JP6772612B2 - How to create a polymer material model - Google Patents

Description

The present invention relates to a method for creating a polymeric material model that can be used in computer simulation.

Generally, a cross-linking agent such as sulfur is blended in a polymer material such as rubber in order to increase the elastic force. The cross-linking agent enhances the elastic force of the polymer material by binding (cross-linking) the molecular chains of the polymer material. When evaluating the physical properties of polymer materials using a computer, it is important to create a polymer material model that reproduces cross-linking.

The following Patent Document 1 proposes a method for creating a polymer material model that models a polymer material containing a cross-linking agent. In the method for creating Patent Document 1 below, first, a matrix model modeled using a plurality of polymer particle models and a cross-linking agent particle model modeled on a cross-linking agent are created as a virtual space corresponding to a part of a polymer material. It is placed in the cell that is. Next, the structural relaxation of the model in the cell is calculated based on the molecular dynamics calculation. Then, when the distance between the polymer particle model and the cross-linking agent particle model is equal to or less than a predetermined distance, the polymer particle model and the cross-linking agent particle model are combined.

JP 2015-187189

In the calculation of structural relaxation in Patent Document 1, the polymer particle model and the cross-linking agent particle model move independently based on the potential defined between the particle models. Therefore, for example, when a small crosslink density is set and the probability that the crosslinkable polymer particle model and the crosslinker particle model meet is low, it is often before the crosslinked polymer material model is created. There was a problem that it took time.

The present invention has been devised in view of the above circumstances, and an object of the present invention is to provide a method for creating a polymer material model capable of producing a crosslinked polymer material model in a short time.

The present invention is a method for creating a polymer material model that models a polymer material containing a cross-linking agent by using a computer, and a plurality of polymer particles are used based on the molecular chains of the polymer material. A process of inputting a matrix model having a model into the computer, a process of inputting a cross-linking agent particle model modeling the cross-linking agent into the computer, and a virtual space corresponding to a part of the polymer material. For the step of inputting a cell into the computer, the step of arranging a plurality of the matrix models in the cell, the step of defining the potential for attractive force and repulsive force acting between the polymer particle models, and the molecular dynamics calculation. Based on the first structural relaxation calculation step of calculating the structural relaxation of the model in the cell, and the pair of the above where the distance between the particle models is smaller than the predetermined distance between the different matrix models by the computer. It is characterized by comprising a bonding step of binding the polymer particle model via at least one of the cross-linking agent particle models.

In the method for producing a polymer material model according to the present invention, it is desirable that the particle size of the cross-linking agent particle model is smaller than the distance between the particle models.

In the method for producing the polymer material model according to the present invention, it is desirable to further include an expansion step of expanding the particle size of the cross-linking agent particle model to a predetermined particle size.

In the method for creating the polymer material model according to the present invention, it is desirable that the expansion step includes a second structural relaxation calculation step for calculating the structural relaxation of the model in the cell based on the molecular dynamics calculation.

In the method for creating a polymer material model according to the present invention, in the bonding step, a pair of polymer particle models in which the distance between the particle models is smaller than the distance between different matrix models is used as the cross-linking agent particle model. A step of defining a bound model pair bound without a bond, and a third structural relaxation calculation step of calculating the structural relaxation of the model in the cell based on the molecular dynamics calculation after defining the binding model pair. After the third structural relaxation calculation step, it is desirable to include a step of replacing the bond between the pair of polymer particle models constituting the bond model pair with a bond via at least one crosslinker particle model. ..

In the method for creating a polymer material model of the present invention, after calculating the structural relaxation of a plurality of matrix models arranged in a cell, a pair in which the distance between particle models is smaller than a predetermined distance between different matrix models. The polymer particle model of is bound via at least one crosslinker particle model. Therefore, the method for creating a polymer material model of the present invention is, for example, to create a polymer material model that reflects the chemical structure and chemical properties as compared with the conventional method for creating a polymer particle model in which a pair of polymer particle models are simply bonded. Can be done.

Moreover, in the method for creating a polymer material model of the present invention, polymer particle models that are close to each other can be bonded to each other via a cross-linking agent particle model without structural relaxation calculation of the cross-linking agent particle model. Therefore, in the method for creating a polymer material model of the present invention, the polymer particle model and the cross-linking agent particle model can be bonded in a short time even if a small cross-linking density is set. Therefore, the method for creating a polymer material model of the present invention can create a crosslinked polymer material model in a short time.

