JP6458097B1 - Coarse-grained molecular dynamics simulation method for polymer materials - Google Patents

Abstract

To obtain a stable simulation result. A method for performing coarse-grained molecular dynamics simulation of a polymer material including a polymer, a filler, and a coupling agent for binding the filler to the polymer, using a computer. This simulation method includes a step S4 of modeling the molecular structure of the coupling agent with a plurality of coarse-grained particles each having a molecular weight of 30 to 550. [Selection] Figure 4

Description

  The present invention relates to a coarse-grained molecular dynamics simulation method for a polymer material, and more particularly, a method for performing coarse-grained molecular dynamics simulation of a polymer material including a coupling agent for bonding a filler to a polymer. About.

  The following Patent Document 1 proposes a simulation method of a polymer material in which a coupling agent for bonding a filler and a polymer is blended using a computer. In this simulation method, a step of setting a coupling agent model obtained by modeling a coupling agent in a computer is included.

Japanese Patent Laying-Open No. 2015-212925

  The above-mentioned Patent Document 1 teaches modeling a coupling agent model with at least one coupling particle model, but does not teach a clear standard for modeling. Therefore, since modeling of the coupling agent is performed at the discretion of the operator, there is a problem that the coupling agent model varies and a stable simulation result cannot be obtained.

  The present invention has been devised in view of the above circumstances, and has as its main object to provide a coarse-grained molecular dynamics simulation method for a polymer material capable of obtaining a stable simulation result.

The present invention relates to a polymer model including a polymer, a filler, and a coupling agent for binding the filler to the polymer, a polymer model modeling the polymer, a filler model modeling the filler, and the A method for performing coarse-grained molecular dynamics simulation using a polymer material model including a coupling agent model modeling a coupling agent using a computer, and corresponding to a part of the polymer material Defining a cell, which is a virtual space, in the computer; and disposing the polymer model, the filler model, and the coupling agent model inside the cell, so that the polymer material model is stored in the computer. The polymer model is a molecule of the polymer The concrete, which each modeled by a plurality of coarse-grained particles having a molecular weight of 30 to 550, wherein the coupling agent model, the molecular structure of the coupling agent, each having a molecular weight of 30 to 550 It is characterized by modeling with a plurality of coarse-grained particles.

  In the coarse-grained molecular dynamics simulation method for the polymer material according to the present invention, the molecular weight of the coarse-grained particles of the coupling agent may be the same as the molecular weight of the coarse-grained particles of the polymer.

In the coarse-grained molecular dynamics simulation method of the polymer material according to the present invention, the computer performs deformation calculation of the polymer material model, and the polymer model, the filler model, and the coupling agent model are calculated. And a step of evaluating the destruction of the polymer material based on the size of the pores of the cell in which the is not disposed.

In the coarse-grained molecular dynamics simulation method of the polymer material according to the present invention, prior to the step of calculating deformation of the polymer material model, the computer calculates structural relaxation of the polymer material model; After calculating the structural relaxation of the polymer material model, the computer connects the filler model and the polymer model through the coupling agent model and connects the adjacent polymer models. And defining a cross-linking model to recalculate the structural relaxation of the polymer material model.

  The coarse-grained molecular dynamics simulation method for a polymer material of the present invention includes a step of modeling the molecular structure of the coupling agent with a plurality of coarse-grained particles each having a molecular weight of 30 to 550. Thereby, in this invention, since the molecular structure of the said coupling agent can be modeled based on a clear reference | standard, the stable simulation result can be obtained.

  Moreover, the molecular weight of 30-550 of the coarse-grained particles approximates the molecular weight of general coarse-grained particles used for modeling the molecular structure of the polymer. Therefore, the coarse-grained molecular dynamics simulation method of the polymer material of the present invention can approximate the molecular weight of the coarse-grained particles of the coupling agent and the molecular weight of the coarse-grained particles of the polymer. Therefore, highly accurate simulation is possible.

