JP6962160B2 - Coarse-grained molecular dynamics simulation method for polymer materials - Google Patents

Description

The present invention relates to a method for comparing the performance of a plurality of types of polymer materials using a computer.

The following Non-Patent Document 1 proposes a method for simulating a polymer material using a computer. In the simulation method of Non-Patent Document 1 below, first, a polymer material model for numerical calculation is set in a computer based on the molecular chains of a plurality of types of polymer materials. Each polymer material model is composed of a monomer of a molecular chain or a plurality of particles in which structural units forming a part of the monomer are substituted.

Interatomic potentials for exerting repulsive or attractive forces are defined between the particles of each polymer material model. The strength of the interaction potential of each polymer material is different. Then, in the simulation method of Non-Patent Document 1 below, the structural relaxation of each polymer material model is calculated based on the interaction potential under the condition that the density and temperature of the particles are the same as each other.

Takeshi Aoyagi, Jun-ichi Takimoto and Masao Doi, "Coarse-Grained Molecular Dynamics Study of Polymer Blend at Interface", Proceedings of the International Conference on Advanced Polymer and Processing, ICAPP 2001 Yonezawa, 2002, p.217-223

Since each polymer material model has a different intensity of interaction potential, the distribution of particles after relaxation calculation is also different. If the distribution of particles after the relaxation calculation is different, each polymer material model calculates the internal stress after the relaxation calculation to a different value. Therefore, in Non-Patent Document 1, there is a problem that the physical quantities associated with the deformation of each polymer material model calculated thereafter cannot be compared with high accuracy.

The present invention has been devised in view of the above circumstances, and is a coarse-grained molecular dynamics simulation method for polymer materials that can accurately compare physical quantities associated with deformation of a plurality of types of polymer material models. The main purpose is to provide.

The present invention is a method for comparing the performance of a plurality of types of polymer materials including at least a first polymer material and a second polymer material using a computer, and is based on the first polymer material. Based on the step of setting the first polymer material model in the computer, which includes a plurality of first particles and in which the first interaction potential is defined between the first particles, and the second polymer material. , A step of setting a second polymer material model in the computer, which includes a plurality of second particles and in which a second interaction potential is defined between the second particles, and the computer causes the first polymer material. The step of calculating the structural relaxation of the model and the second polymer material model, and the computer deforming the first polymer material model and the second polymer material model after the structural relaxation, respectively, and the first The steps of calculating the structural relaxation include the steps of calculating the physical quantities of the polymer material model and the second polymer material model due to the deformation, respectively, and the steps of calculating the structural relaxation include the first polymer material model and the second polymer material. The model is characterized in that it is performed under conditions where the pressure and temperature are the same as each other.

In the coarse-grained molecular dynamics simulation method of the polymer material according to the present invention, the strength of the first interaction potential and the strength of the second interaction potential may be different from each other.

In the coarse-grained molecular dynamics simulation method of the polymer material according to the present invention, the first interaction potential and the second interaction potential are Lennard-Jones potentials, and the intensity is the potential of the Lennard-Jones potentials. Depth ε may be.

In the coarse-grained molecular dynamics simulation method of the polymer material according to the present invention, the first polymer material model may consist of only the first particles.

In the coarse-grained molecular dynamics simulation method for a polymer material according to the present invention, the first polymer material model comprises the first particles and the second particles, and the first particles and the second particles. A third interaction potential may be defined with the particle.

In the coarse-grained molecular dynamics simulation method of the polymer material according to the present invention, the physical quantity may include the stress of the first polymer material model and the stress of the second polymer material model.

In the coarse-grained molecular dynamics simulation method of the polymer material according to the present invention, the physical quantity is a parameter relating to the pores of the first polymer material model and a parameter relating to the pores of the second polymer material model. May include.

In the coarse-grained molecular dynamics simulation method of the polymer material according to the present invention, the parameters relating to the vacancies are the total volume of the vacancies and the total volume of the vacancies with respect to the volume of the first polymer material model. Or the ratio of the total volume of the pores to the volume of the second polymer material model.

In the coarse-grained molecular dynamics simulation method for a polymer material according to the present invention, the computer compares the physical quantity of the first polymer material model with the physical quantity of the second polymer material model. May be further included.

In the coarse-visual molecular dynamics simulation method of the polymer material of the present invention, the computer calculates the structural relaxation of the first polymer material model and the second polymer material model, respectively, and the computer performs the structural relaxation after the structural relaxation. Each of the first polymer material model and the second polymer material model is deformed, and the physical quantities of the first polymer material model and the second polymer material model due to the deformation are calculated respectively. I'm out.

The step of calculating the structural relaxation is performed in the first polymer material model and the second polymer material model under the condition that the pressure and the temperature are the same as each other. Thereby, the coarse-grained molecular dynamics simulation method of the present invention can make the internal stresses of the first polymer material model and the second polymer material model after structural relaxation approximate to each other. Therefore, the coarse-grained molecular dynamics simulation method of the present invention can accurately compare the physical quantities associated with the deformation of the first polymer material model and the second polymer material model.