It is a perspective view which shows an example of the computer which executes the production method of this invention. It is a structural formula of polybutadiene. It is a flowchart which shows an example of the processing procedure of the production method of this embodiment. It is a conceptual diagram which shows an example of a matrix model and a cross-linking agent particle model. It is a figure which shows an example of the cell which the matrix model is arranged inside. It is a flowchart which shows an example of the processing procedure of a bonding process. It is a flowchart which shows an example of the processing procedure of the combination model pair definition process. (A) is a diagram for explaining the combination model pair definition process, and (b) is a diagram for explaining the replacement process. It is a flowchart which shows an example of the processing procedure of a replacement process. It is a flowchart which shows an example of the processing procedure of the production method of another embodiment of this invention. It is a flowchart which shows an example of the processing procedure of the replacement process of another embodiment of this invention. (A) is a diagram for explaining an example of a replacement step of another embodiment of the present invention, and (b) is a diagram for explaining an example of a processing procedure for an expansion step. It is a flowchart which shows an example of the processing procedure of an expansion process. It is a flowchart which shows an example of the processing procedure of the replacement process of still another Embodiment of this invention. (A) is a diagram for explaining an example of a replacement step of still another embodiment of the present invention, and (b) is a diagram for explaining an example of a processing procedure of an expansion step of still another embodiment of the present invention. ..

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
In the method for creating a polymer material model of the present embodiment (hereinafter, may be simply referred to as “creating method”), a polymer material model that models a polymer material containing a cross-linking agent is created using a computer. Is a way to do it.

FIG. 1 is a perspective view showing an example of a computer that executes the production 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, 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 creation method of the present embodiment.

Examples of the polymer material include rubber, resin, elastomer and the like. Examples of the polymer material of the present embodiment include cis-1,4 polybutadiene (hereinafter, may be simply referred to as "polybutadiene"). FIG. 2 is a structural formula of polybutadiene. In the molecular chain 2 constituting this polybutadiene, the monomer 2a {-[CH ₂ -CH = CH-CH ₂ ]-} composed of a methylene group (-CH _2- ) and a methine group (-CH-) has a degree of polymerization. It is configured by being connected by. Further, a methyl group (-CH ₃ ) is linked to the end of the polymer material instead of the methylene group (-CH ₂ ). As the polymer material, a polymer material other than polybutadiene may be used. Examples of the cross-linking agent include sulfur that forms a monosulfide crosslink, a disulfide bridge, or a polysulfide crosslink, and an organic peroxide that forms a peroxide crosslink.

FIG. 3 is a flowchart showing an example of the processing procedure of the production method of the present embodiment. In the method for producing the present embodiment, first, a matrix model having a plurality of polymer particle models is input to the computer 1 based on the molecular chain 2 (shown in FIG. 2) of the polymer material (step S1). FIG. 4 is a conceptual diagram showing an example of the matrix model 3 and the cross-linking agent particle model 4.

As shown in FIG. 4, the matrix model 3 of this embodiment is defined as a coarse-grained model (Kremer-Grest model in this embodiment). The matrix model 3 of the present embodiment is configured to include a plurality of polymer particle models 5 and a first bond chain model 6 that connects adjacent polymer particle models 5 and 5.

The polymer particle model 5 replaces the monomer of the molecular chain or the structural unit forming a part of the monomer. When the polymer chain of the polymer material is polybutadiene, for example, 1.55 monomers are replaced with one polymer particle model 5, as in Japanese Patent Application Laid-Open No. 2015-94750. As a result, a plurality of (for example, 10 to 5000) polymer particle models 5 are set in the matrix model 3.

The polymer particle model 5 is treated as a mass point of the equation of motion in the molecular dynamics calculation. That is, parameters such as mass, volume, particle diameter D1 or electric charge are defined in the polymer particle model 5.

The first bond chain model 6 is defined by the potential P1 in which the extension length is set between the polymer particle models 5 and 5. Potential P1 of the embodiment, for example, like the invention described in JP-A-2015-94750, and LJ potential U _LJ (r _ij), is set as the sum of the binding potential U _FENE. For the LJ potential U _LJ (r _ij ) and the coupling potential U _FENE , the values of each constant and each variable can be set in the same way. This makes it possible to define a linear matrix model 3 in which the polymer particle model 5 is stretchably constrained. The matrix model 3 is stored in the computer 1.

Next, in the method of creating the present embodiment, the cross-linking agent particle model 4 that models the cross-linking agent is input to the computer 1 (step S2). The cross-linking agent particle model 4 of the present embodiment is set as one independent particle model. The cross-linking agent particle model 4 is treated as a mass point of the equation of motion in the molecular dynamics calculation. That is, parameters such as mass, volume, particle diameter D2, and electric charge are defined in the cross-linking agent particle model 4.

The particle size D2 of the cross-linking agent particle model 4 can be appropriately set. The particle size D2 of this embodiment is set to be the same as the particle size D1 of the polymer particle model 5. The cross-linking agent particle model 4 is stored in the computer 1.

Next, in the method of creating the present embodiment, a cell, which is a virtual space corresponding to a part of the polymer material, is input to the computer 1 (step S3). FIG. 5 is a diagram showing an example of a cell 7 in which the matrix model 3 is arranged inside. The cell 7 of the present embodiment is defined as the polymer material model 8 by arranging the matrix model 3 inside the cell 7.

