JP7400538B2 - Simulation method for polymer materials - Google Patents

Description

The present invention relates to a method for simulating polymer materials.

Patent Document 1 listed below describes a simulation method for evaluating the fracture characteristics of a polymer material containing a filler and a polymer. In this method, first, the deformation of a polymer material model for numerical calculation is calculated under deformation conditions such that pores are formed in at least a portion of the polymer of the polymer material model for numerical calculation.

JP2019-032278A

In the above method, the pores formed in the polymer material model are so-called voids in which no polymer (polymer model) or the like exists. Such holes do not have positional information for specifying them. For this reason, the above method has a problem in that it is not possible to quantitatively analyze the position, size, etc. of the pores.

The present invention was devised in view of the above-mentioned circumstances, and its main purpose is to provide a simulation method that allows quantitative analysis of pores.

The present invention is a polymer material simulation method, which includes the step of inputting a polymer material model for numerical calculation into a computer based on the polymer material, and the computer a step of calculating deformation of the polymer material model based on predetermined conditions so that holes are formed in at least a portion of the interior of the polymer material model in which the holes are formed; , a step of arranging a plurality of hole particle models, and a step of defining an interaction between the hole particle model and the polymer material model such that the hole particle models gather in the hole. a step of calculating structural relaxation between the polymer material model in which the holes are formed and the hole particle model based on the interaction; and position information of the hole particle model after the structural relaxation. The method is characterized by performing the step of obtaining the .

In the polymer material simulation method according to the present invention, the interaction may include a first potential that applies an attractive force between the pair of hole particle models.

In the polymer material simulation method according to the present invention, the polymer material model includes a polymer model in which a polymer is modeled, and the interaction exerts a repulsive force between the hole particle model and the polymer model. It may also include a second potential that causes

In the polymer material simulation method according to the present invention, the step of calculating the structural relaxation may be performed while the position of the polymer model within the polymer material model is fixed.

In the polymer material simulation method according to the present invention, the polymer material model includes a filler model in which a filler is modeled, and the interaction exerts a repulsive force between the hole particle model and the filler model. It may also include a third potential that causes

In the polymer material simulation method according to the present invention, the step of calculating the structural relaxation may be performed while the position of the filler model within the polymer material model is fixed.

In the polymer material simulation method according to the present invention, the step of acquiring the position information may acquire a radial distribution function of the void particle model.

The polymer material simulation method of the present invention is based on an interaction in which the pore particle model gathers in the pores formed inside the polymer material model. Structural relaxation between the polymer material model and the void particle model is calculated. In the present invention, the pores can be specified based on the position information acquired from the pore particle model after structural relaxation. Therefore, the present invention makes it possible to quantitatively analyze the pores.

FIG. 1 is a perspective view showing an example of a computer that executes the polymer material simulation method of the present invention. 2 is a flowchart illustrating an example of a processing procedure of a polymer material simulation method. 3 is a flowchart illustrating an example of a processing procedure of a model setting step. FIG. 2 is a conceptual diagram showing an example of a cell in which a filler model, a polymer model, and a coupling agent model are arranged. It is an enlarged view of a filler particle model. FIG. 2 is a conceptual diagram showing an example of a polymer model. It is a conceptual diagram explaining an example of the potential of a filler model, a polymer model, and a coupling agent model. It is a conceptual diagram which shows an example of the coupling agent model which connected the filler model and the polymer model, and a pair of polymer model which were connected by the crosslinking model. (a) is a conceptual diagram showing a part of the polymer material model before deformation calculation, and (b) is a conceptual diagram showing part of the polymer material model after deformation calculation. FIG. 2 is a conceptual diagram showing a portion of a polymer material model in which a hole particle model is arranged. FIG. 2 is a conceptual diagram showing an example of a polymer material model and a hole particle model after structural relaxation calculations. It is a graph which shows an example of the radial distribution function of a hole particle model. FIG. 3 is a conceptual diagram showing a polymer material model after deformation calculation. FIG. 2 is a conceptual diagram showing an example of a polymer material model and a hole particle model after structural relaxation calculations. It is a graph which shows an example of the radial distribution function of a hole particle model.

Hereinafter, one embodiment of the present invention will be described based on the drawings.
In the polymer material simulation method (hereinafter sometimes simply referred to as "simulation method") of the present embodiment, the fracture characteristics of the polymer material are evaluated.