FIG. 5 is a perspective view showing an example of a computer for executing a coarse-grained molecular dynamics simulation method of a polymer material. It is a structural formula which shows an example of a polymer. It is a flowchart which shows an example of the processing procedure of the coarse-grained molecular dynamics simulation method of a polymer material. It is a conceptual diagram which shows an example of the 1st polymer material model. It is a flowchart which shows an example of the processing procedure of the 1st model setting process. It is an enlarged view of the part A of FIG. It is a conceptual diagram which shows an example of the 1st molecular chain model. It is a conceptual diagram which shows an example of the interaction potential between 1st particles. It is a flowchart which shows an example of the processing procedure of the 2nd model setting process. It is a conceptual diagram which shows an example of the interaction potential between 2nd particles. It is a graph which shows the relationship between the volume fraction with respect to the initial volume of the 2nd polymer material model, and time. It is a graph which shows the relationship between the internal stress of a 1st polymer material model, the internal stress of a 2nd polymer material model, and time. (A) is a conceptual diagram showing a part of the first polymer material model before the deformation calculation, and (b) is a conceptual diagram showing a part of the first polymer material model after the deformation calculation. It is a conceptual diagram which shows an example of the 1st polymer material model which includes a 1st particle and a 2nd particle. It is a flowchart which shows an example of the processing procedure of the 1st model setting process of another Embodiment of this invention. It is a graph which shows the relationship between the volume fraction of each polymer material model with respect to the initial volume, and time. 6 is a graph showing the relationship between the internal stress of the first polymer material model, the internal stress of the second polymer material model, the internal stress of the third polymer material model, and the time of the embodiment. It is a graph which shows the relationship between stress and strain of an Example. It is a graph which shows the relationship between the volume fraction of a hole of an Example, and a strain. 6 is a graph showing the relationship between the internal stress of the first polymer material model, the internal stress of the second polymer material model, the internal stress of the third polymer material model, and the time of the comparative example. It is a graph which shows the relationship between the volume fraction of a hole of a comparative example, and time.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
In the coarse-grained molecular dynamics simulation method of the polymer material of the present embodiment (hereinafter, may be simply referred to as “simulation method”), the performances of a plurality of types of polymer materials are compared using a computer.

FIG. 1 is a perspective view showing an example of a computer for executing a coarse-grained molecular dynamics simulation method for a polymer material. 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, an arithmetic processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2. Further, the storage device stores in advance software or the like for executing the simulation method of the present embodiment.

The polymer material can be appropriately selected. Examples of the polymer material include polybutadiene, polystyrene, polyisoprene, polyethylene, polyacrylonitrile, polytetrafluoroethylene and the like. FIG. 2 is a structural formula showing an example of a polymer material.

In FIG. 2, cis-1,4 polyisoprene (hereinafter, may be simply referred to as "polyisoprene") is exemplified. The molecular chain 2 constituting the polyisoprene is an isoprene monomer composed of a methine group or the like (for example, −CH =,> C =), a methylene group (−CH ₂ −), and a methyl group (−CH _3). (Isoprene molecule) 3 is linked at a degree of polymerization n. In addition, a polymer other than polyisoprene may be used as the polymer.

In the simulation method of the present embodiment, the plurality of types of polymer materials whose performances are compared include at least a first polymer material and a second polymer material. In the simulation method of the present embodiment, the performance of the first polymer material and the performance of the second polymer material are compared. As the first polymer material and the second polymer material, for example, different polymer materials are selected from the above-mentioned polymer materials. These first polymer materials and second polymer materials have different interactions between the molecular chains 2 and 2. The second polymer material of the present embodiment is exemplified as having a stronger interaction than the first polymer material, but may have a weaker interaction than the first polymer material.

As the interaction of the present embodiment, the case of physical adsorption is exemplified. The physical adsorption between the molecular chains 2 and 2 is a phenomenon in which the molecular chains 2 and 2 are adsorbed mainly by the van der Waals interaction and the electrostatic interaction acting between the molecular chains 2 and 2. It is expected that the stronger the physical adsorption between the molecular chains 2 and 2, the better the fracture resistance of the polymer material. The strength of such physical adsorption can be appropriately set in an actual polymer material by, for example, adjusting the chemical structure of the molecule.

FIG. 3 is a flowchart showing an example of the processing procedure of the simulation method. In the simulation method of this embodiment, first, the first polymer material model is set in the computer 1 (first model setting step S1). FIG. 4 is a conceptual diagram showing an example of the first polymer material model 10A.

In the first model setting step S1, a first polymer material model 10A including a plurality of first particles 13 (shown in FIG. 7) is defined based on the first polymer material. FIG. 5 is a flowchart showing an example of the processing procedure of the first model setting step S1.

In the first model setting step S1 of the present embodiment, first, the cell 4, which is a virtual space corresponding to a part of the first polymer material, is defined in the computer 1 (step S11). The cell 4 has at least a pair of faces 5, 5 facing each other, and in the present embodiment, three pairs of faces 5, 5 facing each other, and is defined as a rectangular parallelepiped or a cube (in this example, a cube). Periodic boundary conditions are defined on each of the surfaces 5 and 5. By using such a cell 4, in the coarse-grained molecular dynamics calculation described later, for example, the first molecular chain model described later modeling the molecular chain 2 (shown in FIG. 2) of the first polymer material. With respect to 11, it can be calculated that a part of the first molecular chain model 11 that has exited from the surface 5a on one side enters from the surface 5b on the other side. Therefore, the cell 4 can be treated as if the surface 5a on one side and the surface 5b on the other side are continuous (connected).

Each length L1 of one side of the cell 4 can be appropriately set. The length L1 of this embodiment is preferably three times or more the radius of inertia (not shown), which is an amount indicating the spread of the first molecular chain model 11 described later. As a result, in the coarse-grained molecular dynamics calculation described later, it is possible to appropriately calculate the spatial extent of the first molecular chain model 11 by preventing the occurrence of collision with the self-image due to the periodic boundary conditions. Further, the size of the cell 4 is set to a stable volume at, for example, 1 atm. Thereby, the cell 4 can define the volume of at least a part of the polymer material to be analyzed.

FIG. 6 is an enlarged view of part A of FIG. Inside the cell 4, for example, a plurality of small regions 9 divided into cubes are defined. A node 9t is set in each small area 9. Such a small region 9 is used for tracking the first particle 13 (shown in FIG. 7) described later in the molecular dynamics calculation described later. It is desirable that the length L2 of one side of the small region 9 is set to, for example, about 0.1 to 5 times the diameter of the first particle 13.