The cell 7 of the present embodiment is defined as a rectangular parallelepiped having three pairs of planes 9a and 9b facing each other. Periodic boundary conditions are defined on the planes 9a and 9b. Such a cell 7 can be calculated so that, for example, a part of the matrix model 3 exiting from one plane 9a enters from the opposite plane 9b. Therefore, it can be treated as if one plane 9a and the other plane 9b are continuous (connected).

The lengths L3a, L3b and L3c of one side of the cell 7 can be appropriately set. It is desirable that the length L1 of this embodiment is at least twice the inertial radius (not shown) of the matrix model 3. The radius of inertia is a quantity indicating the spread of the matrix model 3. Such a cell 7 can appropriately calculate the spatial extent of the matrix model 3 in the molecular dynamics calculation because it can prevent the occurrence of collision with its own image due to the periodic boundary condition. Further, the size of the cell 7 is set to a stable volume at, for example, 1 atm. Such cells 7 can define at least a portion of the volume of the polymeric material. The cell 7 is stored in the computer 1.

Next, in the method of creating the present embodiment, a plurality of matrix models 3 are arranged in the cell 7 (step S4). In step S4, a plurality of matrix models 3 are randomly arranged in the internal space surrounded by the planes 9a and 9b of the cell 7. The number of matrix models 3 can be appropriately set according to, for example, the performance of the computer 1. Further, the number of matrix models 3 is preferably set based on the number density of 0.85 when the matrix model 3 is a Kremer-Grest model. In the present embodiment, for example, when the number of polymer particle models 5 constituting one matrix model 3 is set to 500 to 1000, the number of matrix models 3 can be set to 200 to 140000. The coordinate values of the polymer particle model 5 of the matrix model 3 arranged in the cell 7 and the like are stored in the computer 1.

Next, in the method for creating the present embodiment, the potential for attractive and repulsive forces to act between the polymer particle models 5 and 5 is defined (step S5). In step S5, the potential P2 is defined between the polymer particle models 5 and 5 of the adjacent matrix models 3 and 3. The potential P2, for example, in accordance with the procedure of JP-A-2015-94750, can be defined using the LJ potential U _LJ (r _ij). As a result, attractive and repulsive forces can be applied between the polymer particle models 5 and 5 in the molecular dynamics calculation described later. These potentials are stored in computer 1.

Next, in the method of creating the present embodiment, the computer 1 calculates the structural relaxation of the model in the cell 7 based on the molecular dynamics calculation (first structural relaxation calculation step S6). In the molecular dynamics calculation of the present embodiment, for example, Newton's equation of motion is applied to cell 7 assuming that the matrix model 3 follows classical mechanics for a predetermined time. Then, the movement of the polymer particle model 5 at each time is tracked for each unit time step. In the molecular dynamics calculation, the pressure and temperature are kept constant, or the volume and temperature are kept constant in the cell 7. As a result, in the first structural relaxation calculation step S6, the initial arrangement of the matrix model 3 can be accurately relaxed by approximating the molecular motion of the actual polymer material. Such a calculation of structural relaxation can be processed using, for example, COGNAC included in a soft material comprehensive simulator (J-OCTA) manufactured by JSOL Corporation.

Next, in the method of creating the present embodiment, the computer 1 determines whether or not the initial arrangement of the matrix model 3 can be sufficiently relaxed (step S7). When it is determined in step S7 that the initial arrangement of the matrix model 3 has been sufficiently relaxed (“Y” in step S7), the next joining step S8 is carried out. On the other hand, when it is determined that the initial arrangement of the matrix model 3 has not been sufficiently relaxed (“N” in step S7), one unit time step is advanced (step S9), and the first structural relaxation calculation step S6 And step S7 is carried out again. As a result, in the first structural relaxation calculation step S6, the equilibrium state (state in which the structure is relaxed) of the matrix model 3 can be reliably calculated. The calculation result of the structural relaxation is stored in the computer 1.

Next, in the production method of the present embodiment, the computer 1 bonds the different matrix models 3 and 3 via at least one cross-linking agent particle model 4 (bonding step S8). In the bonding step S8 of the present embodiment, at least one pair of polymer particle models 5 and 5 having a particle model-to-particle model distance L1 (shown in FIG. 8A) smaller than a predetermined distance L5 (not shown) is provided. It is bound via two cross-linking agent particle models 4. The inter-particle model distance L1 is defined as the shortest distance between the surfaces 5s of each polymer particle model 5, 5. FIG. 6 is a flowchart showing an example of the processing procedure of the joining step S8.