It is a perspective view which shows an example of the computer for performing the coarse-grained molecular dynamics simulation method of the polymeric material of this embodiment. It is a structural formula showing an example of a polymer. It is structural formula which shows an example of a coupling agent. It is a flowchart which shows an example of the process sequence of the coarse-grained molecular dynamics simulation method of the polymeric material of this embodiment. It is a conceptual diagram which shows an example of the cell by which the filler model, the polymer model, and the coupling agent model are arrange | positioned. It is an enlarged view of the filler particle model of a filler model. It is a conceptual diagram which shows an example of a polymer model. It is a conceptual diagram explaining an example of the potential of a filler model, a polymer model, and a coupling agent model. (A) is a conceptual diagram showing an example of a coupling agent model in which a filler model and a polymer model are connected via one coarse-grained particle, and (b) is a diagram between a filler model and a polymer model. It is a conceptual diagram which shows an example of the coupling agent model connected through several coarse-grained particle | grains. It is a figure which shows an example of a pair of polymer model connected with the bridge | crosslinking model. (A) is a conceptual diagram showing a part of a polymer material model before deformation calculation, and (b) is a conceptual diagram showing a part of the polymer material model after deformation calculation.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
The coarse-grained molecular dynamics simulation method (hereinafter sometimes simply referred to as “simulation method”) of the polymer material according to the present embodiment uses a computer to bind a polymer, a filler, and a filler to the polymer. This is a method for performing coarse-grained molecular dynamics calculation on a polymer material containing a coupling agent.

  FIG. 1 is a perspective view showing an example of a computer that executes the simulation method of the present invention. The computer 1 includes a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with, for example, 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 or the like for executing the simulation method of the present embodiment.

As the polymer, for example, natural rubber, synthetic rubber, resin, or the like is employed. FIG. 2 is a structural formula showing an example of a polymer. As a polymer of this embodiment, as shown in FIG. 2, cis-1,4 polyisoprene (hereinafter sometimes simply referred to as “polyisoprene”) is exemplified. Polymer 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 Molecule) 3 is connected with a polymerization degree n. A polymer other than polyisoprene may be used as the polymer.

As the filler, for example, silica, carbon black, alumina, or the like is employed. FIG. 3 is a structural formula showing an example of a coupling agent. As a coupling agent of this embodiment, the case where it is a silane coupling agent (TESPD) is illustrated. As the coupling agent, silane coupling agent disulfide group (TESPD) - a tetrasulfide group (-S ₂₎ - may be a silane coupling agent was changed to (TESPT) (-S ₄₎ And what changed the chain length of the alkyl group of a silane coupling agent (TESPD) may be sufficient, and silane coupling agent NXT or NXT-Z etc. may be employ | adopted.

  FIG. 4 is a flowchart illustrating an example of a processing procedure of the simulation method of the present embodiment. In the simulation method of the present embodiment, first, a cell that is a virtual space corresponding to a part of a polymer material is defined in the computer 1 (step S1). FIG. 5 is a conceptual diagram showing an example of the cell 4 in which the filler model 6, the polymer model 7, and the coupling agent model 8 are arranged.

  The cell 4 has at least a pair of surfaces 5 and 5 that face each other, and in this embodiment, three pairs of surfaces 5 and 5 that face each other, and is defined as a rectangular parallelepiped or a cube (in this embodiment, a cube). . A periodic boundary condition is defined for each of the surfaces 5 and 5. By using such a cell 4, in the later-described coarse-grained molecular dynamics calculation, for example, a later-described polymer model 7 that models a polymer (shown in FIG. 2) comes out from the surface 5a on one side. It can be calculated that a part of the polymer model 7 performed enters from the surface 5b on the other side. Accordingly, the cell 4 can be handled as one in which the surface 5a on one side and the surface 5b on the other side are continuous (connected).

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

  Next, in the simulation method of the present embodiment, a filler model 6 in which a filler is modeled 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 this 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. Thereby, the filler model 6 can accurately represent the shape of the actual filler.

