JP7690845B2 - Polymer material simulation method - Google Patents

Description

This disclosure relates to a method for simulating polymeric materials.

The following Patent Document 1 describes a method for simulating polymeric materials. In this method, a molecular structure model is set in a cell having an arbitrary space, in which a three-dimensional molecular chain model consisting of a finite number of particles representing atoms or their aggregates and bonding chains that connect these particles and define the relative positions of each particle is arranged. Then, a simulation of structural relaxation is performed to stabilize the molecular structure model based on molecular dynamics calculations.

JP 2009-271719 A

Incidentally, polymeric materials may contain multiple types of polymeric components. It is known that in such polymeric materials, interfaces are formed between the polymeric components. Therefore, in order to perform a simulation to investigate the interactions at the interface, it is important to create a mixed system model of two polymeric material models so that the interface is formed.

This disclosure was devised in consideration of the above-mentioned circumstances, and its main objective is to provide a method capable of creating a mixed system model of two polymer material models in which an interface is formed.

The present disclosure is a method for simulating a polymeric material, which includes the steps of inputting a first polymeric material model and a second polymeric material model, which are modeled based on a classical molecular dynamics method, into a computer, inputting a mixed system model in which the first polymeric material model and the second polymeric material model are arranged so that an interface is formed between the first polymeric material model and the second polymeric material model, and performing a molecular dynamics calculation on the mixed system model by the computer to structurally relax the mixed system model, and the structural relaxation step includes a first step of structurally relaxing the mixed system model by constraining the first polymeric material model so that the interface is maintained.

By adopting the above steps, the polymer material simulation method disclosed herein makes it possible to create a mixed system model of two polymer material models in which an interface is formed.

FIG. 1 is a perspective view of a computer for executing a simulation method for a polymer material. 4 is a flowchart showing a processing procedure of a simulation method for a polymer material according to the present embodiment. FIG. 2 is a diagram partially illustrating a first polymer material model and a second polymer material model. FIG. 13 is a diagram showing a second polymer material model. FIG. 1 is a diagram showing a mixed system model. 13 is a flowchart showing a processing procedure of a mixed system model input step. FIG. 4 is a flowchart showing a processing procedure of a structural relaxation step according to the present embodiment. FIG. 13 is a diagram showing a mixed system model in which a first polymer material model is restrained and structurally relaxed. FIG. 13 is a diagram showing a mixed system model in which the constraint of the second polymer material model is released and the structure is relaxed. 13 is a flowchart showing a processing procedure of a simulation method for a polymer material according to another embodiment of the present disclosure. FIG. 13 is a diagram showing a mixed system model of a comparative example.

Below, one 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 dimensional ratios of the actual structure in order to aid in understanding the contents of the disclosure. Furthermore, the same reference numerals are used for identical or common elements throughout each embodiment, and duplicate explanations are omitted. Furthermore, the specific configurations shown in the embodiments and drawings are intended to aid in understanding the contents of this disclosure, and the present disclosure is not limited to the specific configurations shown in the drawings.

In the polymer material simulation method of this embodiment (hereinafter, sometimes simply referred to as the "simulation method"), a mixed system model of two polymer material models in which an interface is formed is created. A computer 1 is used in the simulation method of this embodiment.

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

[Polymer material]
The polymer material of the present 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, and styrene-butadiene rubber.

The first polymer component and the second polymer component are, for example, different polymer components selected from the above polymer components. In this embodiment, the first polymer component 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 an embodiment.

[Simulation method for polymeric material (first embodiment)]
Next, the simulation method of this embodiment will be described with reference to the flowchart of FIG.

[Enter the first polymer material model and the second polymer material model]
In the simulation method of this embodiment, first, the first polymer material model 3 and the second polymer material model 4 are input to 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.

