JP2020027402A - Method for creating polymer material model, method for simulating polymer material, and method for manufacturing polymer material - Google Patents

Abstract

To create a polymer material model capable of reproducing the cross-linked dense structure.SOLUTION: This is a method for creating, using a computer, a polymer material model for numerical analysis of polymer material in which molecular chains are crosslinked. This creating method comprises: a step of inputting, to a computer, a molecular chain model obtained by connecting a plurality of particle models based on the structure of the molecular chain; a step of defining the plurality of molecular chain models inside a cell which is a virtual space corresponding to a part of the polymer material; a step S82 of dividing the inside of the cell into a plurality of regions; a step S83 of setting mutually different cross-link densities in the respective regions; and a step S84 of setting, by the computer, a cross-linking point where a pair of the particle model of molecular chain models are connected to each other. The step S84 of setting the cross-linking point includes a step of setting more cross-linking points in a region having a higher cross-link density based on the cross-link density.SELECTED DRAWING: Figure 9

Description

  The present invention relates to a method for creating a polymer material model that can be used for numerical analysis by a computer, and the like.

  In recent years, for the development of polymer materials such as vulcanized rubber, various simulation methods (numerical calculations) for evaluating the properties of the polymer materials using a computer have been proposed. In this type of method, a polymer material model is created before performing a numerical calculation.

  Patent Document 1 listed below proposes a method for creating a polymer material model. In this method, a coarse-grained model obtained by modeling a polymer chain of a polymer material using a plurality of coarse-grained particles is set, and then the coarse-grained model is arranged in a predetermined space. Is done. Thereby, a polymer material model is set.

JP 2017-224202 A

  In general, it is known that a polymer material in which molecular chains such as vulcanized rubber are crosslinked has a so-called crosslinked dense / dense structure in which a portion having a high crosslinking density and a portion having a low crosslinking density are mixed. Such a cross-linked dense structure affects the physical properties of the polymer material.

  However, in the method of Patent Document 1, there is room for improvement in the above-described procedure because the density of cross-links is not considered.

  The present invention has been devised in view of the above situation, and has as its main object to provide a method for creating a polymer material model capable of reproducing a dense and cross-linked structure.

  The present invention is a method for creating, using a computer, a polymer material model for numerical analysis of a polymer material in which a molecular chain is crosslinked, and a plurality of particle models based on the structure of the molecular chain. Inputting the connected molecular chain model to the computer; defining a plurality of the molecular chain models in a cell which is a virtual space corresponding to a part of the polymer material; and Is divided into a plurality of regions, and the steps of setting different crosslinking densities in the respective regions, and in each of the regions, the computer couples the particle models of the pair of molecular chain models to each other. Setting a cross-linking point, the step of setting the cross-linking point includes a step of setting more cross-linking points in a region where the cross-linking density is higher based on the cross-linking density. It is characterized in.

  In the method of creating a polymer material model according to the present invention, the step of dividing the region may include a step of dividing the region into three types.

  In the method for creating a polymer material model according to the present invention, the step of setting the crosslink density is such that an average value of the crosslink density of all regions is equal to the crosslink density of the polymer material. The method may include a step of setting the crosslink density of the region.

  In the method of creating a polymer material model according to the present invention, the method further includes a step of measuring the size of the non-uniform network structure portion of the polymer material, the step of dividing the region, the step of the non-uniform network structure portion The method may include a step of determining the size of each of the regions based on the size.

  In the method for creating a polymer material model according to the present invention, the method further includes a step of determining a crosslink density of the non-uniform network structure portion, wherein the step of setting the crosslink density includes: The method may include a step of determining the crosslink density of each of the regions based on the information.

  The present invention is a method for simulating a polymer material, wherein the step of calculating a deformation of the polymer material model according to any one of claims 1 to 5, and the step of calculating the deformation of the polymer based on the calculation result of the deformation. Evaluating the performance of the material.

  The present invention is a method for producing a polymer material, wherein in the simulation method according to claim 6, the polymer material is produced based on the polymer material model evaluated as having good performance. It is characterized by including a step.

  A method for creating a polymer material model according to the present invention includes the steps of: inputting a molecular chain model obtained by connecting a plurality of particle models to a computer based on the structure of the molecular chain; and a virtual space corresponding to a part of the polymer material. Defining a plurality of the molecular chain models inside the cell.

  Further, in the creation method of the present invention, the step of dividing the inside of the cell into a plurality of regions, the step of setting different cross-link densities to the respective regions, and the computer in each of the regions, Setting a cross-linking point where the polymer particle models of the pair of molecular chain models are connected to each other. With such a crosslinking point, the polymer material model can reproduce the polymer material in which the molecular chains are crosslinked.

  The step of setting the cross-linking point includes a step of setting more cross-linking points in a region having a higher cross-link density based on the cross-link density. Accordingly, in the production method of the present invention, the number of the cross-linking points can be different for each of the regions, so that a region having a high cross-link density and a region having a low cross-link density can be set. Therefore, it is possible to create a polymer material model that reproduces the dense / dense structure of the bridge.

  In addition, since the polymer material model is used in a simulation for performing a deformation calculation, the polymer material model is useful for evaluating the viscoelasticity and fracture characteristics of the polymer material in consideration of the dense / dense structure of the bridge.