  FIG. 6 is an enlarged view of the filler particle model 11 of the filler model 6. Each filler particle model 11 includes 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 bond chain model (not shown) that constrains between the adjacent small particles 12, 12 may be defined. May be defined. Thereby, the filler model 6 maintains the shape of the filler particle model 11 in the coarse-grained molecular dynamics calculation described later, and can approximate the shape of the filler model 6 to the filler.

  A bond chain model (not shown) that constrains between small particles 12 and 12 is described in, for example, 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) can be defined as the sum of the LJ potential and the FENE potential. In addition, each constant defined in the potential can be appropriately set based on the above paper. 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 small particles 12 constituting the outer surface of the filler particle model 11 may be provided with, for example, a functional group model (not shown) in which a functional group is modeled. Thereby, in the coarse-grained molecular dynamics calculation mentioned later and deformation | transformation calculation of a polymeric material, interaction with the filler and polymer which change with a functional group can be considered. The filler model 6 is stored in the computer 1.

  Next, in the simulation method of the present embodiment, a polymer model 7 that models a polymer is defined inside the cell 4 shown in FIG. 5 (step S3). In the present embodiment, at least one (for example, 10 to 1,000,000) polymer models 7 are arranged in a region where no filler model 6 is arranged inside the cell 4. Thereby, in process S3, polymer model 7 can be defined, avoiding overlap with filler model 6.

  FIG. 7 is a conceptual diagram showing an example of the polymer model 7. The polymer model 7 of this embodiment is obtained by modeling the molecular structure of a polymer with a plurality of coarse-grained particles 15. The adjacent coarse-grained particles 15 and 15 are connected by a bond chain model 16.

  The coarse-grained particle 15 is obtained by substituting a structural monomer constituting a polymer monomer or a part of the monomer. When the polymer is polyisoprene, based on the above paper, for example, 1.73 monomers 3 (shown in FIG. 2) are used as the structural unit and replaced with one coarse-grained particle 15. Thereby, a plurality of (for example, 10 to 5000) coarse-grained particles 15 are set in each polymer model 7.

  The coarse-grained particle 15 is handled as a mass point 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 coarse-grained particles 15.

  FIG. 8 is a conceptual diagram illustrating an example of potentials of the filler model 6, the polymer model 7, and the coupling agent model 8. The bond chain model 16 is defined by a potential P1 in which a full length is set between the coarse-grained particles 15 and 15. The potential P1 can be defined as appropriate. For example, the potential P1 can be defined by the sum of the LJ potential and the FENE potential as in the conventional case. Each constant defined in the potential can be appropriately set based on the above paper. As a result, the linear polymer model 7 in which the coarse-grained particles 15 are constrained to be stretchable can be defined. The polymer model 7 is stored in the computer 1.

  Next, in the simulation method of the present embodiment, a coupling agent model 8 in which a coupling agent is modeled is defined inside the cell 4 shown in FIG. 5 (step S4). In 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 polymer model 7 are not arranged in the cell 4. Thereby, in process S4, coupling agent model 8 can be defined, avoiding overlap with filler model 6 and polymer model 7.

  As illustrated in FIG. 8, the coupling agent model 8 is obtained by modeling the molecular structure of the coupling agent (shown in FIG. 3) with a plurality of coarse-grained particles 19. The adjacent coarse-grained particles 19 are connected by a bond chain model 20.

  The coarse-grained particles 19 are obtained by replacing the structural unit of the coupling agent. Each of the coarse-grained particles 19 of the present embodiment has a molecular weight of 30 to 550. Here, the molecular weight of the coarse-grained particles 19 is set to 30 to 550 because the general coarse-grained particles 15 used for modeling the molecular structure of the polymer have a molecular weight of about 30 to 550. Based on.