FIG. 1 is a perspective view showing an example of a computer that executes the polymer material simulation method of the present invention. The computer 1 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 processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2. Further, software and the like for executing the simulation method of this embodiment are stored in advance in the storage device.

The polymer material of this embodiment contains a polymer and a filler. Note that the polymer material may include only a polymer. Furthermore, the polymer material of this embodiment contains a coupling agent for bonding the polymer and the filler.

As the polymer, filler, and coupling agent, for example, those described in the above-mentioned Patent Document 1 can be appropriately employed. In this embodiment, cis-1,4 polyisoprene (hereinafter sometimes simply referred to as "polyisoprene") is exemplified as the polymer. An example of the filler is silica. An example of the coupling agent is a silane coupling agent (TESPD).

FIG. 2 is a flowchart showing an example of a processing procedure of a polymer material simulation method. In the simulation method of this embodiment, first, a polymer material model for numerical calculation is input into the computer 1 based on the polymer material (model setting step S1). FIG. 3 is a flowchart showing an example of the processing procedure of the model setting step S1.

In the model setting step S1 of this embodiment, first, a cell, which is a virtual space corresponding to a part of the polymer material, is defined in the computer 1 (step S11). FIG. 4 is a conceptual diagram showing an example of a cell 4 in which a filler model 6, a polymer model 7, and a coupling agent model 8 are arranged. In FIG. 4, only one polymer model 7 and only one coupling agent model 8 are displayed.

The cell 4 has at least a pair of surfaces 5, 5 facing each other, in this embodiment, three pairs of surfaces 5, 5 facing each other, and is defined as a rectangular parallelepiped or a cube (in this embodiment, a cube). . A periodic boundary condition is defined for each surface 5, 5. Each length L1 of one side of the cell 4 can be set as appropriate, for example, based on the description in Patent Document 1 mentioned above. Cell 4 is stored in computer 1.

Next, in the model setting step S1 of the present embodiment, a filler model 6 that models the filler is defined (step S12). The filler model 6 of this embodiment is defined by a plurality of filler particle models 11 aggregated inside the cell 4, similar to the above-mentioned Patent Document 1. In this embodiment, filler particle models 11 are arranged based on the positions of primary filler particles in an electron beam transmission image of an actual polymer material. Thereby, the filler model 6 can accurately represent the shape of the actual filler.

FIG. 5 is an enlarged view of the filler particle model 11. Each filler particle model 11 includes a plurality of small particles 12. In the filler particle model 11, a constraint condition that fixes the relative position between the adjacent small particles 12, 12 may be defined, or a bond chain model (not shown) that constrains the adjacent small particles 12, 12 may be defined. May be defined. A bonding chain model (not shown) that binds the small particles 12, 12 may be appropriately defined based on the description in Patent Document 1 mentioned above. Further, the small particles 12 constituting the outer surface of the filler particle model 11 may be provided with, for example, a functional group model (not shown) in which a functional group is modeled. Filler model 6 is stored in computer 1.

Next, in the model setting step S1 of this embodiment, as shown in FIG. 4, a polymer model 7 that models a polymer is defined (step S13). In this embodiment, at least one (for example, 10 to 1,000,000) polymer models 7 are arranged inside the cell 4 in a region where no filler model 6 is arranged.

FIG. 6 is a conceptual diagram showing an example of the polymer model 7. The polymer model 7 of this embodiment is modeled using a plurality of coarse-grained particles 15, the number of which is smaller than the number of atoms constituting the polymer, based on the molecular structure of the polymer. Therefore, polymer model 7 is expressed as a coarse-grained molecular model (in this example, a Kremer-Grest model). Note that the polymer model 7 may be a model based on DPD (dissipative particle dynamics method), which has a larger degree of coarse-graining than the Kremer-Grest model. Further, the polymer model 7 may be an all-atom model (not shown) or a united atom model (not shown) based on the actual structure of the polymer.

The coarse-grained particles 15 of this embodiment are obtained by replacing a polymer monomer or a structural unit forming a part of the monomer. Such coarse-grained particles 15 can be appropriately set, for example, based on the description in Patent Document 1 mentioned above. Adjacent coarse-grained particles 15, 15 are connected by a bond chain model 16.