FIG. 2 is a perspective view showing an example of a computer for executing a method for creating a polymer material model and a method for simulating a polymer material. 2 is a structural formula showing an example of a polymer material. 9 is a flowchart illustrating an example of a processing procedure of a method for creating a polymer material model. It is a conceptual diagram which shows an example of the cell in which the filler model, the molecular chain model, and the coupling agent model were defined. It is an enlarged view of a filler particle model of a filler model. It is a conceptual diagram which shows an example of a molecular chain model. It is a conceptual diagram explaining an example of the potential of a filler model, a molecular chain model, and a coupling agent model. (A), (b) is a conceptual diagram which shows an example of the coupling agent model which connected the filler model and the molecular chain model. It is a flowchart which shows an example of the processing procedure of a bridge point setting process. It is a conceptual diagram showing an example of a cell divided into a plurality of fields. It is a conceptual diagram showing an example of the 1st field in which a bridge point was set. 6 is a flowchart illustrating an example of a processing procedure of a simulation method of a polymer material model. (A) is a conceptual diagram showing a part of the polymer material model before deformation calculation, and (b) is a conceptual diagram showing a part of the polymer material model after deformation calculation. It is a conceptual diagram which shows an example of the polymer material model which has a hole. (A) is a conceptual diagram showing a crosslinking point of an example, and (b) is a conceptual diagram showing a crosslinking point of a comparative example. 4 is a graph showing a relationship between a total volume of holes and a relaxation time.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
The method for creating a polymer material model of the present embodiment (hereinafter, sometimes simply referred to as “creation method”) is a method for creating a polymer material model for numerical analysis of a polymer material using a computer. It is.

  FIG. 1 is a perspective view showing an example of a computer for executing a method for creating a polymer material model and a method for simulating 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. The storage device stores in advance software and the like for executing the creation method and the simulation method of the present embodiment.

  The polymer material has a crosslinked molecular chain. Crosslinking occurs in mutually different molecular chains or in the same molecular chain. The polymer material of the present embodiment contains a crosslinking agent. Examples of the polymer material include rubber, resin, and elastomer. In the present embodiment, cis-1,4 polyisoprene (hereinafter, sometimes simply referred to as “polyisoprene”) is exemplified. FIG. 2 is a structural formula showing an example of a polymer material.

In FIG. 2, cis-1,4 polyisoprene (hereinafter sometimes simply referred to as “polyisoprene”) is exemplified. Molecular chain 2 constituting the polyisoprene methine group (e.g., -CH =,> C =) , methylene group _(-CH 2 -), and a monomer isoprene constituted by a methyl group (-CH ₃₎ (Isoprene molecules) 3 are connected at a degree of polymerization n. Examples of the crosslinking agent include, for example, sulfur that forms a monosulfide bridge, disulfide bridge, or polysulfide bridge, and organic peroxide that forms a peroxide bridge.

  The polymer material of the present embodiment further includes a filler and a coupling agent for binding a molecular chain to the filler. Examples of the filler include silica. The case where the coupling agent is a silane coupling agent (TESPD) is exemplified.

  FIG. 3 is a flowchart illustrating an example of a processing procedure of a method for creating a polymer material model. In the creation method according to the present embodiment, first, the cell 4, which is a virtual space corresponding to a part of the polymer material, is input to the computer 1 (step S1). FIG. 4 is a conceptual diagram showing an example of the cell 4 in which the filler model 6, the molecular chain model 7, and the coupling agent model 8 are defined.

  The cell 4 has at least a pair of surfaces 5 and 5 facing each other, in this embodiment, three pairs of surfaces 5 and 5 facing each other, and is defined as a rectangular parallelepiped or a cube (in the present embodiment, a cube). . A periodic boundary condition is defined for each surface 5,5. By using such a cell 4, in the coarse-grained molecular dynamics calculation described later, for example, a part of the molecular chain model 7 that has gone out of the surface 5 a on one side is described. , Can be calculated so as to enter from the other surface 5b. Therefore, the cell 4 can be handled as if the one surface 5a and the other surface 5b are continuous (connected).

  Each length L1 of one side of the cell 4 can be appropriately set. The length L1 of the present embodiment is desirably three times or more the radius of inertia (not shown) which is an amount indicating the expansion of the molecular chain model 7 described later. Thus, in the coarse-grained molecular dynamics calculation described later, the cell 4 can appropriately calculate the spatial spread of the molecular chain model 7 while preventing collision with its own image due to the periodic boundary condition. . The size of the cell 4 is set to a stable volume at, for example, 1 atmosphere. Thereby, the cell 4 can define the volume of at least a part of the polymer material to be analyzed. Cell 4 is stored in computer 1.

  Next, in the creation method of the present embodiment, a filler model 6 that models a filler is defined inside the cell 4 (step S2). The filler model 6 of the present embodiment is defined by a plurality of filler particle models 11 aggregated inside the cell 4. In the present embodiment, the filler particle model 11 is arranged based on the position of the filler in the electron beam transmission image of the actual polymer material. Thus, the filler model 6 can accurately represent the actual filler shape.