Next, in the first model setting step S1 of the present embodiment, the first molecular chain model in which the molecular chain 2 (shown in FIG. 2) of the first polymer material is modeled inside the cell 4 shown in FIG. 11 is defined (step S12). In step S12, at least one (for example, 10 to 1,000,000) first molecular chain model 11 is arranged inside the cell 4.

FIG. 7 is a conceptual diagram showing an example of the first molecular chain model 11. The first molecular chain model 11 of the present embodiment is defined based on the molecular structure of the molecular chain 2 (shown in FIG. 2) of the first polymer material. The first molecular chain model 11 contains a plurality of first particles 13. The first polymer material model 10A of the present embodiment comprises only the first particles 13. The adjacent first particles 13 and 13 are connected by the first binding chain model 15.

The first particle 13 replaces the monomer 3 (shown in FIG. 2) of the molecular chain 2 (shown in FIG. 2) of the first polymer material or the structural unit forming a part of the monomer 3. As a result, a plurality of (for example, 10 to 5000) first particles 13 are set in the first molecular chain model 11. The first particle 13 is treated as a mass point of the equation of motion in the coarse-grained molecular dynamics calculation described later. That is, parameters such as mass, diameter, charge, and initial coordinates are defined in the first particle 13.

FIG. 8 is a conceptual diagram showing an example of the interaction potential between the first particles 13 and 13. The first binding chain model 15 is defined by the interaction potential P3. In the interaction potential P3, the extension length between the first particles 13 and 13 is defined.

The interaction potential P3 can be appropriately defined. The interaction potential P3 can be defined by, for example, the sum of the Lennard-Jones potential and the FENE potential as in the conventional case. For the constants defined for each potential, see, 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), and can be set as appropriate. Thereby, in step S12, it is possible to define a linear first molecular chain model 11 in which the first particles 13 are elastically constrained.

Next, in the first model setting step S1 of the present embodiment, the first interaction potential P1 is defined between the first particles 13 and 13 (step S13). The first interaction potential P1 of the present embodiment is defined between the first particles 13 and 13 of the adjacent first molecular chain models 11 and 11. The first interaction potential P1 is, for example, the Lennard-Jones potential as in the conventional case. The constant of the first interaction potential P1 can be appropriately set based on the above paper. The first polymer material model 10A is stored in the computer 1.

Next, in the simulation method of the present embodiment, the second polymer material model 10B (shown in FIG. 10) is set in the computer 1 (second model setting step S2). In the second model setting step S2, the second polymer material model 10B including the plurality of second particles 14 (shown in FIG. 10) is defined based on the second polymer material. FIG. 9 is a flowchart showing an example of the processing procedure of the second model setting step S2.

In the second model setting step S2 of the present embodiment, first, a cell which is a virtual space corresponding to a part of the second polymer material is defined in the computer 1 (step S21). As shown in FIG. 4, in the step S21, the cell 4 is defined in the same procedure as the step S11 of the first model setting step S1. Each length L1 of one side of the cell 4 of the second polymer material model 10B (not shown) is an inertial radius (not shown) which is an amount indicating the spread of the second molecular chain model 12 (shown in FIG. 10) described later. 3 times or more is desirable. Similar to cell 4 of the first polymer material model 10A, a plurality of small regions 9 (shown in FIG. 6) divided into cubes are defined inside the cell 4.

Next, in the second model setting step S2 of the present embodiment, the second molecular chain model in which the molecular chain 2 (shown in FIG. 2) of the second polymer material is modeled inside the cell 4 shown in FIG. 12 (shown in FIG. 10) is defined (step S22). In step S22, at least one (for example, 10 to 1,000,000) second molecular chain model 12 is arranged inside the cell 4.

FIG. 10 is a conceptual diagram showing an example of the interaction potential between the second particles 14 and 14. The second molecular chain model 12 of the present embodiment is defined based on the molecular structure of the molecular chain 2 (shown in FIG. 2) of the second polymer material. The second molecular chain model 12 contains a plurality of second particles 14. The second polymer material model 10B of the present embodiment comprises only the second particles 14. The adjacent second particles 14 and 14 are connected by a second binding chain model 16.

The second particle 14 is obtained by substituting the monomer 3 (shown in FIG. 2) of the molecular chain 2 of the second polymer material or the structural unit forming a part of the monomer 3. As a result, a plurality of (for example, 10 to 5000) second particles 14 are set in the second molecular chain model 12. The second particle 14 is treated as a mass point of the equation of motion in the coarse-grained molecular dynamics calculation described later. That is, parameters such as mass, diameter, charge, and initial coordinates are defined in the second particle 14.

The second bound chain model 16 is defined by the interaction potential P4. The extension length between the second particles 14 and 14 is defined in the interaction potential P4. The interaction potential P4 can be appropriately defined. The interaction potential P4 can be defined by, for example, the sum of the Lennard-Jones potential and the FENE potential as in the conventional case. The constants defined for each potential are appropriately set based on the above paper. Thereby, in step S22, it is possible to define a linear second molecular chain model 12 in which the second particle 14 is stretchably constrained.

Next, in the second model setting step S2 of the present embodiment, the second interaction potential P2 is defined between the second particles 14 and 14 (step S23). The second interaction potential P2 of the present embodiment is defined between the second particles 14 and 14 of the adjacent second molecular chain models 12 and 12. The second interaction potential P2 is the Lennard-Jones potential, like the first interaction potential P1. The constant of the second interaction potential P2 can be appropriately set based on the above paper.