  Examples of the polymer modeled by the coarse-grained particles 15 having a small molecular weight include polyethylene (not shown) and polyisoprene (shown in FIG. 2). The coarse-grained particle 15 of the polymer model 7 obtained by modeling polyethylene has a molecular weight of 38.6 as described in “Equivalent mol. Mass” of “TABLE III” in the above paper. The coarse-grained particles 15 of polyisoprene have a molecular weight of 117. On the other hand, polystyrene (not shown) is exemplified as the polymer modeled by the coarse-grained particles 15 having a large molecular weight. The coarse-grained particles 15 have a molecular weight of 515 as described in the above paper. Accordingly, the molecular structure of the coupling agent is modeled with a plurality of coarse-grained particles 19 each having a molecular weight of 30 to 550, so that the molecular weight of the coarse-grained particles 19 of the coupling agent and the polymer model 7 The molecular weight of the coarse-grained particles 15 can be approximated.

  As described above, in the simulation method of the present embodiment, the molecular structure of the coupling agent can be modeled based on the above-described clear criteria. Therefore, the molecular weight of the coarse-grained particles 19 of the coupling agent varies depending on the operator. Can be prevented. Therefore, in this embodiment, a stable simulation result can be obtained.

  Further, in the simulation method of the present embodiment, the molecular weight of the coarse-grained particles 19 of the coupling agent and the molecular weight of the coarse-grained particles 15 of the polymer can be reliably approximated. This makes it possible to express the motion per coarse-grained particle and the kinetic energy per coarse-grained particle with high accuracy in the later-described coarse-grained molecular dynamics calculation and deformation calculation of the polymer material. Accuracy can be improved. When the molecular weight of the coarse-grained particles 19 of the coupling agent is less than 30 or exceeds 550, the size of the coarse-grained particles 19 of the coupling agent and the size of the coarse-grained particles 15 of the polymer are different. For this reason, it becomes difficult to exert the above-described action.

  In addition, about the molecular weight of the coarse-grained particle 19 of a coupling agent, if it is 30-550, it can set suitably. In order to effectively exhibit the above action, the molecular weight of the coarse-grained particles 19 of the coupling agent is desirably set to be the same as the molecular weight of the coarse-grained particles 15 of the polymer. Thereby, since the size of the coarse-grained particles 19 of the coupling agent and the size of the coarse-grained particles 15 of the polymer can be made equal, a more stable simulation result can be obtained.

  The coarse-grained particles 19 of this embodiment are handled as mass points of the equation of motion in the coarse-grained molecular dynamics calculation described later. That is, parameters such as mass, diameter, charge, or initial coordinates are defined for the coarse grained particles 19.

  The bond chain model 20 is defined by a potential P2 in which a full length is set between the coarse-grained particles 19 and 19. The potential P2 can be defined as appropriate. For example, the potential P2 can be defined by the sum of the LJ potential and the FENE potential, as in the conventional case. Each constant defined in the potential can be appropriately set based on the above paper. Thereby, the linear coupling agent model 8 in which the coarse-grained particles 19 are constrained to be stretchable can be defined. The coupling agent model 8 is stored in the computer 1.

Next, in the simulation method of the present embodiment, potentials are defined in the adjacent filler model 6, polymer model 7, and coupling agent model 8 (step S5). In step S5 of the present embodiment, as shown in FIG. 8, the small particles 12 of the filler model 6, the coarse-grained particles 15 of the polymer model 7, or the coarse-grained particles 19 of the coupling agent model 8 are Potentials P3 to P8 are defined.
Potential P3: small particle 12 of filler model 6 and
Between the small particles 12 of the filler model 6 and the potential P4: the coarse-grained particles 15 of the polymer model 7
Between the coarse-grained particles 15 of the polymer model 7 Potential P5: Coarse-grained particles 19 of the coupling agent model 8
Between the coarse-grained particles 19 of the coupling agent model 8 Potential P6: the small particles 12 of the filler model 6
Between the coarse-grained particles 15 of the polymer model 7 Potential P7: the small particles 12 of the filler model 6 and
Between the coarse-grained particles 19 of the coupling agent model 8 Potential P8: The coarse-grained particles 15 of the polymer model 7 and
Between the coarse-grained particles 19 of the coupling agent model 8