FIG. 7 is a conceptual diagram illustrating an example of the potential of the filler model 6, the polymer model 7, and the coupling agent model 8. The bonded chain model 16 is defined by a potential P1 with a fully extended length set between the coarse-grained particles 15, 15. The potential P1 can be defined as appropriate, and for example, based on the description in Patent Document 1 mentioned above, it can be defined as the sum of the LJ (Lennard-Jones) potential and the FENE potential. Polymer model 7 is stored in computer 1.

Next, in the model setting step S1 of this embodiment, as shown in FIG. 4, a coupling agent model 8 modeling a coupling agent is defined (step S14). In this embodiment, at least one (for example, 10 to 1000) coupling agent models 8 are arranged inside the cell 4 in a region where the filler model 6 and the polymer model 7 are not arranged.

As shown in FIG. 7, the coupling agent model 8 is modeled using a plurality of coarse-grained particles 19, which is smaller in number than the number of atoms constituting the coupling agent, based on the molecular structure of the coupling agent. . Therefore, the coupling agent model 8 is expressed as a coarse-grained molecular model (in this example, a Kremer-Grest model). The coupling agent model 8 may be a model based on DPD (dissipative particle dynamics method), an all-atom model (not shown), or a united atom model (not shown).

Each coarse-grained particle 19 can be appropriately set, for example, based on the description in Patent Document 1. Adjacent coarse-grained particles 19, 19 are connected by a bond chain model 20. The bonded chain model 20 is defined by a potential P2 in which an extended length is set between the coarse-grained particles 19, 19. The potential P2 can be defined as appropriate. The potential P2 can be defined as appropriate, and for example, based on the description in Patent Document 1 mentioned above, it can be defined as the sum of the LJ potential and the FENE potential. Coupling agent model 8 is stored in computer 1.

Next, in the model setting step S1 of this embodiment, potentials are defined for the adjacent filler model 6, polymer model 7, and coupling agent model 8 (step S15). In step S15 of this embodiment, as shown in FIG. Potentials P3 to P8 are defined. These potentials P3 to P8 can be defined as LJ potentials based on the description in Patent Document 1 mentioned above. Potentials P3 to P8 are stored in computer 1.
Potential P3: with small particles 12 of filler model 6
Between the small particles 12 of the filler model 6 Potential P4: Between the coarse-grained particles 15 of the polymer model 7
Between coarse-grained particles 15 of polymer model 7 Potential P5: Between coarse-grained particles 19 of coupling agent model 8
Between the coarse-grained particles 19 of the coupling agent model 8 Potential P6: Between the small particles 12 of the filler model 6
Between the coarse grained particles 15 of the polymer model 7 Potential P7: Between the small particles 12 of the filler model 6
Between coarse-grained particles 19 of coupling agent model 8 Potential P8: Between coarse-grained particles 15 of polymer model 7
Between coupling agent model 8 and coarse-grained particles 19

Next, in the model setting step S1 of this embodiment, the computer 1 calculates the structural relaxation of the cell 4 shown in FIG. 4 based on the molecular dynamics calculation (step S16). In the molecular dynamics calculation of this embodiment, Newton's equation of motion is applied to the cell 4 for a predetermined time, assuming that the filler model 6, polymer model 7, and coupling agent model 8 follow classical mechanics, for example. The movements of the filler model 6, polymer model 7, and coupling agent model 8 at each time are tracked for each unit time of simulation. Such molecular dynamics calculations are appropriately performed based on the description in Patent Document 1 mentioned above.

Next, in the model setting step S1 of this embodiment, the computer 1 connects the filler model 6 and the polymer model 7 via the coupling agent model 8 (step S17). FIG. 8 is a conceptual diagram showing an example of a coupling agent model 8 that connects a filler model 6 and a polymer model 7, and a pair of polymer models 7, 7 that are connected by a crosslinking model 17. In FIG. 8, a coupling agent model 8 composed of one coarse-grained particle 19 is illustrated.

In step S18, based on the description of Patent Document 1 above, between the coarse-grained particles 19 of the coupling agent model 8 and the small particles 12 of the filler model 6, and between the coarse-grained particles of the coupling agent model 8. 19 and the coarse-grained particles 15 of the polymer model 7 are connected. A bonding chain model 23 that connects these particles is defined by a potential P9 with a set extension length. This potential P9 is defined, for example, as the sum of the LJ potential and the FENE potential.

Next, in the model setting step S1 of this embodiment, a crosslinked model 17 that connects adjacent polymer models 7 is defined (step S18). The crosslinking model 17 is for connecting the coarse grained particles 15, 15 of the polymer model 7. For example, the potential P10 can be defined as the sum of the LJ potential and the FENE potential, as in the conventional case.