As described above, the first polymer material and the second polymer material of the present embodiment have different interactions between the molecular chains 2 and 2 shown in FIG. Therefore, in the step S23 of the present embodiment, the strength of the second interaction potential P2 (shown in FIG. 10) and the strength of the first interaction potential P1 (shown in FIG. 8) are made different from each other. Further, the second polymer material of the present embodiment has a stronger interaction than the first polymer material. Therefore, in the step S23 of the present embodiment, the strength of the second interaction potential P2 is set to be larger than the strength of the first interaction potential P1.

The intensity of the first interaction potential P1 and the intensity of the second interaction potential P2 are defined by the potential depth ε of the Lennard-Jones potential. In the present embodiment, the depth ε of the second interaction potential P2 is set to be larger than the depth ε of the first interaction potential P1. As a result, in the simulation method of the present embodiment, the first polymer material model 10A and the second polymer material model 10B in which the strength of the first interaction potential P1 and the strength of the second interaction potential P2 are different from each other are set, respectively. be able to. The depth ε of the first interaction potential P1 and the depth ε of the second interaction potential P2 can be set as appropriate, and examples are as follows. The second polymer material model 10B is stored in the computer 1.
Depth of first interaction potential ε: 1.0
Depth of second interaction potential ε: 2.0

Next, in the simulation method of the present embodiment, the computer 1 calculates the structural relaxation of the first polymer material model 10A and the second polymer material model 10B, respectively (step S3). In step S3 of the present embodiment, the structural relaxation of the first polymer material model 10A and the second polymer material model 10B is calculated based on the coarse-grained molecular dynamics calculation, respectively.

In the coarse-grained molecular dynamics calculation of the present embodiment, for example, for cell 4 (shown in FIG. 4), the first molecular chain model 11 (shown in FIG. 8) and the second molecular chain model 12 (shown in FIG. 10) are used for a predetermined time. Newton's equation of motion is applied as if (shown in) follows classical mechanics. Then, the movements of the first molecular chain model 11 and the second molecular chain model 12 at each time are tracked for each unit time of the simulation. The calculation of structural relaxation can be processed using, for example, COGNAC included in the soft material comprehensive simulator (J-OCTA) manufactured by JSOL Corporation, or VSOP.

By the way, in the conventional simulation method, each polymer material model (not shown) defined for comparing the performance of a plurality of types of polymer materials has different strengths of interaction potentials. Then, in the conventional simulation method, the structural relaxation of each polymer material model is calculated based on the interaction potential under the condition that the density and temperature of the particles are the same as each other. Therefore, in each polymer material model, the distribution of particles after the relaxation calculation is different, and the internal stress after the relaxation calculation is calculated to have different values. Therefore, in the conventional simulation method, there is a problem that the physical quantities due to the deformation of each polymer material model calculated after that cannot be compared accurately.

In step S3 of the present embodiment, in the first polymer material model 10A (shown in FIG. 8) and the second polymer material model 10B (shown in FIG. 10) under the condition that the pressure and the temperature are the same as each other. Structural relaxation is calculated. Further, in the step S3 of the present embodiment, the structural relaxation is calculated under the condition that the number (total number) of the first particle 13 and the second particle 14 is constant.

In step S3 of the present embodiment, first, the structural relaxation of the first polymer material model 10A (shown in FIG. 8) is calculated. This structural relaxation calculation is performed under the condition that the pressure, temperature, and the number of particles (first particle 13 in this example) of the first polymer material model 10A are constant (that is, the NPT ensemble). It is calculated until the initial arrangement of the single molecule chain model 11 is sufficiently relaxed. As a result, in step S3, the equilibrium state (state in which the structure is relaxed) of the first molecular chain model 11 can be calculated. The calculation of this structural relaxation is performed under the condition that the volume, temperature, and the number of particles (first particle 13 in this example) of the first polymer material model 10A are constant (that is, NVT ensemble). , It may be calculated until the initial arrangement of the first molecular chain model 11 is sufficiently relaxed. The structurally relaxed first polymer material model 10A is stored in the computer 1.

Next, in step S3 of the present embodiment, the structural relaxation of the second polymer material model 10B (shown in FIG. 8) is calculated. In the calculation of the structural relaxation of the second polymer material model 10B, the pressure and temperature of the second polymer material model 10B are the same as the pressure and temperature of the first polymer material model 10A shown in FIG. 8, respectively. It is calculated until the initial arrangement of the second molecular chain model 12 is sufficiently relaxed under the condition of. Further, the structural relaxation of the present embodiment is calculated under the condition that the number of the second particles 14 is constant.

The pressure control of the second polymer material model 10B is carried out based on, for example, the pressure control of Andersen and the pressure control of Parrinello-Rahman and the like. In step S3, the equilibrium state (state in which the structure is relaxed) of the second molecular chain model 12 can be calculated.

FIG. 11 is a graph showing the relationship between the volume fraction with respect to the initial volume of the second polymer material model 10B and the time. FIG. 12 is a graph showing the relationship between the internal stress of the first polymer material model 10A and the internal stress of the second polymer material model 10B and the time. In the present embodiment, the strength of the second interaction potential P2 of the second polymer material model 10B is larger than the strength of the first interaction potential P1 of the first polymer material model 10A. In such a case, in step S3, as shown in FIG. 11, the volume of the second polymer material model 10B is made smaller than the initial volume, and the structural relaxation of the second polymer material model 10B is calculated. NS. As a result, even if the distribution of the second particles 14 of the second polymer material model 10B and the distribution of the first particles 13 of the first polymer material model 10A are different, as shown in FIG. 12, the second The internal stress of the polymer material model 10B can be approximated to the internal stress of the first polymer material model 10A.