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

[First polymer material model]
As shown in Fig. 3, the first polymer material model 3 of this embodiment is defined as a coarse-grained molecular model in which the first polymer component (butadiene rubber in this example) is expressed using a plurality of coarse-grained particles 3a. The coarse-grained molecular model of this embodiment is exemplified by the Kremer-Grest model, but is not particularly limited thereto. The first polymer material model 3 of this embodiment is configured to include a plurality of coarse-grained particles 3a and a bond chain model 3b that bonds adjacent coarse-grained particles 3a, 3a.

The coarse-grained particles 3a are formed by replacing monomers (not shown) or structural units that form part of monomers in the molecular chain of the first polymer component (butadiene rubber in this example). As a result, a plurality of coarse-grained particles 3a (for example, 10 to 5,000) are set in the first polymer material model 3. The replacement with such coarse-grained particles 3a is appropriately performed based on, for example, the paper (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).

The coarse-grained particles 3a are treated as mass points in the equation of motion in the molecular dynamics calculations described below. For this reason, parameters such as mass, volume, particle diameter, or charge are defined for the coarse-grained particles 3a.

The bond chain model 3b of this embodiment is defined by a bond potential P1 with an extended length set between the coarse-grained particles 3a, 3a. The bond potential P1 can be defined as appropriate. The bond potential P1 of this 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 the patent document (JP Patent Publication No. 2020-042434). In such a bond chain model 3b, a restoring force is defined that attempts to return the distance between the coarse-grained particles 3a, 3a to a position where the LJ potential and the FENE potential are balanced with each other.

The interaction parameter ε between the LJ potential and the FENE potential, the stretched length R ₀ , and the unit length of the coarse-grained particle (a parameter equivalent to the diameter of the coarse-grained particle) σ can be set appropriately. These constants can be set appropriately, for example, based on the above paper. In this way, the first polymer material model 3 is defined.

[Second polymer material model]
3 and 4, the second polymer material model 4 of this embodiment is defined as a coarse-grained molecular model (in this example, the Kremer-Grest model) in which the second polymer component (in this embodiment, natural rubber) is expressed using a plurality of coarse-grained particles 4a. Like the first polymer material model 3, the second polymer material model 4 of this embodiment is configured to include a plurality of coarse-grained particles 4a and a bond chain model 4b that bonds adjacent coarse-grained particles 4a, 4a.

The coarse-grained particles 4a are formed by replacing monomers (not shown) or structural units that form part of monomers in the molecular chain of the second polymer component (butadiene rubber in this example). As a result, multiple (e.g., 10 to 5,000) coarse-grained particles 4a are set in the second polymer material model 4.

The coarse-grained particles 4a are treated as mass points in the equation of motion in the molecular dynamics calculations described below. For this reason, the same parameters as those of the coarse-grained particles 3a of the first polymer material model 3 are defined for the coarse-grained particles 4a.

As shown in FIG. 3, the bond chain model 4b of this embodiment is defined by a bond potential P2 with an extension length set between the coarse-grained particles 4a, 4a. The bond potential P2 can be defined as appropriate. The bond potential P2 of this 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.

The interaction parameter ε between the LJ potential and the FENE potential, the stretched length R ₀ , and the unit length of the coarse-grained particle (a parameter equivalent to the diameter of the coarse-grained particle) σ can be appropriately set based on, for example, the above paper. In this way, the second polymer material model 4 is defined.

[Mixed system model input process]
Next, in the simulation method of this 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.

In the mixed system model 2 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. FIG. 6 is a flowchart showing the processing procedure of the mixed system model input process S2.

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

The cell 6 in this embodiment corresponds to a part of the polymer material (in this example, rubber containing a first polymer component and a second polymer component). The cell 6 in this embodiment has at least a pair of faces 7, 7 facing each other (in this embodiment, three pairs of faces 7, 7 facing each other). The cell 6 in this embodiment is defined as a rectangular parallelepiped or cube (in this embodiment, a rectangular parallelepiped).

Periodic boundary conditions are defined on each face 7, 7 of the cell 6. As a result, in the molecular dynamics calculation described below, for example, it is possible to calculate that a part of the first polymer material model 3 and the second polymer material model 4 (shown in FIG. 5) that has left the face 7a on one side enters the face 7b on the other side. The size of the cell 6 can be set appropriately depending on, 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).

