JP2018101354A - Simulation method of polymer material - Google Patents

Abstract

PROBLEM TO BE SOLVED: To analyze the cutting of a polymer chain.SOLUTION: A simulation method that is a method for analyzing a polymer material by the use of a computer comprises: a step S1 for inputting, into a computer, a polymer chain model including a plurality of particle models and bond models for bonding gaps between the particle models adjacent to each other, on the basis of a polymer chain of a polymer material; a step S2 for defining, to the computer, a first distance for performing the cutting between the adjacent particle models through the bond models; and a simulation step S5 for making the computer deform a polymer material model. The simulation step S5 includes a step for removing the bond model between the particle models when a distance between the adjacent particle models through the bond model is the first distance or more.SELECTED DRAWING: Figure 3

Description

  The present invention relates to a simulation method for a polymer material, and more particularly, to a method useful for analyzing breakage of a polymer chain of the polymer material.

  The following Patent Document 1 proposes various simulation methods (numerical calculations) for evaluating the properties of polymer materials using a computer in order to develop polymer materials such as rubber.

  In this type of simulation method, first, a polymer material model is defined in which a molecular chain model including a plurality of particle models and a bond model connecting the particle models is arranged in a space defined on a computer. Next, relaxation calculation based on molecular dynamics is performed using the polymer material model. Thereafter, deformation calculation of the polymer material model is performed. From the result of the deformation calculation, the performance of the polymer material is estimated.

Japanese Patent No. 5913260

  In the deformation calculation of a polymer material model, the upper limit value of elongation is often defined in the bond model, and is usually set so as not to extend further. Therefore, the simulation method cannot analyze the breakage of the polymer chain. For example, there has been a problem that the state of polymer chain breakage and the bond strength between atoms constituting the polymer chain cannot be evaluated.

  The present invention has been devised in view of the above circumstances, and has as its main object to provide a simulation method for a polymer material capable of analyzing the breakage of a polymer chain.

  The present invention is a method for analyzing a polymer material using a computer, and a bond that couples a plurality of particle models and adjacent particle models based on a polymer chain of the polymer material. A step of inputting a molecular chain model including a model into the computer, a step of defining a first distance in the computer for cutting between the particle models adjacent to each other via the bond model, A placement step of placing a plurality of molecular chain models in a space and setting a polymer material model; and a simulation step in which the computer deforms the polymer material model, the simulation step comprising: When the distance between the adjacent particle models via the bond model is equal to or greater than the first distance, the bond model between the particle models is Characterized in that it comprises a step of dividing.

  In the simulation method of the polymer material according to the present invention, the molecular chain model is preferably a coarse-grained model in which a plurality of atoms constituting the polymer chain are replaced with one particle model.

  In the simulation method of the polymer material according to the present invention, the step of defining the first distance constitutes a main chain of the polymer chain among dissociation energies between the plurality of atoms constituting the particle model. It is desirable to define the first distance based on the dissociation energy between atoms and the smallest dissociation energy.

  In the simulation method of the polymer material according to the present invention, the step of defining the first distance includes a main chain of the polymer chain among activation energies between the plurality of atoms constituting the particle model. It is desirable that the first distance is defined based on the activation energy between the atoms to be activated and the smallest activation energy.

  In the method for simulating a polymer material according to the present invention, the bond model has an extension length that is an upper limit value of a distance between the particle models, and the first distance is smaller than the extension length. Is desirable.

  In the simulation method of the polymer material according to the present invention, a step of setting a cross-linking model that connects the particle models of the adjacent molecular chain models, and cutting between the adjacent particle models via the cross-linking model Defining a second distance for the simulation, wherein the step of simulating the distance between the particle models when the distance between the particle models adjacent via the bridging model is greater than or equal to the second distance. It is desirable to include a step of deleting the cross-linking model.

  In the simulation method of the polymer material according to the present invention, it is preferable that the step of defining the second distance defines the second distance based on a dissociation energy of a crosslinking bond defined by the crosslinking model.