  FIG. 5 is an enlarged view of the filler particle model 11 of the filler model 6. Each filler particle model 11 is configured to include a plurality of small particles 12. In the filler particle model 11, a constraint condition for fixing the relative position between the adjacent small particles 12, 12 may be defined, and a binding chain model (not shown) for restricting between the adjacent small particles 12, 12 may be defined. May be defined. Thereby, in the filler model 6, the shape of the filler particle model 11 is maintained in the coarse-grained molecular dynamics calculation described later, and the shape of the filler model 6 can be approximated to the filler.

  For example, a binding chain model (not shown) constraining the small particles 12, 12 is described in a 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 defined by the sum of the LJ potential and the FENE potential. Further, each constant defined for the potential can be appropriately set based on the above-mentioned paper. Further, the small particles 12 are treated as mass points of the equation of motion in the coarse-grained molecular dynamics calculation. That is, parameters such as mass, diameter, charge, or initial coordinates are defined for the small particles 12. The filler model 6 is stored in the computer 1.

  Next, in the creation method of the present embodiment, a molecular chain model 7 that models the molecular chain 2 is defined inside the cell 4 (step S3). FIG. 6 is a conceptual diagram illustrating an example of the molecular chain model 7.

  In step S3, first, a step of inputting a molecular chain model 7 in which a plurality of particle models 15 are connected to the computer 1 based on the structure of the molecular chain 2 shown in FIG. Adjacent particle models 15 and 15 are connected by a binding chain model 16.

  The particle model 15 is obtained by substituting a monomer of the molecular chain 2 or a structural unit forming a part of the monomer. In the case where the molecular chain 2 is polyisoprene, it is replaced with one particle model 15 based on the above-mentioned paper, for example, using 1.73 monomers 3 (shown in FIG. 2) as a structural unit. Thereby, a plurality (for example, 10 to 5000) of particle models 15 are set in each molecular chain model 7. The particle model 15 is treated as a mass point of the equation of motion in the coarse-grained molecular dynamics calculation. That is, in the particle model 15, for example, parameters such as mass, diameter, charge, or initial coordinates are defined.

  FIG. 7 is a conceptual diagram illustrating an example of the potential of the filler model 6, the molecular chain model 7, and the coupling agent model 8. The bond chain model 16 is defined by a potential P1 in which the extended length is set between the particle models 15, 15. The potential P1 can be appropriately defined. The potential P1 can be defined by, for example, the sum of the LJ potential and the FENE potential, as in the related art. Each constant defined for the potential can be appropriately set based on the above-mentioned paper. Thereby, the linear molecular chain model 7 in which the particle model 15 is elastically constrained can be defined. The molecular chain model 7 is stored in the computer 1.

  Next, in step S3 of the present embodiment, a step of defining a plurality of molecular chain models 7 inside the cell 4 is performed. In the present embodiment, a plurality (for example, 10 to 1,000,000) of molecular chain models 7 are arranged in a region where the filler model 6 is not arranged inside the cell 4. Thereby, in step S3, a plurality of molecular chain models 7 can be defined inside the cell 4 while avoiding overlapping with the filler model 6.

  Next, in the creation method of the present embodiment, a coupling agent model 8 that models a coupling agent is defined inside the cell 4 (step S4). The coupling agent model 8 is obtained by modeling the molecular structure (not shown) of the coupling agent with at least one particle model 19, as shown in FIG. In the coupling agent model 8 composed of a plurality of particle models 19, adjacent particle models 19, 19 are connected by a bond chain model 20.

  The particle model 19 is obtained by replacing the structural unit of the coupling agent. Each of the particle models 19 of the present embodiment has a molecular weight of 30 to 550. Here, the reason why the molecular weight of the particle model 19 is set to 30 to 550 is that the general particle model 15 used for modeling the molecular structure of the molecular chain (molecular chain model 7) has a molecular weight of about 30 to 550. It is based on that.

  The particle model 19 of this embodiment is treated as a mass point of the equation of motion in coarse-grained molecular dynamics calculation described later. That is, in the particle model 19, for example, parameters such as mass, diameter, charge, or initial coordinates are defined.

  The binding chain model 20 is defined by a potential P2 in which a length is set between the particle models 19 and 19. The potential P2 can be appropriately defined. The potential P2 can be defined by, for example, the sum of the LJ potential and the FENE potential, as in the related art. Each constant defined for the potential can be appropriately set based on the above-mentioned paper. Thereby, the linear coupling agent model 8 in which the particle model 19 is elastically constrained can be defined.

  In step S4 of the present embodiment, at least one (for example, 10 to 1000) coupling agent models 8 are arranged in a region where the filler model 6 and the molecular chain model 7 are not arranged inside the cell 4. Is done. Thus, in step S4, the coupling agent model 8 can be arranged while avoiding the overlap between the filler model 6 and the molecular chain model 7. The coupling agent model 8 is stored in the computer 1.