[Placing 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 placed inside the cell 6 shown in Fig. 7 (step S22). As shown in Fig. 5, in step S22 of this embodiment, the first polymer material model 3 and the second polymer material model 4 are placed so that an interface 5 is formed between the first polymer material model 3 and the second polymer material model 4.

In step S22 of this embodiment, first, the first polymer material model 3 shown in FIG. 3 is placed inside the cell 6 shown in FIG. 7. As shown in FIG. 5, in this embodiment, multiple first polymer material models 3 are randomly placed inside the cell 6 so as to be biased toward one side of a first direction selected from the x-axis direction, the y-axis direction, and the z-axis direction (in this example, the z-axis direction).

Next, in step S22 of this embodiment, a second polymer material model 4 (shown in Figures 3 and 4) is placed inside the cell 6. As shown in Figure 5, in this embodiment, a plurality of second polymer material models 4 are randomly placed inside the cell 6 so as to be biased toward the other side of the first direction (in this example, the z-axis direction). As a result, in step S22, the first polymer material model 3 and the second polymer material model 4 are placed so that an interface 5 is formed between the first polymer material model 3 and the second polymer material model 4.

The number of the first polymer material model 3 and the second polymer material model 4 is not particularly limited. For example, the number of the first polymer material model 3 and the second polymer material model 4 (proportion within the cell 6) may be set based on the volume fraction of the first polymer component and the volume fraction of the second polymer component contained in the polymer material to be analyzed.

[Define LJ interaction potential (first polymer material model - second polymer material model)]
Next, in the mixed system model input step S2 of this embodiment, an LJ interaction potential Q1 is defined 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 (step S23), as shown in Fig. 3. The LJ interaction potential Q1 is defined by the following formula (1).

ここで、
Ｕ_nonbond（ｒ_ij）：ＬＪ相互作用ポテンシャル
ｒ_ij：粗視化粒子間の距離
ε：相互作用パラメータ
σ：粗視化粒子の直径に相当
ｒ_c：カットオフ距離
Ｕcutoff：ｒ_ij＝ｒ_cの場合に、Ｕ_nonbond（ｒ_ij）がゼロとなるようにポテンシャルをシフトさせる値

Where:
U _nonbond (r _ij ): LJ interaction potential r _ij : distance between coarse-grained particles ε: interaction parameter σ: equivalent to the diameter of the coarse-grained particle r _c : cutoff distance Ucutoff: value for shifting the potential so that U _nonbond (r _ij ) becomes zero when r _ij =r _c

In the above formula (1), the distance r _ij , the cutoff distance r _c , and the parameter σ (corresponding to the diameter of the coarse-grained particle) are defined based on the coordinates of the centers of the coarse-grained particles 3 a and 4 a. Each constant can be appropriately set based on, for example, a paper (SL Mayo, BD Olafson & WA Goddard III, “DREIDING: A Generic Force Field for Molecular Simulations”, J. Phys. Chem. 1990, 94, 8897).

The LJ interaction potential Q1 in this embodiment is set so that a repulsive force acts 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 becomes less than the cutoff distance r _c . Therefore, in this 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.

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

The LJ interaction potential Q2 in this embodiment is set so that an attractive force and a repulsive force act between the coarse-grained particles 3a, 3a of the adjacent first polymer material models 3, 3. For this reason, in this 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 _rc is set to 2.5. The LJ interaction potential Q2 is stored in the computer 1.

[Define LJ interaction potential (between adjacent second polymer material models)]
Next, in the mixed system model input step S2 of this 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).

The LJ interaction potential Q3 in this embodiment is set so that an attractive force and a repulsive force act between the coarse-grained particles 4a, 4a of the adjacent second polymer material models 4, 4. Therefore, in this 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 _rc is set to 2.5. The LJ interaction potential Q3 is stored in the computer 1.