  In the simulation method of the polymer material according to the present invention, the bridge model has an extension length that is an upper limit value of the distance between the particle models, and the second distance is smaller than the extension length. Is desirable.

  The simulation method of the polymer material of the present invention includes a step of defining a first distance for cutting between adjacent particle models via a bond model in a computer, and a simulation step in which the computer deforms the polymer material model. Is included. The simulation step includes a step of deleting the bond model between the particle models when the distance between the particle models adjacent via the bond model is equal to or greater than the first distance.

  Thus, the polymer material simulation method of the present invention can analyze the breakage of the polymer chain that may occur in the polymer material by deleting the bond model between the particle models. Therefore, the polymer material simulation method of the present invention can evaluate, for example, the state of polymer chain breakage and the bond strength between atoms constituting the polymer chain.

It is a perspective view which shows an example of the computer which performs the simulation method of a polymeric material. It is a structural formula of polybutadiene. It is a flowchart which shows an example of the process sequence of a simulation method. It is a perspective view which shows an example of a molecular chain model. It is a figure which shows an example of the molecular model used for calculating | requiring the energy curve of a 1st potential. It is a graph which shows an example of the energy curve of 1st potential. It is a flowchart which shows an example of an arrangement | positioning process. It is a perspective view which shows an example of a polymeric material model. It is a flowchart which shows an example of the process sequence of a simulation process. (A) is a figure which shows a part of stretched molecular chain model. (B) is a figure which shows a part of cut | disconnected molecular chain model. It is a flowchart which shows an example of the process sequence of the simulation method of other embodiment of this invention. It is a figure which shows an example of a pair of molecular chain model couple | bonded with the bridge | crosslinking model. It is a flowchart explaining an example of the simulation process of other embodiment of this invention.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
The polymer material simulation method of the present embodiment (hereinafter sometimes simply referred to as “simulation method”) is for analyzing the breakage of the polymer chain of the polymer material using a computer.

  FIG. 1 is a perspective view illustrating an example of a computer that executes a simulation method. 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. The storage device stores in advance processing procedures (programs) for executing the simulation method of the present embodiment.

  Examples of the polymer material of the present embodiment include cis-1,4 polybutadiene (hereinafter sometimes simply referred to as “polybutadiene”). FIG. 2 is a structural formula of polybutadiene.

The polymer chain 2 constituting the polybutadiene has a degree of polymerization of a monomer 3 {— [CH ₂ —CH═CH—CH ₂ ] —} composed of a methylene group (—CH ₂ —) and a methine group (—CH—). n is connected. As the polymer material, a polymer material other than polybutadiene may be used.

  FIG. 3 is a flowchart illustrating an example of a processing procedure of the simulation method. In the simulation method of the present embodiment, first, a molecular chain model is input to the computer 1 (step S1). FIG. 4 is a perspective view showing an example of the molecular chain model 4.

  In step S1 of the present embodiment, a molecule including a plurality of particle models 5 and a bond model 6 that connects adjacent particle models 5 and 5 based on the polymer chain 2 of the polymer material shown in FIG. Chain model 4 is set. The molecular chain model 4 is a coarse-grained model (in this embodiment, a Kremer-Grest model) in which a plurality of atoms constituting the polymer chain 2 are replaced with one particle model 5.

  The particle model 5 is obtained by substituting the structural unit forming the monomer 3 or part of the monomer 3 of the polymer chain 2 shown in FIG. When the polymer chain 2 is polybutadiene, for example, 1.55 monomers 3 are replaced with one particle model 5 in the same manner as in Patent Document 1 described above. Thereby, a plurality of (for example, 10 to 5000) particle models 5 are set in the molecular chain model 4. The particle model 5 is handled as a mass point of the equation of motion in the molecular dynamics calculation. That is, the particle model 5 defines parameters such as mass, diameter, or electric charge.