As described above, in step S3, in the first polymer material model 10A and the second polymer material model 10B, the structural relaxation can be calculated under the condition that the pressure and the temperature are the same, so that the relaxation calculation can be performed. The internal stresses of the subsequent polymer material models 10A and 10B can be approximated. Further, in the present embodiment, since the number of the first particles 13 and the number of the second particles 14 are constant, the internal stresses of the polymer material models 10A and 10B after the relaxation calculation are surely obtained. Can be approximated. The structurally relaxed second molecular chain model 12 is stored in the computer 1.

Next, in the simulation method of the present embodiment, the computer 1 deforms the first polymer material model 10A and the second polymer material model 10B, respectively, to transform the first polymer material model 10A and the second polymer material model 10A and the second polymer material model. The physical quantities associated with the deformation of 10B are calculated respectively (step S4).

In step S4, as shown in FIG. 4, a uniaxial tensile test for pulling the first polymer material model 10A and the second polymer material model 10B in a predetermined direction is calculated. The direction of pulling the polymer material model can be appropriately selected, and in this example, the polymer material model is pulled in the z-axis direction.

The deformation calculation of the first polymer material model 10A and the second polymer material model 10B is performed, for example, in the z-axis direction according to the procedure described in Patent Document (Japanese Unexamined Patent Publication No. 2016-81297). One end of the models 10A and 10B (one side surface 5a of the cell 4 shown in FIG. 5) and the other end of the polymer material models 10A and 10B (the other side surface 5b of the cell 4 shown in FIG. 5) The elongations of the polymeric material models 10A and 10B are calculated so as to be separated from each other. The elongation calculation of the polymer material models 10A and 10B is calculated based on the molecular dynamics calculation.

FIG. 13A is a conceptual diagram showing a part of the first polymer material model 10A before the deformation calculation. FIG. 13B is a conceptual diagram showing a part of the first polymer material model 10A after the deformation calculation. As shown in FIG. 13A, before the deformation calculation of each polymer material (in this example, the first polymer material model 10A), each small region 9 inside the cell 4 has the above-mentioned structural relaxation. By calculation, the first particle 13 of the first molecular chain model 11 is arranged.

In step S4, the thermal motions of the first molecular chain model 11 and the second molecular chain model 12 (not shown) are calculated by the elongation calculation of the first polymer material model 10A and the second polymer material model 10B. Such thermal motion is calculated based on the strain applied to each polymer material model 10A and 10B, the above-mentioned interaction potentials P1 to P4 shown in FIGS. 8 and 10, and the equation of motion. As a result, as shown in FIG. 13B, the first particle 13 of the first molecular chain model 11 and the second particle 14 (not shown) of the second molecular chain model 12 are arranged in the cell 4. A small region 9 that is not formed is formed. Such a small region 9 is defined as a void 26 formed in each of the polymer material models 10A and 10B. Such pores 26 reproduce the destruction of each polymer material model.

As a deformation condition, pores 26 are formed in at least a part of the region where the first particle 13 of the first molecular chain model 11 and the second particle (not shown) of the second molecular chain model 12 are arranged. If it can be done, it can be set as appropriate. As an example of the deformation conditions, the strain applied to the first polymer material model 10A and the second polymer material model 10B is about 0.1 to 0.3, and the deformation rate V1 per strain (FIG. 4). (Shown in) is about 1000 to 10000τ.

In step S4, from the start of deformation to the end of deformation of the first polymer material model 10A and the second polymer material model 10B (not shown), each polymer is used for each unit step (MD step) of molecular dynamics calculation. The physical quantities associated with the deformation of the material models 10A and 10B are calculated. As the physical quantity, it can be appropriately adopted. The physical quantity of the present embodiment includes the stress of the first polymer material model 10A and the stress of the second polymer material model 10B. In step S4, the stress components in the elongation direction of the polymer material models 10A and 10B are calculated for each strain applied to the polymer material models 10A and 10B. Thereby, in the simulation method of the present embodiment, the stress-strain curve showing the relationship between the stress and the strain of each polymer material model 10A and 10B can be obtained.

Further, as the physical quantities of the present embodiment, the parameters relating to the pores 26 (shown in FIG. 13B) of the first polymer material model 10A and the pores 26 (not shown) of the second polymer material model 10B are shown. May include parameters related to. Regarding the parameters related to the pores 26, for example, the total volume of the pores 26 formed in the entire system of the first polymer material model 10A and the total volume of the pores 26 formed in the entire system of the second polymer material model 10B. The volume, the ratio of the total volume of the pores 26 to the volume of the first polymer material model 10A (hereinafter, may be simply referred to as "volume fraction of the pores"), or the volume of the second polymer material model 10B. The volume fraction of the vacancies can be appropriately selected.

In step S4 of the present embodiment, the total volume of the pores 26 formed in the entire system of the polymer material model is calculated for each strain applied to each of the polymer material models 10A and 10B. Thereby, in the simulation method of the present embodiment, it is possible to acquire a graph showing the relationship between the parameter (volume fraction of the pores) related to the pores 26 of each polymer material model 10A and 10B and the strain. The volume fraction of the pores may be the ratio of the volume of the pores 26 to the volume change of the polymer material model (cell 4) due to the strain generated by the deformation calculation.

In step S4 of the present embodiment, the deformations of the polymer material models 10A and 10B are calculated for the first polymer material model 10A and the second polymer material model 10B in which the internal stresses after structural relaxation are approximated to each other. NS. Therefore, the scales of physical quantities of the polymer material models 10A and 10B can be aligned with each other. Therefore, in the simulation method of the present embodiment, the deformations of the polymer material models 10A and 10B in consideration of the interaction between the first interaction potential P1 and the second interaction potential P2 are calculated by aligning the scales of physical quantities. Therefore, it is possible to accurately compare the physical quantities associated with the deformation of each polymer material model 10A and 10B. The physical quantities of the polymer material models 10A and 10B are stored in the computer 1.