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

[Structural relaxation process]
Next, in the simulation method of this embodiment, the computer 1 (shown in FIG. 1) performs a molecular dynamics calculation on the mixed model 2 (shown in FIG. 5) to relax the structure of the mixed model 2 (structural relaxation step S3). In the structural relaxation step S3 of this embodiment, a molecular dynamics calculation is 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 this embodiment.

[First step]
In the structural relaxation step S3 of this embodiment, first, the first polymer material model 3 is restrained so as to maintain the interface 5, and the mixed system model 2 is structurally relaxed (first step S31). Here, "the interface 5 is maintained" means that a state is maintained in which the second polymer material model 4 does not enter the region in which the first polymer material model 3 is disposed, and the first polymer material model 3 does not enter the region in which the second polymer material model 4 is disposed.

In the first step S31 of this embodiment, first, the first polymer material model 3 is constrained. The first polymer material model 3 is constrained as appropriate. In this embodiment, the coordinates of the coarse-grained particles 3a of the first polymer material model 3 are fixed inside the cell 6. This causes the first polymer material model 3 to be constrained so as not to move in the molecular dynamics calculation. Note that the bond potential P1 and the LJ interaction potentials Q1 to Q3 (shown in FIG. 3) defined in the first polymer material model 3 are not invalidated.

Next, in the first step S31 of this embodiment, molecular dynamics calculations are performed on the first polymer material model 3 and the second polymer material model 4. Figure 9 shows the mixed system model 2 in which the first polymer material model 3 is restrained and structurally relaxed.

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

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

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 position of the second polymer material model 4 before the structural relaxation step S3 shown in FIG. 5 (position state in the mixed system model input step S2) is relaxed as shown in FIG. 9.

Incidentally, when the distance r _ij between adjacent coarse-grained particles 4a, 4a is small, a large repulsive force acts between the coarse-grained particles 4a, 4a of the second polymer material model 4, and the second polymer material model 4 may move significantly toward the first polymer material model 3. Such a second polymer material model 4 will try to enter (cut in) into the area in which the first polymer material model 3 is arranged, while pushing aside the first polymer material model 3. If the entry of this second polymer material model 4 is permitted, the interface 5 between the first polymer material model 3 and the second polymer material model 4 will no longer be maintained.

In the first step S31 of this embodiment, the first polymer material model 3 is restrained by the second polymer material model 4, which moves significantly toward the first polymer material model 3, and the first polymer material model 3 is not pushed aside by the second polymer material model 4, and the second polymer material model 4 is prevented from entering. As a result, in the simulation method of this embodiment, the interface 5 is maintained between the first polymer material model 3 and the second polymer material model 4, making it possible to create a mixed system model 2 in which the interface 5 is formed.

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. As a result, in the first step S31, the second polymer material model 4 that has moved (approached) toward the first polymer material model 3 can be effectively repelled by the repulsive force of the LJ interaction potential Q1. Therefore, in the first step S31, the second polymer material model can be prevented from entering the area in which the first polymer material model 3 is arranged, so that the interface 5 between the first polymer material model 3 and the second polymer material model 4 can be more reliably maintained.

In the first step S31 of this embodiment, a 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. As a result, in the first step S31, the structure of the second polymer material model 4 can be relaxed (a stable arrangement can be obtained) while maintaining the interface 5 between the first polymer material model 3 and the second polymer material model 4.

[Release constraints on the first polymer material model]
Next, in the structural relaxation step S3 of this embodiment, after the first step S31, the constraint of the first polymer material model 3 is released (step S32). In step S32 of this embodiment, the fixation of the coordinates of the coarse-grained particles 3a of the first polymer material model 3 is released. This allows the first polymer material model 3 to move freely inside the cell 6 in the molecular dynamics calculation.

[Second step]
Next, in the structural relaxation step S3 of this embodiment, the second polymer material model 4 is restrained so as to maintain the interface 5, and the mixed system model 2 is structurally relaxed (second step S33).