The bond model 6 is for connecting the particle models 5 and 5. In the bond model 6, a first potential P1 is defined in which an extension length R ₀ (not shown) that is an upper limit value of the distance r _ij between the particle models 5 and 5 is set. The first potential P1 is set as the sum of the LJ potential U _LJ (r _ij ) and the coupling potential U _FENE as in the above-mentioned Patent Document 1. The values of the constants and variables of the LJ potential U _LJ (r _ij ) and the coupling potential U _FENE can be set based on the above-mentioned Patent Document 1. Thereby, the linear molecular chain model 4 in which the particle model 5 is constrained to be stretchable can be defined.

  Next, in the simulation method of the present embodiment, a first distance for cutting between the adjacent particle models 5 and 5 via the bond model 6 is defined in the computer 1 (step S2). As shown in FIG. 2, the first distance is set based on the dissociation energy or activation energy of a pair of adjacent atoms in the main chain (hereinafter, simply referred to as “atom pair”) 7. be able to.

  The dissociation energy is energy corresponding to an energy difference between a state in which the bond of the atom pair 7 is completely broken and a state in which the bond of the atom pair 7 is stable. The activation energy is energy necessary for exciting from the ground state to the transition state in the bond breaking process. Therefore, when the energy of the atom pair 7 reaches at least the dissociation energy, more precisely, when the energy reaches the activation energy, the bond of the atom pair 7 is broken. In the present embodiment, the first distance is defined based on the dissociation energy that can be used relatively easily.

  The dissociation energy and the activation energy can be appropriately acquired based on, for example, experiments or simulations. In the present embodiment, the dissociation energy is acquired based on the description of the literature (Yu-Ran Luo, “Handbook of Bond Dissociation Energies in Organic Compounds”, CRC Press, December 23, 2002).

  The dissociation energy differs depending on the type of atom pair 7 in the main polymer chain 2 shown in FIG. In the polymer chain 2 of the present embodiment, the atom pair 7 includes a carbon atom-carbon atom single bond and a carbon atom-carbon atom double bond. Among these atom pairs 7, the polymer chain 2 is easily cleaved at the atom pair 7 having a low dissociation energy.

  As shown in FIG. 4, in this embodiment, a plurality of atoms (1.55 monomers 3 in this embodiment) constituting the polymer chain 2 shown in FIG. Has been replaced. For this reason, the first distance between the particle models 5 and 5 constitutes the main chain of the polymer chain 2 out of the dissociation energy of the plurality of atom pairs 7 (shown in FIG. 2) replaced by the particle model 5. The dissociation energy between atoms is preferably defined based on the smallest dissociation energy. Thereby, in the below-mentioned simulation process S5, the state cut | disconnected by the atom pair 7 which is most easily cut | disconnected can be calculated.

  The first distance in the present embodiment is defined using dissociation energy and the energy curve of the first potential P1. FIG. 5 is a diagram illustrating an example of a molecular model used to obtain the energy curve of the first potential P1. FIG. 6 is a graph showing an example of the energy curve of the first potential P1.

As shown in FIG. 6, the energy curve 8 shows the relationship between the potential energy and the distance between the particle models 5 and 5. For the potential energy, the same unit (kcal / mol) as the actual molecule is used. On the other hand, the unit (σ) in the coarse-grained model is used for the distance between the particle models 5 and 5. In step S2, first, in the energy curve 8, the potential energy corresponding to the smallest dissociation energy is specified. In the energy curve 8, the distance between the particle models 5 and 5 corresponding to the potential energy is specified as the first distance. Thereby, the distance actually cut | disconnected between atoms can be converted into the cutting distance (namely, 1st distance) in a coarse-grained model. The first distance in the present embodiment is set to be smaller than the full length R ₀ . Thus, in the simulation step S5 in later, before reaching the length R ₀ endless elongation distance between the particles model 5,5 molecular chain model 4 shown in FIG. 4, the cutting between the particle models 5,5 (present In the embodiment, it is possible to reliably calculate (deletion of the bond model 6).

  Next, in the simulation method of the present embodiment, a plurality of molecular chain models 4 are arranged in a predetermined space to set a polymer material model (arrangement step S3). FIG. 7 is a flowchart showing an example of the arrangement step S3. FIG. 8 is a perspective view showing an example of the polymer material model 10.