Next, in the creation method of the present embodiment, a potential is defined for the adjacent filler model 6, molecular chain model 7, and coupling agent model 8 (step S5). In step S5 of the present embodiment, as shown in FIG. 7, the following potential P3 is applied to the small particles 12 of the filler model 6, the particle model 15 of the molecular chain model 7, or the particle model 19 of the coupling agent model 8. To P8 are defined.
Potential P3: with small particles 12 of filler model 6
Potential P4 between small particles 12 of filler model 6 and particle model 15 of molecular chain model 7
Potential P5 between particle model 15 of molecular chain model 7 and particle model 19 of coupling agent model 8
Potential P6 between the coupling agent model 8 and the particle model 19 and the small particles 12 of the filler model 6
Potential P7 between particle model 15 of molecular chain model 7 and small particle 12 of filler model 6
Potential P8 between the coupling agent model 8 and the particle model 19 and the particle model 15 of the molecular chain model 7
Between the coupling agent model 8 and the particle model 19

  The potentials P3 to P8 can be defined by LJ potentials as in the related art. Each constant of the potentials P3 to P8 can be appropriately set based on the above-mentioned paper. These potentials P3 to P8 are stored in the computer 1.

  Next, in the creation method of the present embodiment, the computer 1 calculates the structural relaxation of the cell 4 shown in FIG. 4 based on the coarse-grained molecular dynamics calculation (step S6). In the coarse-grained molecular dynamics calculation of the present embodiment, for example, assuming that the filler model 6, the molecular chain model 7, and the coupling agent model 8 follow the classical mechanics for a predetermined time for the cell 4, Newton's equation of motion is Applied. Then, the movements of the filler model 6, the molecular chain model 7, and the coupling agent model 8 at each time are tracked for each unit time of the simulation.

  In the calculation of the structural relaxation according to the present embodiment, in the cell 4, the pressure and the temperature are kept constant, or the volume and the temperature are kept constant. Thereby, in the step S6, the initial arrangement of the filler model 6, the molecular chain model 7, and the coupling agent model 8 can be accurately relaxed by approximating the actual molecular motion of the polymer material. Such calculation of structural relaxation can be performed using VSOP or COGNAC included in a soft material integrated simulator (J-OCTA) manufactured by JSOL Corporation, for example.

  In step S6, calculation is performed until the initial arrangement of the filler model 6, the molecular chain model 7, and the coupling agent model 8 can be sufficiently relaxed. Thus, in step S6, the equilibrium state (state in which the structure is relaxed) of the filler model 6, the molecular chain model 7, and the coupling agent model 8 can be reliably calculated.

  Next, in the creation method of the present embodiment, the computer 1 connects the filler model 6 and the molecular chain model 7 via the coupling agent model 8 (Step S7). FIGS. 8A and 8B are conceptual diagrams showing an example of a coupling agent model 8 in which a filler model 6 and a molecular chain model 7 are connected.

  In step S7 of the present embodiment, the small particles 12 of the filler model 6 and the particle model 15 of the molecular chain model 7, which are arranged in a region 22 centered on the particle model 19 of the coupling agent model 8, are connected. ing. The radius r of the region 22 can be appropriately set according to the physical properties of the coupling agent and the like.

  In the present embodiment, when the small particles 12 of the filler model 6 or the particle model 15 of the molecular chain model 7 are arranged in the region 22, the filler model 6 closest to the particle model 19 of the coupling agent model 8 is used. The small particles 12 or the particle model 15 of the molecular chain model 7 and the particle model 19 of the coupling agent model 8 are connected.

  As shown in FIG. 8A, when the coupling agent model 8 is composed of one particle model 19, the small particles 12 of the filler model 6 and the small particles 12 of the molecular chain model 7 are added to the particle model 19. The particle models 15 are connected.

  As shown in FIG. 8B, when the coupling agent model 8 is composed of a plurality of particle models 19, one of the particle models 19t and 19t at both ends of the coupling agent model 8 is one of the particle models 19t. Are connected to the small particles 12 of the filler model 6, and the other particle model 19t is connected to the particle model 15 of the molecular chain model 7.

  In step S7 of the present embodiment, between the particle model 19 of the coupling agent model 8 and the small particles 12 of the filler model 6, and between the particle model 19 of the coupling agent model 8 and the particle model 15 of the molecular chain model 7, Are connected via a binding chain model 21. The binding chain model 21 is defined by a potential P9 in which the extension length is set. The potential P9 can be appropriately defined. The potential P9 can be defined by, for example, the sum of the LJ potential and the FENE potential as in the related art.

  Next, in the creation method of the present embodiment, the computer 1 sets a cross-linking point at which the paired molecular chain models 7 and 7 are connected to each other (cross-linking point setting step S8). In the bridging point setting step S8 of this embodiment, the bridging points are set based on a plurality of different types of crosslink densities. The number of types of crosslinking density can be appropriately defined according to the set crosslinking point. In this embodiment, three types of crosslinking densities are set. FIG. 9 is a flowchart illustrating an example of the processing procedure of the bridge point setting step S8.

  In the bridging point setting step S8 of the present embodiment, first, the size of the non-uniform network structure portion (not shown) is measured (step S81). The non-uniform network structure portion corresponds to a portion of the polymer material having a relatively high crosslink density or a portion having a relatively low crosslink density. In step S81 of the present embodiment, the cross-link density (cross-link density index α) of the non-uniform network structure portion is determined together with the size of the non-uniform network structure portion.

  The smaller the value of the cross-link density index α, the higher the cross-link density of the heterogeneous network structure portion (not shown) as compared with the cross-link density of the other portions. On the other hand, as the value of the cross-link density index α increases, the cross-link density of the heterogeneous network structure portion is lower than the cross-link density of the other portions. Therefore, the cross-linking density index α is an effective parameter for examining the relative cross-linking density between the heterogeneous network structure portion and other portions.