In the second step S33 of this embodiment, first, the second polymer material model 4 is constrained. The second polymer material model 4 is constrained as appropriate. In this embodiment, the coordinates of the coarse-grained particles 4a of the second polymer material model 4 are fixed inside the cell 6. This causes the second polymer material model 4 to be constrained so as not to move in the molecular dynamics calculation. Note that the bond potential P2 and the LJ interaction potentials Q1 to Q3 (shown in FIG. 3) defined in the second polymer material model 4 are not invalidated.

Next, in the second step S33 of this embodiment, a 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 manner as in the first step S31.

In the second step S33 of this embodiment, the second polymer material model 4 is constrained. Therefore, even if a molecular dynamics calculation is performed on the second polymer material model 4 in the second step S33, the arrangement state of the second polymer material model 4 shown in FIG. 9 (the state in which the structure is relaxed in the first step S31) is maintained.

On the other hand, in the second step S33 of this embodiment, the first polymer material model 3 is not constrained. As a result, in the second step S33, the initial position of the first polymer material model 3 before the structural relaxation step S3 (the positioning state in the mixed system model input step S2) is relaxed.

In the second step S33 of this embodiment, the first polymer material model 3, which moves significantly toward the second polymer material model 4, can be prevented from entering by restraining the second polymer material model 4. As a result, in the simulation method of this embodiment, the interface 5 is maintained between the first polymer material model 3 and the second polymer material model 4, making it possible to create a mixed system model 2 in which the interface 5 is formed.

Furthermore, in the second step S33 of this embodiment, the first polymer material model 3 that moves (approaches) 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.

In the second step S33 of this embodiment, a 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. As a result, in the second step S33, the structure of the first polymer material model 3 can be relaxed (a stable arrangement can be obtained) while maintaining the interface 5 between the first polymer material model 3 and the second polymer material model 4.

[Third step]
Next, in the structural relaxation step S3 of this embodiment, after the second step S33, the constraint of the second polymer material model 4 is released and the mixed model 2 is structurally relaxed (third step S34). Fig. 10 is a diagram showing the mixed model 2 structurally relaxed after the constraint of the second polymer material model 4 is released.

In the third step S34 of this embodiment, first, the coordinates of the coarse-grained particles 4a of the second polymer material model 4 are released. This allows the second polymer material model 4, together with the first polymer material model 3, to move freely inside the cell 6 in the molecular dynamics calculation.

Next, in the third step S34 of this embodiment, a 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 manner as in the first step S31.

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

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

In this way, in the third step S34 of this 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 this 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 to a more natural structure while maintaining the interface 5. As a result, in the simulation method of this 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) in which the interface 5 is formed can be created. The mixed system model 2 is stored in the computer 1.

[Simulation process]
As shown in FIG. 2, in the simulation method of the present embodiment, the computer 1 (shown in FIG. 1) calculates the physical quantities and interactions (hereinafter, simply referred to as "physical quantities, etc.") at the interface 5 (shown in FIG. 10) of the mixed 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 mixed system model 2 is calculated, and the physical quantities, etc. at the interface 5 after the deformation are calculated. The deformation of the mixed system model 2 can be appropriately performed, for example, tensile deformation, compressive deformation, etc. The deformation calculation of the mixed system model 2 can be performed based on the conventional method described in the patent document (JP Patent Publication No. 2016-81297).

In the simulation method of this embodiment, a mixed system model 2 of two polymer material models (in this example, a first polymer material model 3 and a second polymer material model 4) forming an interface 5 can be created. As a result, in the simulation method of this embodiment, it is possible to calculate physical quantities at the interface 5 that are difficult to measure in experiments using actual polymer materials. The calculation results are stored in the computer 1 (shown in FIG. 1).

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

In step S5 of this embodiment, it is determined whether the physical quantity at the interface 5 is equal to or greater than a predetermined threshold value. The threshold value is set appropriately according to the performance required of the polymer material (e.g., fracture resistance, etc.).