In the arrangement step S3 of the present embodiment, first, the second potential P2 is defined between the particle models 5 and 5 of the molecular chain models 4 and 4 (step S31). The second potential P2 can be defined using the LJ potential U _LJ (r _ij ) according to the procedure of Patent Document 1. In this embodiment, the value larger than 2 ^1/2 sigma as a cutoff distance r _c of the second potential P2. Thus, between the particle model 5,5, it is possible to define the attraction subatmospheric and cutoff distance r _c than the distance r _ij is 2 ^1/2 sigma between the particles.

  In the arrangement step S3 of the present embodiment, next, a space 11 for arranging a plurality of molecular chain models 4 is defined (step S32). The space (cell) 11 is defined as a rectangular parallelepiped having three pairs of planes 12a and 12b facing each other. A periodic boundary condition is defined for each of the planes 12a and 12b. Thereby, in the space 11, for example, it is possible to calculate so that a part of the molecular chain model 4 that has come out from one plane 12a enters from the opposite plane 12b. Therefore, it can be handled as one plane 12a and the opposite plane 12b being continuous (connected).

  The length L1 of one side of the space 11 can be set as appropriate. The length L1 of the present embodiment is preferably at least three times the radius of inertia (not shown) of the molecular chain model 4. The radius of inertia is an amount indicating the spread of the molecular chain model 4. In such a space 11, in the molecular dynamics calculation, collision with the self image due to the periodic boundary condition hardly occurs, so that the spatial spread of the molecular chain model 4 can be appropriately calculated. Further, the size of the space 11 is set to a stable volume at 1 atmosphere, for example. Such a space 11 can define the volume of at least a part of the polymer material.

  Next, in the arrangement step S3 of this embodiment, a plurality of molecular chain models 4 are arranged in the space 11 (step S33). In step S33, the polymer material model 10 is defined by arranging a plurality of molecular chain models 4 in the space 11. The molecular chain model 4 of this embodiment is arrange | positioned in the space 11 based on the Monte Carlo method, for example. The polymer material model 10 is input to the computer 1.

The number density of the particle model 5 in the space 11 (hereinafter sometimes simply referred to as “number density”) can be set as appropriate. In this embodiment, since the attractive force is defined between the particle models 5 and 5, when the normal number density (for example, 0.85σ ⁻³ ) is set, voids (not shown) are formed in the space 11. There is a risk of formation. For this reason, the number density of the particle model 5 is desirably set to a number density (preferably 0.90σ ⁻³ or more) larger than the normal number density.

  Next, in the simulation method of the present embodiment, the computer 1 calculates the structural relaxation of the polymer material model 10 based on the molecular dynamics calculation (step S4). In the molecular dynamics calculation of the present embodiment, for example, Newton's equation of motion is applied on the assumption that the molecular chain model 4 follows classical mechanics for a predetermined time in the space 11. The movement of the molecular chain model 4 at each time is tracked every unit time.

  In the calculation of structural relaxation, the pressure and temperature are constant or the volume and temperature are kept constant in the space 11. Thus, in step S4, the initial arrangement of the molecular chain model 4 can be relaxed with high accuracy by approximating the actual molecular motion of the polymer material. Such calculation of structural relaxation can be processed using, for example, COGNAC or VSOP included in a soft material general simulator (J-OCTA) manufactured by JSOL Corporation. The relaxed polymer material model 10 is stored in the computer 1.

  Next, in the simulation method of the present embodiment, the computer 1 deforms the polymer material model 10 (simulation step S5). In the simulation step S5, for example, the polymer material model 10 is extended in one direction (for example, 0% to 300% in the Z-axis direction) based on a uniaxial tensile test that is generally performed. FIG. 9 is a flowchart illustrating an example of the processing procedure of the simulation step S5.