Next, in the model setting step S1 of this embodiment, the computer 1 recalculates the structural relaxation of the cell 4 (shown in FIG. 5) based on the molecular dynamics calculation (step S19). Recalculation of the structural relaxation is performed using the same processing procedure as step S16, and the filler model 6 and polymer model 7 connected via the coupling agent model 8 and the polymer model 7 connected via the crosslinking model 17 are Calculations are made until sufficient relaxation is achieved. Thereby, in the simulation method of this embodiment, it is possible to define a polymer material model 10 that reproduces a crosslinked polymer material after a coupling reaction. The polymer material model 10 is stored in the computer 1.

Next, in the simulation method of the present embodiment, the computer 1 creates the polymer material model 10 based on predetermined conditions so that pores are formed in at least a portion of the interior of the polymer material model 10. The deformation of is calculated (step S2). In step S2 of this embodiment, as shown in FIG. 4, a uniaxial tensile test is calculated in which the polymer material model 10 is pulled in a predetermined direction. The direction in which the polymer material model 10 is pulled can be selected as appropriate, and in this example, it is pulled in the z-axis direction.

The deformation calculation of the polymer material model 10 can be performed, for example, according to the procedures described in the above-mentioned Patent Document 1 and Patent Document (Japanese Patent Laid-Open No. 2016-81297). That is, in this embodiment, in the z-axis direction, one end of the polymer material model 10 (the surface 5a on one side of the cell 4 shown in FIG. 4) and the other end of the polymer material model 10 (the surface 5a on one side of the cell 4 shown in FIG. 4) The elongation of the polymer material model 10 is calculated so that the surfaces 5b) on the other side of the cell 4 are spaced apart from each other.

FIG. 9(a) is a conceptual diagram showing a part of the polymer material model 10 before deformation calculation. FIG. 9(b) is a conceptual diagram showing a part of the polymer material model 10 after deformation calculation. In FIG. 9(b), the holes 21 are indicated by two-dot chain lines.

As shown in FIG. 9(a), the polymer material model 10 before the deformation calculation has two points shown in FIG. The voids 21 shown by the chain lines are not formed. Here, the void 21 is a region in the cell 4 of the polymer material model 10 where the filler model 6, polymer model 7, and coupling agent model 8 are not present.

The pores 21 can be defined as appropriate based on the sizes of the filler model 6, the polymer model 7, and the coupling agent model 8. The hole 21 of this embodiment has a diameter (in the case of an ellipse, the length of the short axis) L1 of the region in which the filler model 6, the polymer model 7, and the coupling agent model 8 are not present. , is defined as a region where the diameter L3 or more of the coarse-grained particles 15 of the polymer model 7 is greater than or equal to the diameter L3 (that is, the diameter L1 is one or more times the diameter L3).

In step S2, thermal motion of the filler model 6, polymer model 7, and coupling agent model 8 is calculated by elongation calculation of the polymer material model 10. Such thermal motion is calculated based on the strain given to the polymer material model 10, the potentials P1 to P10 shown in FIGS. 7 and 8, and the equation of motion. As a result, as shown in FIG. 9(b), the above-mentioned voids 21 in which no filler model 6, polymer model 7, and coupling agent model 8 are present are formed in the cell 4. Ru. Due to such holes 21, destruction of the polymer material is reproduced in the polymer material model 10. Conditions for the deformation can be appropriately set, for example, based on the description in Patent Document 1 mentioned above, as long as the pores 21 can be formed inside the polymer material model 10.

Next, in the simulation method of this embodiment, as shown in FIG. S3). FIG. 10 is a conceptual diagram showing a portion of the polymer material model 10 in which the void particle model 22 is arranged. In FIG. 10, the hole particle models 22 are colored to make it easier to distinguish between the hole particle models 22.

The pore particle model 22 is for specifying the pores 21. Therefore, unlike the filler model 6, polymer model 7, and coupling agent model 8, the void particle model 22 is based on components contained in a polymeric material (in this example, a polymer, a filler, a coupling agent, etc.). isn't it.

The pore particle model 22 can be set as appropriate. The hole particle model 22 of this embodiment is treated as a mass point in the equation of motion in molecular dynamics calculations. That is, in the hole particle model 22, parameters such as diameter, mass, electric charge, or initial coordinates are defined similarly to the coarse-grained particles 15.