In the binding step S8 of the present embodiment, first, the computer 1 defines a binding model pair 10 in which a pair of polymer particle models 5 and 5 are bound between different matrix models 3 and 3 arranged in the cell 7 ( Combined model pair definition step S81). In the binding model pair definition step S81, a pair of polymer particles whose particle model-to-particle model distance L1 is smaller than the distance L5 (not shown) for all the matrix models 3 arranged in the cell 7 shown in FIG. The model 5 is bound without the cross-linking agent particle model 4. The distance L5 is appropriately set based on, for example, the structure of the matrix model 3 and the particle diameter D1 (shown in FIG. 4) of the polymer particle model 5. The distance L5 of this embodiment is set to, for example, 0.8 to 2.0σ. FIG. 7 is a flowchart showing an example of the processing procedure of the combination model pair definition step S81. FIG. 8A is a diagram for explaining the combination model pair definition step S81, and FIG. 8B is a diagram for explaining the replacement step.

In the binding model pair definition step S81 of the present embodiment, first, a pair of polymer particle models 5 and 5 to be bonded are specified between the different matrix models 3 and 3 (step S811). As shown in FIG. 8A, in step S811, a pair of polymer particle models 5 in which the inter-particle model distance L1 is smaller than the distance L5 (not shown) are specified. When a plurality of polymer particle models 5 having a particle model-to-particle model distance L1 smaller than the distance L5 are specified in one polymer particle model 5, they are bound to the polymer particle model 5 having the smallest particle-model distance L1. Specified as being.

Next, in the binding model pair definition step S81 of the present embodiment, the pair of polymer particle models 5 and 5 specified in step S811 are bound (step S812). In step S812, the pair of polymer particle models 5 and 5 are bonded via the second bond chain model 11. As a result, a binding model pair 10 in which the pair of matrix models 3 and 3 are coupled is defined. After step S812, the combined model pair 10 (shown in FIG. 8A) and the single matrix model 3 may coexist in the internal space of the cell 7 shown in FIG.

The second bond model 11 is defined by the potential P3 in which the extension length is set between the pair of polymer particle models 5 and 5. The second binding chain model 11 is also set by the sum of the LJ potential _ULJ (r _ij ) and the binding potential U _{FEN E} , similarly to the first binding chain model 6. In the present embodiment, the constants and variables set in the second binding chain model 11 are the same as the constants and variables set in the first binding chain model 6. The combined model pair 10 is stored in computer 1.

In the binding model pair definition step S81, when a pair of polymer particle models 5 and 5 satisfying the above conditions are bound to all the polymer particle models 5 constituting the matrix model 3 shown in FIG. The number of second bond model 11s tends to be larger than necessary between the matrix models 3 and 3. Therefore, in each matrix model 3, it is desirable that the polymer particle model 5 to be bonded (hereinafter, may be simply referred to as “bonding target polymer particle model 5A”) is predetermined. The number of the polymer particle model 5A to be bound defined in each matrix model 3 is set based on, for example, the crosslink density of the polymer material. The polymer particle model 5A to be bound in this embodiment is defined one by one in each matrix model 3. Thereby, in the production method of the present embodiment, for example, the upper limit of the number of the second bond chain model 11 can be set based on the crosslink density.

In the binding step S8 of the present embodiment, after the first structural relaxation calculation step S6 in which the initial arrangement of the matrix model 3 is relaxed, a pair of polymer particle models 5 and 5 are bonded to define a binding model pair 10. Therefore, the inside of the cell 7 including the combined model pair 10 tends to be unstable as a structure.

Therefore, in the coupling step S8 of the present embodiment, the computer 1 calculates the structural relaxation of the model in the cell 7 based on the molecular dynamics calculation (third structural relaxation calculation step S82).

In the third structural relaxation calculation step S82 of the present embodiment, the structural relaxation is calculated for each unit time step for the combined model pair 10 arranged in the cell 7. When the single matrix model 3 is included in the cell 7, the structural relaxation is calculated for the single matrix model 3 as well. The molecular dynamics calculation is carried out in the same procedure as in the first structural relaxation calculation step S6. As a result, in the third structural relaxation calculation step S82, the initial arrangement of the binding model vs. 10 can be accurately relaxed by approximating the molecular motion of the actual polymer material.

Next, in the coupling step S8 of the present embodiment, the computer 1 determines whether or not the initial arrangement of the coupling model vs. 10 has been sufficiently relaxed (step S83). When it is determined in step S83 that the initial arrangement of the coupling model vs. 10 has been sufficiently relaxed (“Y” in step S83), the next replacement step S84 is performed. On the other hand, when it is determined that the initial arrangement of the combined model vs. 10 has not been sufficiently relaxed (“N” in step S83), one unit time step is advanced (step S85), and the third structural relaxation calculation step S82 and step S83 are carried out again. As a result, in the third structural relaxation calculation step S82, the structural relaxation of the model in the cell 7 can be reliably calculated, and the inside of the cell 7 can be stabilized. The calculation result of the structural relaxation is stored in the computer 1.