In the simulation step S5 of the present embodiment, first, deformation conditions of the polymer material model 10 are input (step S51). The deformation conditions can be set as appropriate. In the present embodiment, for example, the deformation speed, the friction coefficient, or the Poisson's ratio of the polymer material model 10 is set as the deformation condition. The range of these deformation conditions can be set as appropriate. The deformation speed (strain per unit time (for example, 0.006τ)) is preferably 1.0 × 10 ^{−3 to} 5.0 × 10 ⁻³ . The coefficient of friction is preferably about 2 to 8, for example. The Poisson's ratio is preferably 0 to 0.5. These deformation conditions are stored in the computer 1.

Next, in the simulation step S5 of the present embodiment, the polymer material model 10 is deformed (step S52). In step S52, based on the deformation conditions set in step S51, the polymer material model 10 stretched in the uniaxial direction is calculated for each unit time. Due to the deformation of the polymer material model 10, each molecular chain model 4 is also stretched. FIG. 10A is a diagram illustrating a part of the stretched molecular chain model 4. The distance r _ij between the adjacent particle models 5 and 5 through the bond model 6 increases. The polymer material model 10 deformed every unit time is stored in the computer 1.

Next, in the simulation step S5 of the present embodiment, it is determined whether or not the distance r _ij between the adjacent particle models 5 and 5 via the bond model 6 is equal to or greater than the first distance (step S53). In step S53, it is determined whether or not the distance between adjacent particle models 5 and 5 is greater than or equal to the first distance for all molecular chain models 4 arranged in the space 11.

The first distance in the present embodiment is defined based on the dissociation energy. For this reason, it can be considered that the polymer chain is broken between the particle models 5 and 5 that are separated by a distance greater than or equal to the first distance. Accordingly, in step S53, when the distance r _ij between the particle models 5 and 5 is equal to or greater than the first distance (“Y” in step S53), the bond model 6 between the particle models 5 and 5 is deleted (step S53). S54). FIG. 10B shows a part of the molecular chain model 4 that has been cut. Thereby, the molecular chain model 4 can be cut | disconnected between the particle models 5 and 5 from which the bond model 6 was deleted.

On the other hand, between the particle models 5 and 5 less than the first distance, it can be considered that the polymer chain 2 is not yet broken. Therefore, in step S53, when the distance r _ij between the particle models 5 and 5 is less than the first distance (“N” in step S53), the bond model 6 between the particle models 5 and 5 is not deleted. Next step S55 is performed.

  Next, in the simulation step S5 of the present embodiment, it is determined whether or not the polymer material model 10 has been extended to a predetermined size (step S55). If it is determined in step S55 that the polymer material model 10 has been expanded to a predetermined size (“Y” in step S55), a series of processes in the simulation step S5 is completed, and the next step S6 is performed. Is done. On the other hand, when it is determined that the polymer material model 10 has not expanded to a predetermined size (“N” in step S55), the unit time is advanced by one (step S56), and steps S52 to S55 are performed. Will be implemented again. Thereby, in simulation process S5, the cutting | disconnection of the molecular chain model 4 can be calculated until the polymeric material model 10 is expanded | stretched to the predetermined magnitude | size.

  Thus, the simulation method of the present embodiment can analyze the breakage of the polymer chain 2 that may occur in the polymer material by deleting the bond model 6 between the particle models 5 and 5. Therefore, the simulation method of the present embodiment can evaluate, for example, the cutting state of the polymer chain 2 accompanying the deformation of the polymer material.

  In the simulation method of the present embodiment, one type of molecular chain model 4 is input, but a plurality of different types of molecular chain models 4 may be input. By setting different first distances for each molecular chain model 4, it is possible to evaluate the bond strength between atoms constituting the polymer chain 2 shown in FIG. Further, a plurality of filler models obtained by modeling fillers blended in the polymer material may be input.

  Next, in the simulation method of the present embodiment, the computer 1 determines whether or not the result of deformation calculation of the polymer material model 10 is good (step S6). In step S6, the quality of the deformation calculation is determined based on, for example, the number of cuts of the molecular chain model 4 and the cut positions of the molecular chain model 4.