The diameter L2 of the hole particle model 22 can be set as appropriate as long as it is equal to or less than the diameter L1 (shown in FIG. 9(b)) defined as the hole 21 described above. The diameter L2 of the void particle model 22 of this embodiment is set to be the same as the diameter L3 of the coarse-grained particles 15 of the polymer model 7. Further, the mass of the void particle model 22 can be set as appropriate, and is set to be the same as the mass of the coarse-grained particles 15 of the polymer model 7, for example.

Unlike the polymer model 7, the hole particle model 22 is not connected to other hole particle models 22 by a bonding chain model or the like. Conditions are defined for the void particle model 22 of this embodiment to allow overlap with the polymer model 7 and the coupling agent model 8. In step S3, the pore particle models 22 are randomly arranged inside the polymer material model 10 in areas where the filler models 6 are not arranged. The reason why the pore particle model 22 is arranged in a region where no filler model is arranged in this way is that the pores 21 are not formed inside the strong filler model 6.

The number of hole particle models 22 can be set as appropriate. The number of hole particle models 22 in this embodiment is set to a value obtained by dividing the total volume of holes 21 by the volume of one hole particle model 22. Thereby, the total volume of the pore particle model 22 and the total volume of the pores 21 can be made the same. In addition, the total volume of the pores 21 can be calculated from the volume of the polymer material model 10 (cell 4) after deformation shown in FIG. 9(b) to the volume of the polymer material model 10 before deformation shown in FIG. 9(a). It is obtained by subtracting the volume of (cell 4). The pore particle model 22 is stored in the computer 1.

Next, in the simulation method of this embodiment, as shown in FIG. 2 and FIG. and the polymer material model 10 (step S4).

The interaction can be appropriately set as long as the pore particle model 22 can be gathered within the pores 21 in step S5 of calculating structural relaxation, which will be described later. The interaction in this embodiment includes the first potential P11.

The first potential P11 is for applying an attractive force between the pair of hole particle models 22, 22. The first potential P11 of this embodiment is defined by the LJ potential. Such a first potential P11 applies an attractive force to the hole particle models 22 and 22 that are close to each other in the calculation of structural relaxation described later, and causes a cluster (group) of the hole particle models 22 to move inside the holes 21. It helps to form.

Each constant defined in the first potential (LJ potential) P11 is, for example, described in paper 1 (Kurt Kremer & Gary S. Grest, "Dynamics of entangled linear polymer melts: A molecular-dynamics simulation", J. Chem Phys. vol.92, No.8, 15 April 1990, p5057-5086). The first potential P11 is stored in the computer 1.

Furthermore, the interaction in this embodiment includes the second potential P12. The second potential P12 is for applying a repulsive force between the hole particle model 22 and the polymer model 7. The second potential P12 of this embodiment is set between the void particle model 22 and the coarse-grained particles 15 of the polymer model 7. Furthermore, the second potential P12 of this embodiment is set between the hole particle model 22 and the coarse-grained particles 19 of the coupling agent model 8.

As the second potential P12 of this embodiment, the soft core potential U _soft of the following formula (1) is defined.

ここで、定数及び変数は、次のとおりである。
Ａ：斥力の高さ（強度）に対応する定数
ｒ_ij：粗視化粒子間の距離
ｒ_c：カットオフ距離
なお、粗視化粒子間の距離ｒ_ij及びカットオフ距離ｒ_cは、粒子（粒子モデル）の中心間の距離として定義される。

Here, the constants and variables are as follows.
A: Constant corresponding to the height (strength) of repulsive force r _ij : Distance between coarse-grained particles r _c : Cutoff distance Note that the distance r _ij between coarse-grained particles and the cutoff distance r _c are particle model).

The soft core potential U _soft is based on dissipative particle dynamics (DPD). In the soft core potential U _soft , the repulsive force becomes 0 when the distance r _ij is equal to or greater than the cutoff distance r _c . On the other hand, when the distance r _ij is less than the cutoff distance r _c , the repulsive force becomes large. Furthermore, even if the distance r _ij converges to 0, the repulsive force becomes a finite value. Therefore, the soft core potential U _soft does not diverge to infinity, unlike a potential that increases infinitely as the distance between particles becomes smaller.