In step S5, if the physical quantity at interface 5 is equal to or greater than the threshold value (step S5: "Yes"), a product (e.g., a tire) using the polymer material is manufactured (step S6). On the other hand, in step S5, if the physical quantity at interface 5 is smaller than the threshold value (step S5: "No"), the composition of the first polymer component and the second polymer component is changed (step S7), and steps S1 to S5 are performed again.

In this way, in the simulation method of this embodiment, the blending of the first polymer component and the second polymer component is changed until the physical quantity at the interface 5 (shown in FIG. 10) of the mixed system model 2 reaches or exceeds a threshold value. As a result, in the simulation method of this embodiment, it becomes possible to reliably manufacture products such as tires using polymer materials having the desired performance, for example.

[Simulation method for polymeric material (second embodiment)]
In the above embodiment, the LJ interaction potential Q1 (shown in FIG. 3) defined 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 defined as it is after the structural relaxation step S3, but is not limited to such an embodiment. For example, instead of the LJ interaction potential Q1, an interaction potential based on a dissipative particle dynamics method may be defined. FIG. 11 is a flowchart showing the processing procedure of a polymer material simulation method according to another embodiment of the present disclosure. The same reference numerals are attached to the same configurations as those in the above embodiment, and the description may be omitted.

[Define the interaction potential based on the 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 (step S8) instead of the LJ interaction potential Q1 shown in Fig. 3. The DPD potential (soft core potential) is defined by the following formula (2).

ここで、
Ｕ_nonbond（ｒ_ij）：ＤＰＤポテンシャル
ｒ_ij：粗視化粒子間の距離
ａ_ij：粗視化粒子間に定義される斥力の強度に対応する定数
ｒ_c：カットオフ距離

Where:
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

The constants in the above formula (2) can be set appropriately depending on, for example, the structure of the polymer component. In this embodiment, the constant a _ij is set to 25, and the cutoff distance _rc is set to 1.0, but are not particularly limited and can be set appropriately depending on, for example, the structure of the polymer component.

Unlike the LJ interaction potential Q1 (shown in FIG. 3), the DPD potential of this embodiment can have a finite value without diverging even if the distance r _ij between the coarse-grained particles 3a and 4a becomes zero. Therefore, in the simulation method of this embodiment, it is possible to reliably prevent calculation failure (divergence of potential energy) in the simulation step S4 performed thereafter, and stable calculation is possible.

In addition, in the simulation method of this embodiment, as in the previous embodiments, the LJ interaction potential Q1 (shown in FIG. 3) is defined prior to the structural relaxation step S3. Because of K, the simulation method of this embodiment can reliably create 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.

In step S8 of this embodiment, a DPD potential may be defined 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. Furthermore, in step S8, a DPD potential may be defined 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. This allows the simulation method of this embodiment to perform more stable calculations in the simulation step S4 that is performed thereafter.

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

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

In Examples 1 and 2, a first step was carried out based on the processing procedure shown in FIG. 8, in which the first polymer material model was constrained and the mixed system model was structurally relaxed so that the interface was maintained. Next, in Examples 1 and 2, a step was carried out of releasing the constraint on the first polymer material model, and a second step was carried out of constraining the second polymer material model and structurally relaxing the mixed system model so that the interface was maintained. Then, in Examples 1 and 2, a third step was carried out of releasing the constraint on the second polymer material model and structurally relaxing the mixed system model.

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

In the comparative example, unlike the examples 1 and 2, the step of structurally relaxing the mixed system model was carried out without constraining the first polymer material model and the second polymer material model. The common specifications are as follows.
Polymer component:
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/particle Second polymer material model:
Total number: 160
Number of coarse-grained particles: 500/particle Bond potentials P1, P2 (LJ potential, FENE potential):
Cutoff distance r _c : 1.5
Stretched length _R0 : 2 ^1/6
Spring constant k: 30
Interaction parameter ε: 1.0
Parameter σ corresponding to the diameter of the coarse-grained particles: 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 particles: 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 particles: 1.0
Molecular dynamics calculations (Examples 1 and 2):
Unit time step: 0.006
First step: 10,000 steps Second step: 10,000 steps Third step: 20,000 steps Molecular dynamics calculation (comparative example):
Unit time step: 0.006
Structural relaxation calculation: 20,000 steps DPD potential (Example 2):
Constant a _ij corresponding to the strength of the repulsive force defined between coarse-grained particles: 25
Cutoff distance r _c : 1.0

Figure 10 is a diagram showing the mixed system models of Examples 1 and 2. Figure 12 is a diagram showing the mixed system model of the comparative example. In Examples 1 and 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 together, and the interface could not be maintained. Therefore, in Examples 1 and 2, a mixed system model of two polymer material models in which an interface was formed could be created.