  The size of the non-uniform network structure portion (not shown) and the crosslink density (crosslink density index α) are measured using a polymer material sample based on, for example, the method described in JP-A-2016-223806. can do. If the size and the crosslink density of the non-uniform network structure are known, step S81 can be omitted. Further, the measurement of the size and the crosslinking density of the non-uniform network structure portion may be performed before the crosslinking point setting step S8 of the present embodiment is performed. The size of the non-uniform network structure portion and its crosslink density (crosslink density index α) are stored in the computer 1.

  Next, in the bridging point setting step S8 of the present embodiment, the inside of the cell 4 is divided into a plurality of regions T (step S82). The region T is for setting a bridge point inside the cell 4 in a step S84 described later. FIG. 10 is a partial conceptual diagram illustrating an example of a cell 4 divided into a plurality of regions T. In FIG. 10, the first area T1 and the second area T2 are displayed by hatching.

  In step S82 of the present embodiment, the inside of the cell 4 is divided into a plurality of types of regions T according to the number of types of crosslink density. As described above, in the present embodiment, three types of crosslinking densities are set. Therefore, in step S82, the region T is divided into three types.

  The region T according to the present embodiment includes a first region T1, a second region T2, and a third region T3. The first region T1 is for setting a portion having a low crosslinking density in the cell 4. The second region T2 is for setting a portion having a high crosslinking density inside the cell 4. The third region T <b> 3 is for setting a portion where the crosslink density is other than low density (that is, a portion where the crosslink density is higher than the low density portion and smaller than the high density portion) inside the cell 4. belongs to.

  In step S82 of the present embodiment, first, inside the cell 4, a plurality of first regions T1 and a plurality of second regions T2 are randomly divided. Thereby, inside the cell 4, the first region T1 and the second region T2 are set, and the third region T3 divided into regions other than the first region T1 and the second region T2 is set.

  The first region T1, the second region T2, and the third region T3 are divided only inside the cell 4 into portions where the filler model 6 (the filler particle model 11) is not arranged. This is because no cross-linking point is generated inside the filler in the actual polymer material. The first area T1 and the second area T2 are set so as not to overlap with the other areas T1 and T2. This is because in the step S84 described later, the bridging points overlap in the overlapping portion of the first regions T1, T1, the overlapping portion of the second regions T2, T2, and the overlapping portion of the first region T1 and the second region T2. This is to prevent the setting.

  The shapes of the first region T1 and the second region T2 can be set as appropriate. The first region T1 and the second region T2 of the present embodiment are set in a spherical shape having a diameter D1. As a result, the first area T1 and the second area T2 can be easily defined by setting the center coordinates of the area T and the diameter D1. And the processing time can be shortened.

  The diameter D1 of the first region T1 and the second region T2 can be set as appropriate. The diameter D1 of the present embodiment is set based on the size of the non-uniform network structure portion. As described above, the non-uniform network structure portion corresponds to a portion of the polymer material having a relatively high crosslink density or a portion having a relatively low crosslink density. By setting the diameter D1 of the first region T1 and the second region T2 based on the size of such a non-uniform network structure portion, it is possible to reproduce an actual cross-linked structure of the polymer material. Note that the first region T1 and the second region T2 may be set to different diameters.

  The diameter D1 of the first region T1 and the second region T2 may be set to be substantially the same (for example, about 10 to 30 nm) as the diameter of the primary particles of the filler (the diameter D2 of the filler particle model 11). Thereby, the filler region close to the rigid body corresponding to the limit of the crosslinking density, the region where the crosslinking density is more easily deformed than the filler region (the second region T2), and the crosslinking density which is more easily deformed than the dense region are less dense. In the region (first region T1), the stress applied when the deformation of the polymer material model 10 is calculated and the influence on the vicinity of each region can be calculated on substantially the same scale. Can be easily compared.

  Regarding the ratio V1 / V of the total volume V1 of the first region T1 to the volume V of the cell 4 (shown in FIG. 4) and the ratio V2 / V of the total volume V2 of the second region T2 to the volume V of the cell 4, It can be set appropriately. In the present embodiment, the ratio V1 / V can be set by a ratio of the total size of the heterogeneous network structure portion having a relatively low crosslink density to the size of the sample of the polymer material. On the other hand, the ratio V2 / V can be set as a ratio of the total size of the heterogeneous network structure portion having a relatively high crosslinking density to the size of the sample of the polymer material. Thus, in step S82, the first region T1 and the second region T2 can be set based on the actual density structure of the crosslinked polymer material.

  Next, in the bridging point setting step S8 of the present embodiment, different crosslink densities are set in the respective regions T (step S83). In step S83 of the present embodiment, different crosslink densities are set in the first region T1, the second region T2, and the third region T3. In step S83 of the present embodiment, a lower bridge density is set in the first region T1 than in the third region T3. In step S83, a higher crosslinking density is set in the second region T2 than in the third region T3.

  Each crosslink density of the first region T1, the second region T2, and the third region T3 can be set as appropriate. In step S83 of the present embodiment, the crosslink density of each of the regions T1, T2, and T3 is determined based on the crosslink density (crosslink density index α) of the non-uniform network structure portion (not shown).