The constant A in the above formula (1) is for adjusting the height (strength) of the potential. In the second potential P12 of this embodiment, the constant A in the above equation (1) is set smaller than in the third potential P13. As a result, the second potential P12 can reduce the repulsive force when the distance r _ij converges to 0, and the overlap between the hole particle model 22 and the polymer model 7 (and the coupling agent model 8) is allowed. sell. The constant A can be appropriately set as long as the void particle model 22 and the polymer model 7 (and the coupling agent model 8) are allowed to overlap. It is desirable that the constant A is set between 0.5 and 2.0.

In the second potential P12, the values of other constants and variables in the above equation (1) can be set as appropriate. The values of this embodiment are based on paper 2 (Robert D. Groot and Patrick B. Warren, "Dissipative particle dynamics: Bridging the gap between atomic and mesoscopic simulation", J. Chem Phys. vol.107, No.11, 15 September 1997) as appropriate. The second potential P12 is stored in the computer 1.

Furthermore, the interaction in this embodiment includes the third potential P13. The third potential P13 is for applying a repulsive force between the hole particle model 22 and the filler model 6. The third potential P13 of this embodiment is set between the hole particle model 22 and the small particles 12 of the filler model 6 (filler particle model 11). As the third potential P13 of this embodiment, the soft core potential U _soft of the above equation (1) is defined similarly to the second potential P12.

The constant A in the above equation (1) of the third potential P13 of this embodiment is set larger than the constant A of the second potential P12. Thereby, the third potential P13 can increase the repulsive force when the distance r _ij converges to 0, and can prevent the hole particle model 22 and the filler model 6 from overlapping. Therefore, in step S5 of calculating structural relaxation, which will be described later, it is possible to prevent the pore particle model 22 from being placed inside the filler model 6 in which the pores 21 are not formed.

Note that the constant A can be set as appropriate as long as it is possible to prevent the void particle model 22 and the filler model 6 from overlapping. It is desirable that the constant A is set between 50 and 150. In the third potential P13, the values of other constants and variables in the above equation (1) can be appropriately set based on the above paper 2. The third potential P13 is stored in the computer 1.

Next, in the simulation method of this embodiment, the computer 1 calculates the structural relaxation between the polymer material model 10 in which the holes 21 are formed and the hole particle model 22 based on the interaction (step S5). . In step S5, structural relaxation based on molecular dynamics calculation is calculated based on the interactions defined in step S4 (in this example, first potential P11 to third potential P13). Molecular dynamics calculations are appropriately performed based on the description in Patent Document 1 mentioned above. FIG. 11 is a conceptual diagram showing an example of the polymer material model 10 and the void particle model 22 after structural relaxation calculation.

In step S5, a repulsive force acts between the hole particle model 22 and the polymer model 7 (and the coupling agent model 8) due to the second potential P12 (shown in FIG. 10). Due to such repulsive force, in step S5, the pore particle model 22 can be moved to the pores 21 in which the polymer model 7 (coupling agent model 8) is not arranged. Further, in step S5, a repulsive force between the pore particle model 22 and the filler model 6 due to the third potential P13 (shown in FIG. 10) causes the pore particle model 22 to It can be moved to 21. Thereby, in step S5, the pore particle model 22 can be placed in the pores 21 of the polymer material model 10.

In step S5, it is desirable that the structural relaxation be calculated while the position of the polymer model 7 inside the polymer material model 10 is fixed. Furthermore, in step S5, it is desirable that the structural relaxation be calculated while the position of the filler model 6 inside the polymer material model 10 is fixed. Thereby, in step S5, the pore particle models 22 can be placed in the pores 21 while maintaining the shapes of the pores 21 formed in step S2.

In step S5, a cluster (group) 25 of the pore particle models 22 arranged in the pores 21 is generated by the attraction force due to the first potential P11 (shown in FIG. 10) defined between the pair of pore particle models 22, 22. is formed. As a result, in step S5, the pore particle models 22 placed inside the pores 21 are prevented from being placed outside the pores 21, and the pore particle models 22 are collected inside the pores 21. I can do it. The calculation results of structural relaxation of the polymer material model 10 and the void particle model 22 are stored in the computer 1.

Next, in the simulation method of this embodiment, the computer 1 acquires position information of the pore particle model 22 after structural relaxation (step S6). As for the position information, in the polymer material model 10 (cell 4) after structural relaxation with the hole particle model 22, the coordinate values of the hole particle model 22 inside the cell 4 are acquired.