Next, in the binding step S8 of the present embodiment, the computer 1 replaces the bond between the pair of polymer particle models 5 and 5 constituting the bond model pair 10 with a bond via at least one cross-linking agent particle model 4 ( Replacement step S84). In the replacement step S84 of the present embodiment, an embodiment in which the pair of polymer particle models 5 and 5 are bonded via one cross-linking agent particle model 4 will be described. FIG. 9 is a flowchart showing an example of the processing procedure of the replacement step S84.

In the replacement step S84 of the present embodiment, first, the second bond chain model 11 (shown in FIG. 8A) to which the pair of polymer particle models 5 and 5 are bonded is deleted (step S841). Next, as shown in FIG. 8B, in the replacement step S84 of the present embodiment, one cross-linking agent particle is formed between the pair of polymer particle models 5 and 5 in which the second bond chain model 11 is deleted. Model 4 is arranged (step S842).

In step S842 of the present embodiment, the center 4c of the cross-linking agent particle model 4 is located at the center between the pair of polymer particle models 5 and 5. Thereby, the overlap between the cross-linking agent particle model 4 and the polymer particle model 5 can be suppressed. Such overlap between the cross-linking agent particle model 4 and the polymer particle model 5 is calculated by calculating a large repulsive force between the cross-linking agent particle model 4 and the polymer particle model 5 in the simulation using the polymer material model 8. It is easy to cause falling. Therefore, in the present embodiment, the overlap between the cross-linking agent particle model 4 and the polymer particle model 5 can be suppressed, so that the cross-linked polymer material model 8 (not shown) can be stably produced.

A potential P5 is defined between the crosslinker particle model 4 and the polymer particle model 5. The potential P5 is defined using the LJ potential _ULJ (r _ij ), similarly to the potential P2 shown in FIG. As a result, attractive and repulsive forces can be applied between the cross-linking agent particle model 4 and the polymer particle model 5.

Next, in the replacement step S84 of the present embodiment, the cross-linking agent particle model 4 and the polymer particle model 5 are connected via the third bond chain model 12 (step S843). The third bond model 12 is defined by the potential P4 in which the extension length is set between the pair of polymer particle models 5 and 5. Similar to the first bond model 6, the third bond model 12 is also set by the sum of the LJ potential _ULJ (r _ij ) and the bond potential U _{FEN E.} As the constants and variables set in the third binding chain model 12, the same constants and variables as those set in the first binding chain model 6 and the second binding chain model 11 are set.

As described above, in the replacement step S84 of the present embodiment, the pair of matrix models 3 and 3 are bonded via the cross-linking agent particle model 4, so that the cross-linked high molecular weight is reflected while reflecting the chemical structure and chemical properties. A molecular material model 8 (not shown) can be created. Moreover, in the method of creating the present embodiment, the polymer particle models 5 that are close to each other can be bonded to each other via the cross-linking agent particle model 4 without the structural relaxation calculation of the cross-linking agent particle model 4. Thereby, in the production method of the present embodiment, for example, even if a small cross-linking density is set, the polymer particle model 5 and the cross-linking agent particle model 4 can be bonded in a short time. Therefore, the method for creating the present embodiment can create a crosslinked polymer material model 8 (not shown) in a short time.

The polymer material model 8 (not shown) created in this embodiment is, for example, unidirectionally (for example, 0% to 20% in the Y-axis direction) based on a generally performed uniaxial tensile test. ) It can be used for deformation simulation to extend. Therefore, the method for producing the present embodiment is useful for the development of polymer materials. Moreover, since the method for producing the present embodiment can produce the polymer material model 8 containing the cross-linking agent in a short time, the time required for developing the polymer material can be significantly shortened.

In the production method of the present embodiment, as shown in FIG. 8B, the pair of polymer particle models 5 and 5 have the same particle diameter D2 (shown in FIG. 4) as the particle diameter D1 of the polymer particle model 5. Although bound via the cross-linking agent particle model 4 having (shown in FIG. 4), the present invention is not limited to such an embodiment. In the present embodiment, by locating the center 4c of the cross-linking agent particle model 4 at the center between the pair of polymer particle models 5 and 5, it is possible to suppress the overlap between the cross-linking agent particle model 4 and the polymer particle model 5. However, if the inter-particle model distance L1 (shown in FIG. 8A) is small, the cross-linking agent particle model 4 may be overlapped with the polymer particle model 5.

In order to prevent such overlap between the cross-linking agent particle model 4 and the polymer particle model 5, the replacement step S84 of this embodiment includes a pair of cross-linking agent particle models 4 having a particle diameter D2 smaller than the inter-particle model distance L1. It is bonded between the polymer particle models 5 and 5 of the above. FIG. 10 is a flowchart showing an example of a processing procedure of the method for creating another embodiment of the present invention. FIG. 11 is a flowchart showing an example of the processing procedure of the replacement step S84 according to another embodiment of the present invention. FIG. 12A is a diagram illustrating an example of a replacement step according to another embodiment of the present invention.