  As described above, the cross-link density index α is a parameter indicating the relative cross-link density between the non-uniform network structure portion and the other portions. The cross-link density index α of the non-uniform network structure portion having a relatively low cross-link density is determined by comparing the cross-link density of the third region T 3 (that is, the other portion) with the first region T 1 (that is, the non-uniform cross-link density is relatively low). The ratio (magnification) of the crosslink density of the network structure portion) is shown. By multiplying the cross-link density index α by the cross-link density of the third region T3 (hereinafter sometimes simply referred to as “third cross-link density”), the cross-link density of the first region T1 (hereinafter simply referred to as “first Crosslink density "). The first crosslink density is set in each of the first regions T1.

  As the third crosslinking density of the present embodiment, the crosslinking density (average crosslinking density) of the polymer material is set. The third crosslinking density is set in the third region T3.

  On the other hand, the cross-link density index α of the non-uniform network structure portion having a relatively high cross-link density is the cross-link density index α of the second region T2 (that is, the non-uniform network structure portion having a relatively high cross-link density) relative to the cross-link density of the third region T3. The ratio (magnification) of the crosslink density is shown. By multiplying the cross-link density index α by the third cross-link density, the cross-link density of the second region T2 (hereinafter, may be simply referred to as “second cross-link density”) is obtained. The second crosslink density is set in each of the second regions T2.

  In the bridge point setting step S8, the average value of the bridge densities of all the regions T (in the present embodiment, the first region T1, the second region T2, and the third region T3) (that is, the average crosslink density in the cell) However, it is desirable that the crosslink density of each region T is set so as to be equal to the actual crosslink density (average crosslink density) of the polymer material. Thereby, in the crosslink point setting step S8, the average crosslink density in the cell 4 can be set to the actual crosslink density (average crosslink density) of the polymer material while reproducing the dense / dense structure of the crosslinks.

  Next, in the bridging point setting step S8 of the present embodiment, in each region T (in the present embodiment, the first region T1, the second region T2, and the third region T3), the particle model 15 of the pair of molecular chain models 7 is used. Are set to each other (Step S84). In step S84 of the present embodiment, the cross-linking points of the regions T1, T2, and T3 are respectively set based on the first cross-link density, the second cross-link density, and the third cross-link density. FIG. 11 is a conceptual diagram illustrating an example of the first region T1 in which the bridge points 17 are set.

  The cross-linking points 17 are for connecting the particle models 15 of the pair of adjacent molecular chain models 7 to each other. At the bridging point 17, a potential P10 in which the extended length is set is defined. The potential P10 can be defined by, for example, the sum of the LJ potential and the FENE potential, as in the related art. With such crosslink points 17, the polymer material model 10 can reproduce a polymer material in which molecular chains are crosslinked.

  In step S84 of the present embodiment, first, the bridging points 17 of each first region T1 are set based on the first bridging density. As shown in FIG. 11, in each of the first regions T1 of the present embodiment, for the molecular chain model 7 arranged in the first region T1, the cross-linking density of the first region T1 becomes the first cross-link density. Point 17 is set randomly. As a result, in the first region T1, a portion having a low crosslinking density is set inside the cell 4.

  Next, in step S84 of the present embodiment, the bridging points 17 of each second region T2 (shown in FIG. 10) are set based on the second bridging density. In each of the second regions T2 of the present embodiment, for the molecular chain model 7 arranged in the second region T2, the crosslinking points 17 are randomly set until the crosslinking density of the second region T2 becomes the second crosslinking density. . As a result, in the second region T2, a portion having a high crosslinking density is set inside the cell 4.

  Next, in step S84 of the present embodiment, a bridge point 17 (shown in FIG. 10) of the third region T3 is set based on the third bridge density. In the third region T3 of the present embodiment, the crosslinking points 17 are randomly set until the crosslinking density of the third region T3 becomes the third crosslinking density. As a result, in the third region T3, a portion (intermediate portion) having a crosslink density other than sparse / dense is set inside the cell 4.

  As described above, in step S84, based on the bridge density set in each region T (in the present embodiment, the first region T1, the second region T2, and the third region T3), the region T having a large bridge density (for example, , The second region T2), more bridging points 17 are set. On the other hand, in step S84 of the present embodiment, the number of cross-linking points 17 is set to be smaller in a region T (for example, the first region T1) having a lower cross-link density. Thereby, the creation method of the present embodiment can make the number of the cross-linking points 17 different for each of the regions T1, T2, and T3, so that the region having a high cross-link density (the region T2 in the present embodiment) is low. The polymer material model 10 that reproduces the dense / dense structure of the bridge including the region (the region T1 in the present embodiment) can be created.

  Further, in the bridging point setting step S8 of the present embodiment, a predetermined region T (in the present embodiment, the first region T1, the second region T2, and the third region T3) that divides the inside of the cell 4 is predetermined. Crosslinking points 17 are set until the crosslinking density is reached. Thus, in the crosslinking point setting step S8 of the present embodiment, for example, the number of the crosslinking points 17 does not depend on the position of the molecular chain model 7 after relaxation by the molecular dynamics calculation. Therefore, the production method of the present embodiment can surely produce the polymer material model 10 that reproduces the dense / dense structure of the bridge.