  In step S6, when it is determined that the deformation calculation of the polymer material model 10 is good (“Y” in step S6), a polymer material is manufactured based on the polymer material model 10 (step S7). On the other hand, when it is determined in step S6 that the deformation calculation of the polymer material model 10 is not good (“N” in step S6), the structure and conditions of the polymer chain 2 are changed (step S8), Steps S1 to S6 are performed again. Thus, the simulation method of the present embodiment is useful for improving a polymer material and developing an unknown polymer material (not shown) having a desired performance.

  In the step S2 for defining the first distance of the present embodiment, among the dissociation energies of the plurality of atom pairs 7 (shown in FIG. 2) substituted by the particle model 5, the interatomic atoms constituting the main chain of the polymer chain 2 The first distance is defined on the basis of the lowest dissociation energy and the minimum dissociation energy. However, the present invention is not limited to such a mode. For example, among the activation energies of a plurality of atom pairs 7 (shown in FIG. 2) substituted by the particle model 5, it is the activation energy between atoms constituting the main chain of the polymer chain 2, and is the smallest A first distance may be defined based on the activation energy.

  In the method of setting based on such activation energy, the first distance can be determined more strictly than the method of setting based on dissociation energy. In this embodiment, the first distance can be defined using the activation energy and the energy curve of the first potential P1. More specifically, in the energy curve 8 shown in FIG. 6, the potential energy corresponding to the smallest activation energy is specified, and the distance between the particle models 5 and 5 corresponding to the potential energy is specified as the first distance. be able to.

  In the simulation method of the present embodiment, the cutting of only the molecular chain model 4 (polymer chain 2) is calculated, but is not limited to such a mode. In general, a polymer material such as rubber is blended with a crosslinking agent (not shown) such as sulfur in order to increase the elastic force. Such a cross-linking agent increases the elastic force of the polymer material by crosslinking the molecular chains of the polymer material. Examples of the cross-linking structure in this embodiment include monosulfide bridges, disulfide bridges, and polysulfide bridges.

  In the simulation method of this embodiment, not only the molecular chain model 4 (polymer chain 2) shown in FIG. In addition, in this embodiment, about the same structure as previous embodiment, the same code | symbol may be attached | subjected and description may be abbreviate | omitted. FIG. 11 is a flowchart illustrating an example of a processing procedure of a simulation method according to another embodiment of the present invention.

  In the simulation method of this embodiment, the cross-linking model 16 that connects the particle models 5 and 5 of the adjacent molecular chain model 4 is set after the arrangement step S3 (step S9). FIG. 12 is a diagram illustrating an example of a pair of molecular chain models 4 that are coupled by the crosslinking model 16.

The cross-linking model 16 is for connecting the particle models 5 and 5. The bridge model 16 is set based on a predetermined bridge point. The bridging model 16 defines a third potential P3 in which an extension length R ₀ that is an upper limit value of the distance r _ij between the particle models 5 and 5 is set. The third potential P3 is set by the sum of the LJ potential U _LJ (r _ij ) and the coupling potential U _FENE as in the above-mentioned Patent Document 1. The bridge model 16 is input to the computer 1.

  The cross-linking model 16 is preferably set in consideration of the cross-linking structure (for example, monosulfide bridge, disulfide bridge, and polysulfide bridge). In the cross-linking model 16, it is desirable that different third potentials P3 are defined depending on the cross-linking structure. Thereby, in a simulation process S5, a cross-linking can be considered with high accuracy.

  Next, in the simulation method of this embodiment, a second distance for cutting between adjacent particle models 5 and 5 via the bridge model 16 is defined in the computer 1 (step S10). Similarly to the first distance, the second distance can be set based on the dissociation energy of the cross-linking bond defined by the cross-linking model 16 or the activation energy. The second distance in the present embodiment is defined based on the dissociation energy.

  The dissociation energy varies depending on the structure of the cross-linked bond (for example, monosulfide bridge, disulfide bridge, and polysulfide bridge). The lower the dissociation energy, the easier it is to break. In the present embodiment, a different second distance is defined for each cross-linking structure.