In the replacement step S84 of this embodiment, after the second bond chain model 11 (shown in FIG. 8A) to which the pair of polymer particle models 5 and 5 are bonded is deleted (step S841), the computer 1 is subjected to The particle diameter D2 (shown in FIG. 4) of the cross-linking agent particle model 4 shown in FIG. 4 is made smaller than the inter-particle model distance L1 (shown in FIG. 12A) (step S844). In step S844, first, the distance L1 between the particle models (shown in FIG. 12A) between the pair of matrix models 3 and 3 is calculated. Next, in step S844, the particle diameter D2 of the cross-linking agent particle model 4 is reduced so that the distance between the particle models is smaller than L1.

Next, in the replacement step S84 of this embodiment, as shown in FIG. 12A, the pair of polymer particle models 5 and 5 in which the second bond chain model 11 (shown in FIG. 8A) is deleted is deleted. A cross-linking agent particle model 4 having a reduced particle diameter D2 is arranged between the two (step S842). In step S842, the center 4c of the cross-linking agent particle model 4 is located at the center between the pair of polymer particle models 5 and 5. This makes it possible to reliably prevent the cross-linking agent particle model 4 and the polymer particle model 5 from overlapping.

Next, in the replacement step S84 of this embodiment, the cross-linking agent particle model 4 and the polymer particle model 5 are connected via the third bond chain model 12 (step S843). As a result, the pair of matrix models 3 and 3 are combined via the cross-linking agent particle model 4 to create a cross-linked polymer material model 8 (not shown).

In this embodiment, since the particle diameter D2 of the cross-linking agent particle model 4 is reduced so as to be smaller than the particle model distance L1 (shown in FIG. 12A), the cross-linking agent particle model 4 and the polymer particles It is possible to surely prevent duplication with the model 5. This makes it possible to prevent a large repulsive force from being calculated between the cross-linking agent particle model 4 and the polymer particle model 5.

When the polymer material model 8 in which the particle size D2 of the cross-linking agent particle model 4 is set to be small is used in the simulation, the handling is different between the cross-linking agent particle model 4 and the polymer particle model 5, which complicates the calculation. It will be easier. In addition, it tends to be difficult to qualitatively compare the simulation results of a plurality of polymer material models 8 having different sizes of the cross-linking agent particle models. From this point of view, in the method of creating the embodiment, after the replacement step S84, the computer 1 expands the particle diameter D2 of the cross-linking agent particle model 4 to a predetermined particle diameter (not shown) (expansion). Step S10). In this embodiment, the particle size D2 of the crosslinker particle model 4 is expanded to be the same as the particle size D1 of the polymer particle model 5. FIG. 12B is a diagram illustrating an example of a processing procedure in the enlargement process. FIG. 13 is a flowchart showing an example of the processing procedure of the expansion step S10 of this embodiment.

In the expansion step S10 of this embodiment, first, the computer 1 expands the particle diameter D2 of the cross-linking agent particle model 4 (step S101). In step S101, the particle diameter D2 of the cross-linking agent particle model 4 is increased by a predetermined incremental value for each unit time step.

Next, in the expansion step S10 of this embodiment, the computer 1 calculates the structural relaxation of the model in the cell 7 (shown in FIG. 5) based on the molecular dynamics calculation (second structural relaxation calculation step S102). .. The molecular dynamics calculation is carried out in the same procedure as in the first structural relaxation calculation step S6. In the second structure relaxation calculation step S102, the structure is set for each unit time step for the model arranged in the cell 7 (that is, the polymer particle model 5 and the cross-linking agent particle model 4 constituting the matrix model 3). The mitigation is calculated. As a result, in the second structural relaxation calculation step S102, the equilibrium state of the cross-linking agent particle model 4 and the polymer particle model 5 in which the particle diameter D2 is increased can be calculated by approximating the molecular motion of the actual polymer material. it can.

Next, in the expansion step S10 of this embodiment, whether or not the computer 1 has expanded the cross-linking agent particle model 4 to a predetermined particle size (in this embodiment, the particle size D1 of the polymer particle model 5). (Step S103). When it is determined in step S103 that the cross-linking agent particle model 4 has expanded to a predetermined particle size (“Y” in step S103), a series of processes of the method for creating this embodiment is completed, and the high molecular weight is high. The molecular material model 8 is created. The polymer material model 8 is input to the computer 1.

On the other hand, if it is determined that the cross-linking agent particle model 4 has not expanded to a predetermined particle size (in this embodiment, the particle size D1 of the polymer particle model 5), the unit time step is advanced by one ( Steps S104) and S101 to S103 are performed again. As a result, in the expansion step S10, the particle size D2 of the cross-linking agent particle model 4 can be set to a predetermined particle size, so that the above-mentioned problem can be prevented. The polymer material model 8 of this embodiment is stored in the computer 1.

