 (shown in FIG. 5).

[0086] In Examples 1 and 2, based on the processing procedure shown in FIG. 8, a first step of relaxing the structure of the mixed system model by restraining the first polymer material model so that the interface is maintained was performed. Next, in Examples 1 and 2, a step of releasing the restraint on the first polymer material model and a second step of relaxing the structure of the mixed system model by restraining the second polymer material model so that the interface is maintained were performed. Then, in Examples 1 and 2, a third step of releasing the restraint on the second polymer material model and relaxing the structure of the mixed system model was performed.

[0087] In Example 2, after the structure relaxation step, an interaction potential (DPD potential) based on the dissipative particle dynamics method was defined instead of the LJ interaction potential. On the other hand, in Example 1, the LJ interaction potential was defined as it was.

[0088] In the comparative example, different from Examples 1 and 2, a step of structurally relaxing the mixed system model was performed without restraining the first polymer material model and the second polymer material model. The common specifications are as follows. Polymer components: First polymer component: Butadiene rubber Second polymer component: Natural rubber Mixed system model: First polymer material model: Total number: 20 Number of coarse-grained particles: 250 / 1 Second polymer material model: Total number: 160 Number of coarse-grained particles: 500 / 1 Binding potentials P1, P2 (LJ potential · FENE potential): Cutoff distance r c : 1.5 Maximum elongation R 0 : 2 1 / 6 Spring constant k: 30 Interaction parameter ε: 1.0 Parameter σ corresponding to the diameter of the coarse-grained particle: 1.0 LJ interaction potential Q1: Cutoff distance r c : 2 1 / 6 Interaction parameter ε: 1.0 Parameter σ corresponding to the diameter of the coarse-grained particle: 1.0 LJ interaction potentials Q2 and Q3: Cutoff distance r c : 2.5 Interaction parameter ε: 1.0 Parameter σ corresponding to the diameter of the coarse-grained particle: 1.0 Molecular dynamics calculation (Examples 1 and 2): Unit time step: 0.006 First step: 10000 steps Second step: 10000 steps Third step: 20000 steps Molecular dynamics calculation (comparative example): Unit time step: 0.006 Structural relaxation calculation: 20,000 steps DPD potential (Example 2): Constant a corresponding to the strength of the repulsive force defined between coarse-grained particles ij : 25 Cutoff distance r c : 1.0

[0089] FIG. 10 is a diagram showing the mixed system models of Example 1 and Example 2. FIG. 12 is a diagram showing the mixed system model of the comparative example. In Example 1 and Example 2, the mixed system model could be structurally relaxed while maintaining the interface between the first polymer material model and the second polymer material model. On the other hand, in the comparative example, the first polymer material model and the second polymer material model were mixed and the interface could not be maintained. Therefore, Example 1 and Example 2 were able to create a mixed system model of two polymer material models with an interface formed therebetween.

[0090] Also, in Example 2, after the structural relaxation step, instead of the LJ interaction potential, a DPD potential was defined. As a result, Example 2 was able to prevent calculation crashes in the subsequent simulation step compared to Example 1 in which the LJ interaction potential was defined.

[0091] [Appendix] The present disclosure includes the following aspects.

[0092] [Disclosure 1] A method for simulating a polymer material, comprising: inputting, into a computer, a first polymer material model and a second polymer material model obtained by modeling a first polymer component and a second polymer component respectively based on the classical molecular dynamics method; inputting, into the computer, a mixed system model in which the first polymer material model and the second polymer material model are arranged so that an interface is formed between the first polymer material model and the second polymer material model; The computer performs molecular dynamics calculations on the hybrid model to relax the structure of the hybrid model, The step of relaxing the structure includes a first step of relaxing the structure of the hybrid model by restraining the first polymer material model so that the interface is maintained. A method for simulating polymer materials. [Disclosure 2] After the first step, the step of relaxing the structure includes a step of releasing the restraint on the first polymer material model, The method for simulating a polymer material according to Disclosure 1, further including a second step of relaxing the structure of the hybrid model by restraining the second polymer material model so that the interface is maintained. [Disclosure 3] After the second step, the step of relaxing the structure includes a third step of releasing the restraint on the second polymer material model and relaxing the structure of the hybrid model, and the method for simulating a polymer material according to Disclosure 2. [Disclosure 4] The step of inputting the first polymer material model and the second polymer material model includes a step of defining the first polymer component and the second polymer component as a coarse-grained molecular model represented by a plurality of coarse-grained particles, and the method for simulating a polymer material according to any one of Disclosures 1 to 3. [Disclosure 5] Before the step of relaxing the structure, the method for simulating a polymer material according to Disclosure 4 further includes a step of defining an LJ interaction potential between the coarse-grained particles of the first polymer material model and the coarse-grained particles of the second polymer material model. [Disclosure 6] After the step of relaxing the structure, the method for simulating a polymer material according to Disclosure 5 further includes a step of defining an interaction potential based on the dissipative particle dynamics method instead of the LJ interaction potential.

Explanation of symbols

[0093] S1 Step of inputting the first polymer material model and the second polymer material model Step of inputting S2 mixture model Step of structurally relaxing S3 mixture model

Claims

1. A method for simulating a polymer material, comprising: inputting into a computer a first polymer material model and a second polymer material model, which are respectively modeled for a first polymer component and a second polymer component based on a classical molecular dynamics method; inputting into the computer a mixed system model in which the first polymer material model and the second polymer material model are arranged so that an interface is formed between the first polymer material model and the second polymer material model; the computer performing a molecular dynamics calculation on the mixed system model to structurally relax the mixed system model, wherein the step of structurally relaxing includes a first step of structurally relaxing the mixed system model by restraining the first polymer material model so that the interface is maintained; A method for simulating a polymer material.

2. After the first step, the step of structurally relaxing includes releasing the restraint on the first polymer material model; The method for simulating a polymer material according to claim 1, wherein after the first step, the step of structurally relaxing includes a second step of structurally relaxing the mixed system model by restraining the second polymer material model so that the interface is maintained.

3. After the second step, the step of structurally relaxing includes a third step of structurally relaxing the mixed system model by releasing the restraint on the second polymer material model. The method for simulating a polymer material according to claim 2.

4. The step of inputting the first polymer material model and the second polymer material model includes defining the first polymer component and the second polymer component as a coarse-grained molecular model represented by a plurality of coarse-grained particles. The method for simulating a polymer material according to any one of claims 1 to 3.

5. Before the step of structurally relaxing, the method includes defining a Lennard-Jones (LJ) interaction potential between the coarse-grained particles of the first polymer material model and the coarse-grained particles of the second polymer material model. The method for simulating a polymer material according to claim 4.

6. After the step of structurally relaxing, the method further includes defining an interaction potential based on a dissipative particle dynamics method instead of the LJ interaction potential. The method for simulating a polymer material according to claim 5.

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