  Next, in the creation method of the present embodiment, the computer 1 recalculates the structural relaxation of the cell 4 based on the coarse-grained molecular dynamics calculation (step S9). The calculation of the structural relaxation is performed based on the same processing procedure as in step S6, based on the filler model 6 and the molecular chain model 7 connected via the coupling agent model 8 shown in FIG. 8, and the crosslinking shown in FIG. The calculation is performed until the molecular chain model 7 connected at the point 17 can be sufficiently relaxed. Thereby, the molecular chains are crosslinked, and the equilibrium state (state in which the structure is relaxed) of the filler model 6, the molecular chain model 7, and the coupling agent model 8 after the coupling reaction can be calculated. The polymer material model 10 after the relaxation calculation is stored in the computer 1.

  In the creation method according to the present embodiment, the inside of the cell 4 is divided into three types of regions T (that is, the first region T1, the second region T2, and the third region T3). For example, it may be divided into two types of regions T (for example, a first region T1 and a second region T2), or may be divided into four or more types of regions T. The type of the region T (the type of the crosslink density) can be appropriately set, for example, based on the required density structure of the crosslinks.

  In the bridging point setting step S8 of the above-described embodiments, after dividing the inside of the cell 4 into regions T (for example, a first region T1, a second region T2, and a third region T3) (step S83), each region T Is set (step S84), and the cross-linking points 17 are set in each region T, but the present invention is not limited to such an embodiment. For example, the division inside the cell 4, the setting of the crosslinking density, and the setting of the crosslinking point 17 may be performed for each region T.

  In the creation method of the embodiment described above, the polymer material model 10 including the filler model 6 and the coupling agent model 8 is set inside the cell 4, but the invention is not limited to such a mode. The filler model 6 and the coupling agent model 8 can be omitted, or models of other components can be added, depending on the components to be blended in the polymer material to be analyzed.

  Next, a simulation method of a polymer material using the polymer material model 10 created by the creation method of the present invention and a method of manufacturing the polymer material will be described. FIG. 12 is a flowchart illustrating an example of a processing procedure of a simulation method of the polymer material model 10.

  In the simulation method of the present embodiment, first, the computer 1 performs a deformation calculation of the polymer material model 10 (step S11). The deformation calculation of the polymer material model 10 is performed, for example, according to the procedure described in Japanese Patent Application Laid-Open No. 2006-081297, on one end of the polymer material model 10 (one surface 5a of the cell 4 shown in FIG. 4). The elongation of the polymer material model 10 is calculated so that the other end of the polymer material model 10 (the other surface 5b of the cell 4 shown in FIG. 5) is separated from each other. In this example, the elongation of the polymer material model 10 is calculated by separating one end and the other end of the polymer material model 10 in the z-axis direction.

  FIG. 13A is a conceptual diagram showing a part of the polymer material model 10 before the deformation calculation. FIG. 13B is a conceptual diagram showing a part of the polymer material model 10 after the deformation calculation. In FIG. 13A and FIG. 13B, for example, a plurality of small regions 25 divided into a cubic shape are defined inside the cell 4. Before the deformation calculation of the polymer material model 10, any one of the filler model 6, the molecular chain model 7, and the coupling agent model 8 is arranged in each small region 25 by the above-described structural relaxation calculation.

  In step S11, the thermal motion of the filler model 6, molecular chain model 7, and coupling agent model 8 is calculated by elongation calculation of the polymer material model 10. Such thermal motion is calculated based on the strain given to the polymer material model 10, the potentials P1 to P10 shown in FIGS. 7, 8 and 11, and the equation of motion. Thus, a small region 25 in which the filler model 6, the molecular chain model 7, and the coupling agent model 8 are not arranged is formed in the cell 4. Such a small region 25 is defined as a void (void) 26 formed in the polymer material model 10. Such holes 26 reproduce the destruction of the polymer material model 10. FIG. 14 is a conceptual diagram illustrating an example of the polymer material model 10 having the holes 26.

  Generally, pores tend to be formed in portions where the crosslinking density is low. For this reason, a polymer material having a cross-linked dense structure has more holes formed than a polymer material having no cross-linked dense structure. In the simulation method of the present embodiment, the use of the polymer material model 10 in which the dense / dense structure of the crosslinks is reproduced allows calculation of the destruction of the polymer material model 10 in consideration of the dense / dense structure of the crosslinks. Therefore, in the simulation method of the present embodiment, it is possible to evaluate the fracture characteristics and the viscoelasticity of the polymer material in consideration of the cross-linked dense / dense structure.

  Next, in the simulation method of the present embodiment, the performance of the polymer material is evaluated based on the calculation result of the deformation of the polymer material model 10 (Step S12). In step S12, the total volume of all the holes 26 formed in the cell 4 is calculated, and when the total volume is smaller than a predetermined threshold, the performance (fracture resistance, and , Abrasion resistance). The threshold is appropriately set according to the performance required of the polymer material.

  If the size of the holes 26 is smaller than the threshold value in step S12, the performance of the polymer material model 10 is evaluated as being good ("Y" in step S12). In this case, a polymer material is manufactured based on the polymer material model 10 (various conditions set in the polymer material model 10) (step S13).