Next, in the simulation method of the present embodiment, the computer 1 compares the physical quantities of the first polymer material model 10A and the second polymer material model 10B (step S5). In step S5, the parameters related to stress and pores are compared for each polymer material model 10A and 10B, respectively. As a result, in the simulation method of the present embodiment, the performance (for example, fracture characteristics, etc.) of polymer materials having different interactions (physisorption in this example) between the molecular chains 2 and 2 can be evaluated. , Useful for the development of polymer materials. Further, in the simulation method of the present embodiment, various interaction potentials are set between the first particles 13 and 13 or between the second particles 14 and 14, and parameters for evaluating the physical quantities of the polymer material models 10A and 10B are evaluated. The study makes it possible to present the direction of development of polymer materials.

Next, in the simulation method of the present embodiment, the computer 1 determines whether or not there is a polymer material model having a good physical quantity (step S6). In step S6, the quality of the physical quantities of the polymer material models 10A and 10B is determined based on a predetermined threshold value. In the present embodiment, when the stress of each polymer material model 10A and 10B is larger than the threshold value, it is judged that the fracture resistance is excellent. Further, in the present embodiment, when the parameters relating to the pores 26 of the polymer material models 10A and 10B are smaller than the threshold value, it is judged that the fracture resistance is excellent. The threshold value can be appropriately set according to, for example, the fracture resistance required for the polymer material.

When it is determined in step S6 that a polymer material model having a good physical quantity (first polymer material model 10A or second polymer material model 10B) exists (“Y” in step S6), the physical quantity is good. A polymer material is produced based on various conditions set in the polymer material model (step S7). On the other hand, when it is determined in step S6 that there is no polymer material model having a good physical quantity (“N” in step S6), the first interaction potential P1 (shown in FIG. 8) or the second interaction potential P2 (shown in FIG. 10) is changed (step S8), and steps S3 to S6 are carried out again. As a result, the simulation method of the present embodiment can develop a polymer material having excellent fracture resistance.

The first polymer material model 10A of the present embodiment is exemplified to be composed of only the first particle 13, but is not limited to such an embodiment. The first polymer material model 10A may be composed of the first particle 13 and the second particle 14. Thereby, the first polymer material model 10A can model the third polymer material in which a plurality of types of polymer materials (in this example, the first polymer material and the second polymer material) are blended. .. In this embodiment, the second polymer material is exemplified as having a stronger interaction than the first polymer material. FIG. 14 is a conceptual diagram showing an example of the first polymer material model 10A including the first particle 13 and the second particle 14. In this embodiment, the same configurations as those in the previous embodiments may be designated by the same reference numerals and description thereof may be omitted.

In the first model setting step S1 of this embodiment, the first polymer material model 10A including the plurality of first particles 13 and the plurality of second particles 14 is defined based on the third polymer material. FIG. 15 is a flowchart showing an example of the processing procedure of the first model setting step S1 of another embodiment of the present invention.

In the first model setting step S1 of this embodiment, the first molecular chain model 11 and the second molecular chain model 12 are defined inside the cell 4 (step S14). In step S14, at least one (for example, 5 to 500,000) first molecular chain model 11 and at least one (for example, 5 to 500,000) first molecular chain model 11 inside the cell 4. The bimolecular chain model 12 is arranged.

The first molecular chain model 11 is defined based on the molecular structure of the molecular chain 2 (shown in FIG. 2) of the first polymer material constituting the third polymer material. The details of the first molecular chain model 11 are as described in the previous embodiment. Thereby, in step S14, the linear first molecular chain model 11 is defined.

The second molecular chain model 12 is defined based on the molecular structure of the molecular chain 2 (shown in FIG. 2) of the second polymer material constituting the third polymer material. The details of the second molecular chain model 12 are as described in the previous embodiment. Thereby, in step S14, the linear second molecular chain model 12 is defined.

Next, in the first model setting step S1 of this embodiment, the first interaction potential P1 is defined between the first particles 13 and 13 (step S13), and the second mutual between the second particles 14 and 14 is defined. The working potential P2 is defined (step S15). The first interaction potential P1 is defined between the first particles 13 and 13 of the adjacent first molecular chain models 11 and 11. The second interaction potential P2 is defined between the second particles 14, 14 of the adjacent second molecule chain models 12, 12. The details of the first interaction potential P1 and the second interaction potential P2 are as described in the previous embodiment.

Next, in the first model setting step S1 of this embodiment, the third interaction potential P7 is defined between the first particle 13 and the second particle 14 (step S16). The third interaction potential P7 is defined between the first particle 13 of the adjacent first molecular chain model 11 and the second particle 14 of the second molecular chain model 12. The third interaction potential P7 is, for example, the Lennard-Jones potential as in the conventional case. The constant of the third interaction potential P7 can be appropriately set based on the above paper. The depth ε of the third interaction potential of this embodiment is set to, for example, 1.0. The first polymer material model 10A of this embodiment is stored in the computer 1.

Next, in the step S3 of this embodiment, similarly to the step S3 of the previous embodiment, in the first polymer material model 10A and the second polymer material model 10B, under the condition that the pressure and the temperature are the same as each other. , Structural relaxation is calculated respectively. Further, in the step S3 of this embodiment, the structural relaxation is calculated under the condition that the numbers (total number) of the first particles 13 and the second particles 14 are constant, as in the step S3 of the previous embodiment. Is desirable.

In the second polymer material model 10B of this embodiment, only the second interaction potential P2, which is stronger than the first interaction potential P1, is defined. In such a case, in step S3, the volume of the second polymer material model 10B is made smaller than the volume of the first polymer material model 10A, and the structural relaxation of the second polymer material model 10B is calculated. As a result, even if the distribution of the second particle 14 of the second polymer material model 10B and the distribution of the first particle 13 and the second particle 14 of the first polymer material model 10A are different, the second polymer material The internal stress of the model 10B can be approximated to the internal stress of the first polymer material model 10A.