In the expansion step S10 of this embodiment, the cross-linking agent particle model 4 is expanded while calculating the structural relaxation of the cross-linking agent particle model 4 and the polymer particle model 5. Therefore, in the expansion step S10, the cross-linking agent particle model 4 can be expanded and the cross-linking agent particle model 4 and the adjacent polymer particle model 5 can be gradually separated from each other via the third bond chain model 12. It is possible to effectively prevent duplication of the cross-linking agent particle model 4 and the polymer particle model 5 due to the expansion of the cross-linking agent particle model 4.

In this embodiment, the step S101 for expanding the cross-linking agent particle model 4 and the second structural relaxation calculation step S102 were performed for each unit time step, but the step S101 for expanding the cross-linking agent particle model 4 was performed. Later, mitigation calculations may be performed during multiple unit time steps. As a result, the cross-linking agent particle model 4 can be stably expanded.

In the replacement step S84 of the previous embodiments, the pair of polymer particle models 5 and 5 are bonded via one cross-linking agent particle model 4, but the present invention is not limited to such an embodiment. For example, a pair of polymer particle models 5 and 5 may be bonded via a plurality of cross-linking agent particle models 4. FIG. 14 is a flowchart showing an example of the processing procedure of the replacement step S84 according to still another embodiment of the present invention. FIG. 15A is a diagram illustrating an example of a replacement step according to still another embodiment of the present invention. In this embodiment, the same configurations as those in the previous embodiment are designated by the same reference numerals, and the description thereof may be omitted. Further, in this embodiment, an embodiment in which a pair of polymer particle models 5 and 5 are bonded via three cross-linking agent particle models 4 will be described.

In the replacement step S84 of this embodiment, after the second bond chain model 11 (shown in FIG. 8A) to which the pair of polymer particle models 5 and 5 are bonded is deleted (step S841), the cross-linking agent particle model 4 The particle size D2 (shown in FIG. 4) is reduced (step S845). In this step S845, first, the distance L1 between the particle models (shown in FIG. 15A) between the pair of matrix models 3 and 3 is calculated. Next, in step S845, the total of the particle diameters D2 of the plurality of (three in the present embodiment) cross-linking agent particle models 4 bonded to the pair of polymer particle models 5 and 5 is larger than the inter-particle model distance L1. The particle diameter D2 of each cross-linking agent particle model 4 is reduced so as to be smaller.

Next, in the replacement step S84 of this embodiment, as shown in FIG. 15A, the pair of polymer particle models 5 and 5 in which the second bond chain model 11 (shown in FIG. 8A) is deleted is deleted. A plurality of cross-linking agent particle models 4 are arranged between the two (step S846). In this step S845, the total of the particle diameters D2 of the cross-linking agent particle models 4 arranged in the pair of polymer particle models 5 and 5 is set to be smaller than the inter-particle model distance L1. Therefore, it is possible to prevent the cross-linking agent particle model 4 and the polymer particle model 5 from overlapping. In order to ensure that the cross-linking agent particle model 4 and the polymer particle model 5 do not overlap with each other, in step S846, each cross-linking agent particle model 4 is evenly arranged between the pair of polymer particle models 5 and 5. desirable.

Next, in the replacement step S84 of this embodiment, the cross-linking agent particle model 4 and the polymer particle model 5 and the cross-linking agent particle models 4 and 4 are connected via the third bond chain model 12. (Step S843). The third bound chain model 12 is set by the same processing procedure as in the previous embodiment. As a result, between the different matrix models 3 and 3, the pair of polymer particle models 5 and 5 are bonded via a plurality of (three in this embodiment) cross-linking agent particle models 4.

As described above, in the replacement step of this embodiment, the pair of polymer particle models 5 and 5 can be bonded via an arbitrary number of cross-linking agent particle models 4. Therefore, in the method for creating a polymer material model of the present invention, a polymer material model 8 (not shown) having a predetermined crosslink length can be created in a short time. Further, the method for producing this embodiment utilizes the results of the structural relaxation calculation (third structural relaxation calculation step S82) of the binding model pair 10 (shown in FIG. 8A) to obtain a different number of cross-linking agent particles. By binding the model 4 to the pair of polymer particle models 5 and 5, it is possible to create a plurality of polymer material models 8 (not shown) having different crosslink lengths. As a result, in the method of creating this embodiment, it is not necessary to carry out the first structural relaxation calculation step S6 and the second structural relaxation calculation step S102 each time a plurality of polymer material models 8 having different crosslink lengths are created. Therefore, the creation time can be significantly reduced.

Next, in the production method of this embodiment, after the replacement step S84, the computer 1 expands the particle diameter D2 of each cross-linking agent particle model 4 to a predetermined particle diameter (expansion step S10). FIG. 15B is a diagram illustrating an example of a processing procedure of the expansion step of still another embodiment of the present invention.