  On the other hand, when the size of the holes 26 is equal to or larger than the threshold value in the step S12, it is evaluated that the performance of the polymer material model 10 is not good (“N” in the step S12). In this case, the conditions (for example, the molecular structure of the cross-linking agent or the coupling agent) of the polymer material are changed (step S14), and the polymer material model 10 is re-created based on the procedure shown in FIG. (Step S15), Steps S11 to S12 are performed again.

  As described above, in the simulation method and the manufacturing method according to the present embodiment, various conditions of the polymer material are changed until the performance of the polymer material is improved. In addition, a polymer material having excellent wear resistance) can be efficiently produced.

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

  According to the processing procedure shown in FIG. 3, a polymer material model for numerical analysis of a polymer material in which molecular chains were cross-linked was created (Example, Comparative Example).

  In the example, according to the processing procedure shown in FIG. 9, the step of dividing the inside of the cell into a plurality of regions, the step of setting different crosslinking densities in each region, and the crosslinking density based on the crosslinking density The step of setting more cross-linking points in a larger area was performed. On the other hand, in the comparative example, the cross-linking points were randomly set so that the cross-linking density inside the cells became uniform. FIG. 15A is a conceptual diagram illustrating a cross-linking point in the example. FIG. 15B is a conceptual diagram illustrating a cross-linking point of a comparative example. In FIG. 15A, the cross-linking points in the second region having a relatively high cross-link density are shown as representatives.

Then, according to the processing procedure shown in FIG. 12, the deformation calculation of the polymer material models of the example and the comparative example was performed. In the deformation calculation, after the tensile calculation in the z-axis direction was performed, the same friction coefficient as in the above-mentioned paper was set, and the relaxation calculation of 900τ was performed after fixing the volume of the polymer material model. The common specifications are as follows.
cell:
Length of one side L1: 350σ
Length of one side of small area: 1.5σ
Filler model:
Volume fraction: 16.2%
The number of filler particle models: 1973 The diameter D2 of the filler particle model: 28.2σ
Number of small particles constituting the filler particle model: 16,589 Molecular chain model:
Quantity: 100,000 pieces Number of particle models constituting one molecular chain model: 1,000 pieces Coupling agent model:
Number of particle models constituting one coupling agent model: 1 Number of coupling agent models per one filler particle model: 80 Crosslinking points of Examples:
Average crosslink density in cell: 0.007245 (1 / σ ³ )
region:
Crosslink density of the first region: 1/10 times the crosslink density of the third region
Crosslink density of the second region: 10 times the crosslink density of the third region
Crosslink density of third region: 0.007245 (1 / σ ³ )
Volume fraction of the first region and the second region: 5%
Diameter D1: 20 nm of first region and second region
Crosslinking point of comparative example Average crosslink density in cell: 0.007245 (1 / σ ³ )
Deformation calculation:
Distortion: 0.15
Initial friction coefficient: 10 times that of the above paper
Initial deformation speed: 6.3τ / strain

  FIG. 16 is a graph showing the relationship between the total volume of holes and the relaxation time. As a result of the test, more holes were formed in the polymer material model of the example than in the polymer material model of the comparative example. As described above, a polymer material having a crosslinked dense / closed structure tends to form more holes than a polymer material having no crosslinked dense / closed structure. Therefore, the polymer material model of the example was able to reproduce the cross-linked dense structure compared to the polymer material model of the comparative example.

S82 Step of dividing the inside of the cell into a plurality of areas S83 Step of setting a bridge density in each area S84 Step of setting a bridge point in each area

Claims (7)

A method for creating, using a computer, a polymer material model for numerical analysis of a polymer material having a crosslinked molecular chain,
Based on the structure of the molecular chain, a step of inputting a molecular chain model connecting a plurality of particle models to the computer,
A step of defining a plurality of the molecular chain models inside a cell which is a virtual space corresponding to a part of the polymer material,
Dividing the inside of the cell into a plurality of regions;
In each of the regions, a step of setting a mutually different crosslinking density,
In each of the regions, the computer sets a cross-linking point where the particle models of the pair of molecular chain models are connected to each other,
The step of setting the cross-linking point includes a step of setting a larger number of the cross-linking points in a region where the cross-linking density is larger, based on the cross-linking density.
How to create a polymer material model.   The method for creating a polymer material model according to claim 1, wherein the step of dividing the region includes a step of dividing the region into three types.   The step of setting the crosslink density includes the step of setting the crosslink density of each region such that the average value of the crosslink density of all the regions is equal to the crosslink density of the polymer material. 3. The method for creating a polymer material model according to 1 or 2. The method further includes the step of measuring the size of the non-uniform network structure portion of the polymer material,
4. The method according to claim 1, wherein the step of dividing the region includes a step of determining a size of each of the regions based on the size of the non-uniform network structure portion. How to make. The method further includes a step of determining a crosslinking density of the non-uniform network structure portion,
The method for creating a polymer material model according to claim 4, wherein the step of setting the crosslink density includes a step of determining the crosslink density of each of the regions based on the crosslink density of the non-uniform network structure portion. Calculating a deformation of the polymer material model according to any one of claims 1 to 5,
Evaluating the performance of the polymer material based on the calculation result of the deformation,
Simulation method for polymer materials. The simulation method according to claim 6, further comprising a step of manufacturing the polymer material based on the polymer material model evaluated as having good performance,
A method for producing a polymer material.