In step S4 of this embodiment, deformation calculation is performed on the first polymer material model 10A and the second polymer material model 10B in which the internal stresses after structural relaxation are approximated to each other. In the simulation method of this embodiment, as in the previous embodiments, each polymer material model considering the interaction of the first interaction potential P1, the second interaction potential P2, and the third interaction potential P3. The deformations of 10A and 10B can be calculated by aligning the scales of physical quantities. Therefore, the simulation method of this embodiment can accurately compare the physical quantities associated with the deformation of the polymer material models 10A and 10B.

The second polymer material model 10B (shown in FIG. 10) of the embodiment so far has been exemplified to consist of only the second particle 14, but is not limited to such an embodiment. The second polymer material model 10B may be composed of the first particle 13 and the second particle 14, as in the case of the first polymer material model 10A (shown in FIG. 14) of the previous embodiment, for example.

The first polymer material model 10A and the second polymer material model 10B of the embodiments so far have been exemplified to be composed of the first particle 13 or the second particle 14, but the present invention is not limited to such an embodiment. The first polymer material model 10A and the second polymer material model 10B include, for example, particles different from the first particles 13 and the second particles 14 (not shown), and the first interaction potential between the particles is included. Interaction potentials (not shown) different from P1, the second interaction potential P2, and the third interaction potential P7 may be defined. Since various interaction potentials can be defined in such a first polymer material model 10A and a second polymer material model 10B, it is useful for developing a polymer material having excellent fracture resistance.

Further, inside the cell 4, a coupling modeling a particle (not shown) constituting a filler model modeling a filler contained in a polymer material and a coupling agent for binding the molecular chain 2 to the filler is modeled. Particles (not shown) that make up the agent model may be further defined. These particles may be defined as the first particle 13 or the second particle 14. As a result, in the simulation method, it is possible to accurately compare the physical quantities associated with the deformation of the polymer material model after the coupling reaction.

In the simulation methods of the conventional embodiments, the first polymer material model 10A and the second polymer material model 10B are set and the performances of the polymer materials are compared, but the present invention is not limited to such an embodiment. For example, a third polymer material model (not shown) may be set together with the first polymer material model 10A and the second polymer material model 10B to compare the performance of the polymer materials. Such a third polymer material model has a structure under the condition that the pressure and temperature of the first polymer material model 10A and the second polymer material model 10B are the same in the step S3 for calculating the structural relaxation. The mitigation is calculated. Thereby, the internal stress of the third polymer material model can be approximated to the internal stress of the first polymer material model 10A and the internal stress of the second polymer material model 10B. Therefore, since the scales of the physical quantities of the first polymer material model 10A, the second polymer material model 10B, and the third polymer material model can be aligned with each other, the physical quantities accompanying the deformation of each polymer material model can be obtained. It is possible to compare with high accuracy. In step S3, it is desirable that the structural relaxation is calculated under the condition that the number of particles of each polymer material is constant, as in the conventional embodiments. In addition to the first polymer material model 10A, the second polymer material model 10B, and the third polymer material model, a plurality of polymer material models are set to compare the performance of the polymer materials. May be good.

Although the particularly preferable 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 into various embodiments.

Based on the treatment procedure shown in FIG. 3, the performances of the first polymer material, the second polymer material, and the third polymer material blended with the first polymer material and the second polymer material were compared. (Examples and comparative examples). In the examples and comparative examples, the first polymer material model that models the first polymer material, the second polymer material model that models the second polymer material, and the third polymer material are modeled. A third polymer material model was set for each.

The first polymer material model is composed of only the first particles, and the first interaction potential is defined between the first particles. The second polymer material model is composed of only the second particles, and the second interaction potential is defined between the second particles. The third polymer material model is composed of the first particle and the second particle, and has a first interaction potential, a second interaction potential, and a second particle between the first particle and the second particle. 3 Interaction potentials are defined.

Then, in the examples and comparative examples, the structural relaxations of the first polymer material model, the second polymer material model, and the third polymer material model were calculated, and the physical quantities associated with the deformation after the structural relaxation were calculated. ..

The step of calculating the structural relaxation of the examples was performed in each polymer material model under the condition that the pressure and temperature were the same as each other. Further, in the examples, the structural relaxation was calculated under the condition that the number (total number) of the first particles and the second particles was constant. On the other hand, in the comparative example, the volume and temperature of each polymer material model and the conditions under which the numbers of the first particles and the second particles are constant are the same as the simulation method of Patent Document (Japanese Unexamined Patent Publication No. 2016-81297). Under, the structural relaxation of each polymer material model was calculated.

In the deformation calculation of the example, the tension calculation in the z-axis direction was performed based on the following friction coefficient and deformation speed. In the deformation calculation of the comparative example, after the tensile calculation in the z-axis direction is performed based on the following initial friction coefficient and initial deformation rate, the friction coefficient is set to be the same as the friction coefficient in the above paper, and the polymer is polymerized. A relaxation calculation of 138τ was performed with the volume of the material model fixed. The common specifications of the examples and the comparative examples are as follows.