Similar to the first distance, the second distance is defined using the dissociation energy and the energy curve of the third potential P3. Further, the second distance is set smaller than the full length R ₀ . Thus, in the simulation step S5, before the distance r _ij between the adjacent particle models 5 and 5 via the bridge model 16 reaches the full length R ₀ , the cutting between the particle models 5 and 5 (this embodiment) Then, the deletion of the bridge model 16) can be calculated reliably.

FIG. 13 is a flowchart for explaining an example of the simulation step S5 according to another embodiment of the present invention. In the simulation step S <b> 5, each bridge model 16 is also stretched by the deformation of the polymer material model 10. In the simulation step S5 of this embodiment, as shown in FIG. 12, it is determined whether or not the distance r _ij between the adjacent particle models 5 and 5 via the bridge model 16 is equal to or larger than the second distance. Is included. In step S57, for all molecular chain models 4 arranged in the space 11, it is determined whether or not the distance r _ij between the adjacent particle models 5 and 5 via the bridge model 16 is equal to or greater than the second distance.

The second distance is defined based on the dissociation energy of the crosslinking bond. For this reason, it can be considered that the cross-linked bond is broken between the particle models 5 and 5 that are separated by the second distance or more. Accordingly, in step S57, when the distance r _ij between the adjacent particle models 5 and 5 via the bridging model 16 is equal to or greater than the second distance (“Y” in step S57), the particle models 5 and 5 are between. The cross-linking model 16 is deleted (Step S58). Thereby, the cross-linking bond between the molecular chain models 4 and 4 can be cut.

On the other hand, between the particle models 5 and 5 less than the second distance, it can be considered that the cross-linking bond is not yet broken. Therefore, in step S57, when the distance r _ij between the adjacent particle models 5 and 5 via the bridge model 16 is less than the second distance (“N” in step S57), the bridge model 16 is deleted. Instead, the next step S55 is performed.

  As described above, in the simulation method of this embodiment, by deleting the cross-linking model 16, it is possible to analyze the breakage of the cross-linking bond that may occur in the polymer material. Therefore, the simulation method of this embodiment can evaluate, for example, the cutting state of the polymer chain 2 and the cutting state of the cross-linked bond accompanying deformation of the polymer material.

  Also, when different cross-linking models 16 are defined according to the cross-linking structure (for example, monosulfide cross-linking, disulfide cross-linking, and polysulfide cross-linking), the bond strength and the like should be evaluated for each cross-linking structure. Can do.

  In the step S10 for defining the second distance in this embodiment, the second distance is defined based on the dissociation energy of the cross-linking bond, but the present invention is not limited to such a mode. For example, the second distance may be defined based on the activation energy of the cross-linking. In the method of setting based on such activation energy, the second distance can be determined more strictly than the method of setting based on dissociation energy. In this embodiment, similarly to the step of setting the first distance, the second distance can be defined using the activation energy and the energy curve of the third potential P3.

  The particularly preferred embodiment of the present invention has been described in detail above. However, the present invention is not limited to the illustrated embodiment, and can be implemented by being modified into various modes such as inputting a plurality of filler models. .

  Based on the processing procedure shown in FIG. 11, the cutting of the polymer material model was analyzed (Example 1, Example 2). In Example 1 and Example 2, based on the polymer chain of the polymer material shown in FIG. 2, a molecular chain model including a plurality of particle models and a bond model that connects adjacent particle models is stored in the computer. Entered. And the 1st distance for cut | disconnecting between the particle | grain models adjacent via a bond model was defined.

  In Example 1 and Example 2, based on the following cross-linking points, a cross-linking model that connects the particle models of adjacent molecular chain models was set. And the 2nd distance for cut | disconnecting between adjacent particle | grain models via a bridge | crosslinking model was defined.