In addition, in Example 2, after the structural relaxation process, the DPD potential was defined instead of the LJ interaction potential. As a result, Example 2 was able to prevent calculation errors in the simulation process that was performed thereafter, compared to Example 1, in which the LJ interaction potential remained defined.

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

[Disclosure 1]
A method for simulating a polymeric material, comprising the steps of:
inputting a first polymer material model and a second polymer material model, which are models of the first polymer component and the second polymer component, respectively, based on a classical molecular dynamics method, into a computer;
inputting 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 into the computer;
and performing a molecular dynamics calculation on the mixed system model by the computer to relax the structure of the mixed system model,
The step of structurally relaxing the mixed system model includes a first step of structurally relaxing the mixed system model by constraining the first polymer material model so as to maintain the interface.
Simulation methods for polymeric materials.
[Disclosure 2]
the step of relaxing the structure includes, after the first step, releasing constraints on the first polymer material model;
The polymer material simulation method described in the present disclosure 1, comprising a second step of constraining the second polymer material model and structurally relaxing the mixed system model so as to maintain the interface.
[Disclosure 3]
The method for simulating a polymer material described in Disclosure 2, wherein the structural relaxation step includes a third step of releasing the constraint of the second polymer material model after the second step and structurally relaxing the mixed system model.
[Disclosure 4]
The method for simulating a polymer material described in any one of Disclosures 1 to 3, wherein 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 coarse-grained molecular models represented using a plurality of coarse-grained particles.
[Disclosure 5]
The method for simulating a polymer material described in Disclosure 4, comprising, prior to the structural relaxation step, a step of defining an LJ interaction potential between a coarse-grained particle of the first polymer material model and a coarse-grained particle of the second polymer material model.
[Disclosure 6]
The method for simulating a polymer material described in the present disclosure 5 further includes, after the structural relaxation step, a step of defining an interaction potential based on a dissipative particle dynamics method instead of the LJ interaction potential.

S1: Step of inputting a first polymer material model and a second polymer material model; S2: Step of inputting a mixed system model; S3: Step of relaxing the mixed system model

Claims (6)

A method for simulating a polymeric material, comprising the steps of:
inputting a first polymer material model and a second polymer material model, which are models of the first polymer component and the second polymer component, respectively, based on a classical molecular dynamics method, into a computer;
inputting 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 into the computer;
and performing a molecular dynamics calculation on the mixed system model by the computer to relax the structure of the mixed system model,
The step of structurally relaxing the mixed system model includes a first step of structurally relaxing the mixed system model by constraining the first polymer material model so as to maintain the interface.
Simulation methods for polymeric materials. the step of relaxing the structure includes, after the first step, releasing constraints on the first polymer material model;
2. The method for simulating a polymer material according to claim 1, further comprising a second step of constraining the second polymer material model so as to maintain the interface, and structurally relaxing the mixed system model. The polymer material simulation method according to claim 2, wherein the structural relaxation step includes a third step of releasing the constraints of the second polymer material model after the second step and structurally relaxing the mixed system model. The polymer material simulation method according to any one of claims 1 to 3, wherein 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 coarse-grained molecular models represented using a plurality of coarse-grained particles. The polymer material simulation method according to claim 4, further comprising 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 prior to the structural relaxation step. The polymer material simulation method according to claim 5, further comprising a step of defining an interaction potential based on a dissipative particle dynamics method instead of the LJ interaction potential after the structural relaxation step.

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