The expansion step S10 of this embodiment is carried out based on the processing procedure shown in FIG. Therefore, in the expansion step S10, the cross-linking agent particle model 4 can be expanded while calculating the structural relaxation of each cross-linking agent particle model 4 and the polymer particle model 5, so that the cross-linking agent particle model 4 and the polymer particle model 5 overlap. Can be effectively prevented.

In previous embodiments, the matrix model 3 has been defined as a coarse-grained model, but is not limited to such aspects. For example, the matrix model 3 may be defined as an atomic model.

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.

A polymer material model modeling a polymer material containing a cross-linking agent was created (Example, Comparative Example). In the embodiment, a first structural relaxation calculation step was performed in which a plurality of matrix models were placed in the cell and the structural relaxation of the model in the cell was calculated. Then, in the examples, a bonding step of binding the pair of polymer particle models via at least one cross-linking agent particle model was carried out according to the treatment procedure shown in FIG.

In the comparative example, a plurality of matrix models and crosslinker particle models were placed in the cell, and the structural relaxation of the model in the cell was calculated. Next, in the comparative example, when the distance between the polymer particle model and the cross-linking agent particle model was equal to or less than a predetermined distance, a step of combining the polymer particle model and the cross-linking agent particle model was carried out. Furthermore, in the comparative example, the structural relaxation of the model in the cell was further calculated.

Then, in Examples and Comparative Examples, the time required to create a crosslinked polymer material model was measured. The potentials and software set between the particle models are as described in the specification. The common specifications are as follows.
Computer: SGI workstation
Number of CPU cores: 12 cores
On-board memory: 64GB
Polymer material model:
Length of one side of cell L3a, L3b, L3c: 44.8σ
Matrix model:
Number placed in cell: 150 Number of polymer particle models per matrix model: 200 Particle diameter of polymer particle model D1: 1σ
Crosslinker particle model:
Number placed in cell: 1500 Particle diameter D2: 1σ
Note that σ is a dimensionless length unit.

As a result of the test, the example was able to calculate the bond between the polymer particle model and the cross-linking agent particle model in a short time. As a result, the examples were able to create a crosslinked polymer material model in a shorter time (51.5% of the comparative examples) than in the comparative examples.

Further, in the embodiment, since the pair of polymer particle models can be bonded via an arbitrary number of cross-linking agent particle models, the cross-linking length without performing the first structural relaxation calculation step and the second structural relaxation calculation step again. We were able to create polymer material models with different sizes in a short time. On the other hand, in the comparative example, each time a polymer material model having a different crosslink length is created, it is necessary to calculate the structural relaxation for the entire model in the cell twice, which is significantly larger than that in the example. It took time to create.

S6 First structure relaxation calculation step S8 Bonding step

Claims (5)

A method for creating a polymer material model using a computer, which models a polymer material containing a cross-linking agent.
A step of inputting a matrix model having a plurality of polymer particle models to the computer based on the molecular chain of the polymer material,
A step of inputting a cross-linking agent particle model modeling the cross-linking agent into the computer, and
A process of inputting a cell, which is a virtual space corresponding to a part of the polymer material, into the computer,
A step of arranging a plurality of the matrix models in the cell, and
A step of defining the potential of attractive and repulsive forces acting between the polymer particle models, and
Based on the molecular dynamics calculation, the first structural relaxation calculation step for calculating the structural relaxation only for the matrix model in the cell, and
A bonding step in which the computer binds a pair of polymer particle models with a particle model-to-particle model distance smaller than a predetermined distance between different matrix models via at least one cross-linking agent particle model. A method for creating a polymer material model, which comprises including.
The method for creating a polymer material model according to claim 1, wherein the particle size of the cross-linking agent particle model is smaller than the distance between the particle models. The method for creating a polymer material model according to claim 2, further comprising an expansion step of expanding the particle size of the cross-linking agent particle model to a predetermined particle size. The expansion step is a second structural relaxation calculation step for calculating structural relaxation for the polymer particle model constituting the matrix model in the cell and the cross-linking agent particle model based on the molecular dynamics calculation. The method for creating a polymer material model according to claim 3, which includes the method.
The bonding step is a step of defining a bonding model pair in which a pair of polymer particle models whose distance between the particle models is smaller than the distance are bonded between different matrix models without using the cross-linking agent particle model. ,
After defining the binding model pair, a third structural relaxation calculation step of calculating the structural relaxation for the binding model pair in the cell or the matrix model of a single substance based on the molecular dynamics calculation.
The third structure relaxation calculation step is followed by a step of replacing the bond between the pair of polymer particle models constituting the bond model pair with a bond via at least one crosslinker particle model. The method for creating a polymer material model according to any one of 4.

Images