As described above, the hole particle model 22 is placed inside the hole 21 . Therefore, in step S6, the position of the pores 21 formed in the polymer material model 10 (cell 4) can be specified based on the position information (coordinate values) of the pore particle model 22. Furthermore, the size of the pores 21 can be specified based on the density of the pore particle model 22.

In this way, in the simulation method of this embodiment, the pores 21 formed inside the polymer material model 10 can be specified from the position information of the pore particle model 22. Therefore, the simulation method of the present embodiment makes it possible to identify locations where fractures (vacancies) are likely to occur and the factors that cause fractures (vacancies) in a polymer material, resulting in excellent fracture resistance. It can be useful for the development of polymer materials.

Furthermore, in this embodiment, as shown in FIG. 10, the size (diameter L2) of the pore particle model 22 is set to be the same as the size (diameter L3) of the coarse-grained particles 15 of the polymer model 7. ing. Therefore, by specifying the positional information of the pore particle model 22, the pores 21 formed inside the polymer material model 10 can be quantitatively specified on the same scale as the coarse-grained particles 15. I can do it.

In step S6, it is desirable that the radial distribution function of the void particle model 22 is acquired as the position information of the void particle model 22. The radial distribution function of this embodiment is a function representing the probability density that the hole particle model 22 exists at a distance r (not shown) from the coarse-grained particle 19 of each coupling agent model 8. Calculation of the radial distribution function is performed as appropriate based on, for example, the description in patent document (Japanese Patent Laid-Open No. 2015-56002). FIG. 12 is a graph showing an example of the radial distribution function of the hole particle model 22.

Generally, a coupling agent is used to bond a polymer and a filler to improve the strength of a polymeric material. Therefore, in the polymer material model 10, when the reinforcing effect of the coupling agent model 8 is high, the pores 21 are less likely to be formed near the coarse-grained particles 19 of the coupling agent model 8. In this case, in the graph shown in FIG. 12, the smaller the distance r, the lower the probability that the hole particle model 22 exists there, and the smaller the radial distribution becomes.

In this manner, in step S6, the radial distribution function of the pore particle model 22 is acquired, thereby making it possible to quantitatively analyze the pores 21. The position information of the hole particle model 22 is stored in the computer 1.

Next, in the simulation method of this embodiment, the computer 1 determines whether the size of the pores 21 in the polymer material model 10 is smaller than a predetermined threshold (step S7). In step S7 of this embodiment, the size of the pores 21 is acquired based on the position information of the pore particle model 22 (in this example, the radial distribution function). Further, the threshold value is appropriately set based on the strength required of the polymer material, the reinforcement required of the coupling agent, and the like.

In step S7, if the size of the pores 21 is smaller than the threshold value (“Y” in step S7), the polymer material model 10 can be evaluated as having desired fracture resistance. Therefore, in the simulation method of this embodiment, a polymer material is manufactured based on the conditions set in the polymer material model 10 (step S8).

On the other hand, in step S7, if the size of the pores 21 is equal to or larger than the threshold value ("N" in step S7), it can be evaluated that the polymer material model 10 does not have the desired fracture resistance. . Therefore, in the simulation method of this embodiment, the conditions of the polymer material (for example, the molecular structure of the coupling agent and the molecular structure of the crosslinking agent) are changed (step S9), and the model setting steps S1 to S7 are repeated. Implemented. As a result, the simulation method of this embodiment can produce a polymer material with excellent fracture resistance and wear resistance.

The polymer material model 10 of the embodiments so far included a filler model 6, a polymer model 7, and a coupling agent model 8, but is not limited to such aspects. For example, the polymer material model 10 may omit the filler model 6 and the coupling agent model 8, or may include models in which other components are modeled, based on the components of the polymer material to be analyzed. Good too.

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

Based on the processing procedure shown in FIG. (Example) In the polymer material model b, a larger number of coupling agent models were input than in the polymer material model a. In the example, the deformation of these polymer material models a and b is calculated based on the processing procedure shown in FIG. 2 so that holes are formed in some of the polymer material models a and b. It was done. FIG. 13 is a conceptual diagram showing the polymer material model b after deformation calculation.

In the example, a plurality of pore particle models were placed inside polymer material models a and b in which pores were formed, respectively. Between the pore particle model and the polymer material model (coarse-grained particles in the polymer model, small particles in the filler model, and coarse-grained particles in the coupling agent model), the pore particle model is created so that it gathers within the pores. interactions were defined. The interactions are defined as a first potential between a pair of hole particle models, a second potential between the hole particle model and the polymer model, and a third potential between the hole particle model and the filler model. It was done.