cell:
One side length L1: 22.74σ (coarse grained particle density: 0.85 (1 / σ ³ ))
Length of one side of small area L2: 1.5σ
First polymer material model:
Number of first molecular chain models: 500
First particles constituting the first molecular chain model: 20
Intensity of first interaction potential (depth ε): 1.0
Second polymer material model:
Number of second molecular chain models: 500
Second particles constituting the second molecular chain model: 20
Intensity of second interaction potential (depth ε): 2.0
Third polymer material model:
Number of first molecular chain models: 250
First particles constituting the first molecular chain model: 20
Intensity of first interaction potential (depth ε): 1.0
Number of second molecular chain models: 250
Second particles constituting the second molecular chain model: 20
Intensity of second interaction potential (depth ε): 2.0
Intensity of third interaction potential (depth ε): 1.0
Crosslink density: 0.0072245 (1 / σ ³ )
Deformation calculation:
Distortion: 0.3
Example:
Friction coefficient: Same as the friction coefficient in the above paper
Deformation speed: 460τ / distortion
Comparative example:
Initial coefficient of friction: 10 times that of the above paper
Initial deformation rate: 0.4τ / distortion

FIG. 16 is a graph showing the relationship between the volume fraction of each polymer material model and the time of day with respect to the initial volume of the example. FIG. 17 is a graph showing the relationship between the internal stress of the first polymer material model, the internal stress of the second polymer material model, the internal stress of the third polymer material model, and the time of the embodiment. In the embodiment, as shown in FIG. 16, the volumes of the second polymer material model and the third polymer material model are made smaller than the initial volume, and the second polymer material model and the third polymer material are made smaller. The structural relaxation of the model was calculated. As a result, as shown in FIG. 17, the internal stress of the second polymer material model and the internal stress of the third polymer material model could be approximated to the internal stress of the first polymer material model.

FIG. 18 is a graph showing the relationship between stress and strain in Examples. FIG. 19 is a graph showing the relationship between the volume fraction of the pores of the embodiment and the strain. The volume fraction was calculated as the ratio of the volume of the pores to the amount of volume deformation of the cell due to the strain of 0.3. As shown in FIG. 18, the stress of the second polymer material model and the third polymer material model was calculated to be larger than that of the first polymer material model. As shown in FIG. 19, at 10 to 30% strain, the volume fraction of the pores of the second polymer material model and the third polymer material model is calculated to be smaller than that of the first polymer material model. rice field. In this way, in the examples, since the scales of the physical quantities of each polymer material model could be aligned with each other, the deformation of each polymer material model in consideration of the first interaction potential to the third interaction potential (physical adsorption). Was able to be calculated. These calculation results are close to the actual measurement results of physical quantities due to deformation of the first polymer material, the second polymer material, and the third polymer material. Therefore, in the examples, the physical quantities associated with the deformation of each polymer material model could be compared with high accuracy.

FIG. 20 is a graph showing the relationship between the internal stress and the time of each polymer material model of the comparative example. FIG. 21 is a graph showing the relationship between the volume fraction of the pores of the comparative example and the time. As shown in FIG. 20, in the comparative example, the internal stresses of the polymer material models after structural relaxation were significantly different from each other. Therefore, the comparative examples could not align the physical quantity scales of each polymer material model with each other. As a result, in the comparative example, the deformation of each polymer material model considering the first interaction potential to the third interaction potential (physisorption) could not be calculated. Therefore, as shown in FIG. 21, the first polymer In the material model, the body integration rate of the pores was calculated to be smaller than that in the second polymer material model and the third polymer material model. Therefore, in the comparative example, the physical quantities associated with the deformation of each polymer material model could not be compared accurately.

S3 Step of calculating the structural relaxation of the first polymer material model and the second polymer material model S4 Step of calculating the physical quantities of the first polymer material model and the second polymer material model

Claims (9)

A method for comparing the performance of a plurality of types of polymer materials including at least a first polymer material and a second polymer material using a computer.
A step of setting a first polymer material model in the computer, which includes a plurality of first particles based on the first polymer material and in which a first interaction potential is defined between the first particles.
A step of setting a second polymer material model in the computer, which includes a plurality of second particles based on the second polymer material and in which a second interaction potential is defined between the second particles.
A step in which the computer calculates the structural relaxation of the first polymer material model and the second polymer material model, respectively.
The computer deforms the first polymer material model and the second polymer material model after structural relaxation, respectively, and calculates the physical quantities of the first polymer material model and the second polymer material model due to the deformation. Including each calculation process
The step of calculating the structural relaxation is performed in the first polymer material model and the second polymer material model under the condition that the pressure and the temperature are the same as each other.
Coarse-grained molecular dynamics simulation method for polymer materials. The coarse-grained molecular dynamics simulation method according to claim 1, wherein the intensity of the first interaction potential and the intensity of the second interaction potential are different from each other. The first interaction potential and the second interaction potential are Lennard-Jones potentials.
The coarse-grained molecular dynamics simulation method for a polymer material according to claim 2, wherein the strength is the potential depth ε of the Lennard-Jones potential. The coarse-grained molecular dynamics simulation method for a polymer material according to any one of claims 1 to 3, wherein the first polymer material model comprises only the first particles. The first polymer material model comprises the first particles and the second particles.
The coarse-grained molecular dynamics simulation method for a polymer material according to any one of claims 1 to 3, wherein a third interaction potential is defined between the first particle and the second particle. The coarse-grained molecular dynamics simulation of a polymer material according to any one of claims 1 to 5, wherein the physical quantity includes the stress of the first polymer material model and the stress of the second polymer material model. Method. The coarse graining of the polymer material according to any one of claims 1 to 6, wherein the physical quantity includes a parameter relating to the pores of the first polymer material model and a parameter relating to the pores of the second polymer material model. Chemical molecular dynamics simulation method. The parameters related to the vacancies are the total volume of the vacancies, the ratio of the total volume of the vacancies to the volume of the first polymer material model, or the volume of the vacancies to the volume of the second polymer material model. The coarse-grained molecular dynamics simulation method for a polymer material according to claim 7, which is the ratio of the total volume. The crude polymer material according to any one of claims 1 to 8, further comprising a step in which the computer compares the physical quantity of the first polymer material model with the physical quantity of the second polymer material model. Visualization molecular dynamics simulation method.

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