The crosslinking model of Example 1 was set as a monosulfide bridge, and the following second distance was defined. The crosslinking model of Example 2 was set as a polysulfide bridge that was easier to cut than the monosulfide bridge of Example 1, and the following second distance was defined. And based on the process sequence shown in FIG. 13, Example 1 and Example 2 deform | transformed the polymeric material model, and the cutting | disconnection of the bond model and the bridge | crosslinking model was calculated. The common specifications of Example 1 and Example 2 are as follows.
Polymer chain: Polybutadiene Molecular chain model:
Total number of molecular chain models arranged in space: 100 Number of particle models constituting one molecular chain model: 1000 Number density of particle models arranged in space: 0.9σ ⁻³
Cut-off distance: 2.5σ
First distance: 1.49σ
Cross-linking model:
Crosslinking point: 805 locations Second distance (Example 1): 1.485σ
Second distance (Example 2): 1.42σ
Deformation simulation:
Unit time (minute time): 0.006τ
Deformation speed (strain per unit time): 2.2 × 10 ⁻³
Total deformation simulation time: 6τ
Friction coefficient Γ: 250 (500 times the Kremer-Grest model)
Poisson's ratio: 0

As a result of the test, in Example 1 and Example 2, the number of cuts of the bond model and the number of cuts of the cross-linked model were as follows.
Example 1:
Number of cuts of the bond model: 9 Number of cuts of the cross-linked model: 0 Example 2:
Number of cuts in the bond model: 6 Number of cuts in the bridge model: 5

  In Example 1 and Example 2, it was possible to calculate the breakage of the molecular chain model or the crosslinking model by the deformation calculation of the polymer material model. Therefore, Example 1 and Example 2 were able to analyze polymer chain breakage. Moreover, compared with Example 1, Example 2 was able to express the ease of cutting | disconnection of a bridge | crosslinking model. Therefore, Example 1 and Example 2 were able to evaluate the breaking state of the polymer chain, the bond strength between atoms constituting the polymer chain, and the like.

S1 step of defining a molecular chain model S2 step of defining a first distance S5 step of deforming a polymer material model

Claims (8)

A method for analyzing a polymer material using a computer,
Inputting a molecular chain model including a plurality of particle models and a bond model for connecting adjacent particle models to the computer based on the polymer chains of the polymer material;
Defining a first distance in the computer for cutting between adjacent particle models via the bond model;
An arrangement step of arranging a plurality of molecular chain models in a predetermined space and setting a polymer material model;
The computer includes a simulation step of deforming the polymer material model,
The simulation step includes a step of deleting the bond model between the particle models when a distance between the particle models adjacent via the bond model is equal to or greater than the first distance. .   2. The method for simulating a polymer material according to claim 1, wherein the molecular chain model is a coarse-grained model in which a plurality of atoms constituting the polymer chain are replaced with one particle model.   The step of defining the first distance is the dissociation energy between atoms constituting the main chain of the polymer chain among the dissociation energy between the plurality of atoms constituting the particle model, and the smallest dissociation The polymer material simulation method according to claim 2, wherein the first distance is defined based on energy.   The step of defining the first distance is the activation energy between atoms constituting the main chain of the polymer chain among the activation energies between the plurality of atoms constituting the particle model, and most The method for simulating a polymer material according to claim 2, wherein the first distance is defined based on a small activation energy. The bond model is set with an extension length that is an upper limit value of the distance between the particle models,
The method for simulating a polymer material according to claim 1, wherein the first distance is smaller than the full length. Setting a cross-linking model for bonding between the particle models of adjacent molecular chain models;
Defining a second distance for cutting between adjacent particle models via the bridging model,
The said simulation process includes the process of deleting the said bridge | crosslinking model between the said particle models, when the distance between the said particle models adjacent via the said bridge | crosslinking model is more than the said 2nd distance. The simulation method of the polymeric material in any one.   The method for simulating a polymer material according to claim 6, wherein the step of defining the second distance defines the second distance based on a dissociation energy or activation energy of a cross-linking bond defined by the cross-linking model. The cross-linking model is set with an extension length that is an upper limit value of the distance between the particle models,
The method for simulating a polymer material according to claim 6 or 7, wherein the second distance is smaller than the full length.

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