In the example, the structural relaxation between the polymer material models a and b in which holes were formed and the hole particle model was calculated based on the interaction. This structural relaxation calculation was performed with the positions of the filler model and the polymer model inside the polymer material models a and b fixed.

FIG. 14 is a conceptual diagram showing an example of a polymer material model b and a hole particle model after structural relaxation calculation. In the example, a cluster (group) 25 of the pore particle model was formed in the pores 21 formed inside the polymer material model. In the example, positional information of the pore particle model after structural relaxation was obtained. The common specifications are as follows.
cell:
Length of one side L1: 350σ
Filler model:
Filler particle model:
Radius: 12σ
(σ: unit of length of coarse-grained MD simulation)
Number of pieces: 4 pieces
Small particles in one filler particle model: 16,589 pieces Polymer model:
Quantity: 500 pieces
Coarse-grained particles constituting one polymer model: 200 Crosslinking points: 714 points Number of coarse-grained particles in coupling agent model:
Polymer material model a: 114 pieces
Polymer material model b: 700 pieces Deformation calculation:
Poisson's ratio: 0
Strain rate: 50%/600τ
(τ: unit of time for coarse-grained MD simulation)
Hole particle model:
Number: 17412 1st potential (LJ potential)
ε:1
_rc :2 ^1/6
Second potential (soft core potential):
A:15.0
_rc :2 ^1/6
Third potential (soft core potential):
A:100.0
_rc :2 ^1/6

As shown in Figure 13, it can be confirmed that pores are formed in the polymer material model after the deformation calculation, but since position information cannot be obtained for the pores, it is necessary to quantitatively analyze the pores. I can't. However, in the example, as shown in FIG. 14, since the vacancy particle models were able to be collected in the pores of the polymer material model, the vacancies could be quantitatively identified based on the position information of the vacancy particle models. I was able to analyze it.

FIG. 15 is a graph showing an example of the radial distribution function of the void particle model. In FIG. 15, the polymer material model a is shown by a solid line, and the polymer material model b is shown by a broken line. As shown in FIG. 15, the polymer material model b has a higher probability (radial distribution function g(r)) of the existence of the pore particle model in the portion where the distance r is smaller than that of the polymer material model a. This shows that the reinforcing effect is high. Therefore, the example was able to quantitatively demonstrate that the larger the coupling agent, the higher the strength of the polymer material.

S1 Step of inputting the polymer material model S2 Step of calculating deformation of the polymer material model S3 Step of arranging a plurality of hole particle models inside the polymer material model S4 Step of combining the hole particle model and the polymer material model In between, a step of defining the interaction S5 a step of calculating structural relaxation between the polymer material model and the hole particle model S6 a step of acquiring position information of the hole particle model after structural relaxation

Claims (7)

A simulation method for polymer materials, the method comprising:
A step of inputting a polymer material model for numerical calculation into a computer based on the polymer material,
The computer,
calculating a deformation of the polymer material model based on predetermined conditions so that pores are formed in at least a portion of the interior of the polymer material model;
arranging a plurality of pore particle models inside the polymer material model in which the pores are formed;
defining an interaction between the void particle model and the polymer material model such that the void particle model gathers within the void;
calculating structural relaxation between the polymer material model in which the vacancies are formed and the vacancy particle model based on the interaction;
acquiring positional information of the hole particle model after the structural relaxation;
Simulation methods for polymer materials. 2. The polymer material simulation method according to claim 1, wherein the interaction includes a first potential that applies an attractive force between the pair of hole particle models. The polymer material model includes a polymer model modeling a polymer,
3. The polymer material simulation method according to claim 1, wherein the interaction includes a second potential that causes a repulsive force to act between the hole particle model and the polymer model. 4. The polymer material simulation method according to claim 3, wherein the step of calculating the structural relaxation is performed while the position of the polymer model within the polymer material model is fixed. The polymer material model includes a filler model modeling a filler,
5. The polymer material simulation method according to claim 1, wherein the interaction includes a third potential that causes a repulsive force to act between the hole particle model and the filler model. 6. The polymer material simulation method according to claim 5, wherein the step of calculating the structural relaxation is performed while the position of the filler model within the polymer material model is fixed. 7. The polymer material simulation method according to claim 1, wherein the step of acquiring the position information acquires a radial distribution function of the hole particle model.

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