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

  Next, in the simulation method of the present embodiment, the computer 1 calculates the structural relaxation of the cell 4 shown in FIG. 5 based on the coarse-grained molecular dynamics calculation (step S6). In the coarse-grained molecular dynamics calculation of the present embodiment, for example, Newton's equation of motion is applied on the assumption that the cell 4 has a predetermined time, the filler model 6, the polymer model 7, and the coupling agent model 8 follow classical mechanics. Is done. Then, the movement of the filler model 6, the polymer model 7, and the coupling agent model 8 at each time is tracked for each unit time of the simulation.

  In the calculation of the structure relaxation of this embodiment, in the cell 4, the pressure and temperature are constant, or the volume and temperature are kept constant. Thereby, in step S6, the initial arrangement of the filler model 6, the polymer model 7, and the coupling agent model 8 can be relaxed with high accuracy by approximating the molecular motion of the actual polymer material. Such calculation of structural relaxation can be processed using COGNAC or VSOP included in a soft material general simulator (J-OCTA) manufactured by JSOL Corporation.

  In step S6, calculation is performed until the initial arrangement of the filler model 6, the polymer model 7, and the coupling agent model 8 can be sufficiently relaxed. Thereby, in process S6, the equilibrium state (state where the structure was relaxed) of filler model 6, polymer model 7, and coupling agent model 8 can be calculated reliably.

  Next, in the simulation method of the present embodiment, the computer 1 connects the filler model 6 and the polymer model 7 via the coupling agent model 8 (step S7). FIGS. 9A and 9B are conceptual diagrams showing an example of a coupling agent model 8 in which a filler model 6 and a polymer model 7 are connected.

  In step S7 of this embodiment, the small particles 12 of the filler model 6 and the coarse-grained particles 15 of the polymer model 7 disposed in the region 22 centering on the coarse-grained particles 19 of the coupling agent model 8 Are connected. About the radius r of the area | region 22, it can set suitably according to the physical property etc. of a coupling agent.

  In step S7 of the present embodiment, first, with respect to the coarse-grained particles 19 of the coupling agent model 8, the small particles 12 of the filler model 6 or the polymer model 7 in the region 22 centering on the coarse-grained particles 19 are used. Whether or not coarse-grained particles 15 are present is determined. When the small particles 12 of the filler model 6 or the coarse-grained particles 15 of the polymer model 7 are arranged in the region 22, the filler model 6 closest to the coarse-grained particles 19 of the coupling agent model 8 is used. The small particles 12 or the coarse-grained particles 15 of the polymer model 7 and the coarse-grained particles 19 of the coupling agent model 8 are connected.

  As shown in FIG. 9A, when the coupling agent model 8 is composed of one coarse-grained particle 19, the coarse-grained particle 19 includes small particles 12 of the filler model 6 and a polymer. Both coarse-grained particles 15 of the model 7 are connected.

  As shown in FIG. 9B, when the coupling agent model 8 includes a plurality of coarse-grained particles 19, one of the coarse-grained particles 19t and 19t at both ends of the coupling agent model 8 is used. The coarse particles 19t are connected to the small particles 12 of the filler model 6, and the coarse particles 15t of the polymer model 7 are connected to the other coarse particles 19t.

  In step S7 of this embodiment, the coarsening particles 19 of the coupling agent model 8 and the small particles 12 of the filler model 6 and between the coarsening particles 19 of the coupling agent model 8 and the polymer model 7 are coarse. The visualization particles 15 are connected via a bond chain model 21. The bond chain model 21 is defined by a potential P9 in which a full length is set. The potential P9 can be defined as appropriate. The potential P9 can be defined by the sum of the LJ potential and the FENE potential, for example, as in the conventional case.

  Next, in the simulation method of the present embodiment, a cross-linking model 17 that connects adjacent polymer models 7 is defined (step S8). FIG. 10 is a diagram illustrating an example of a pair of polymer models 7 connected by a crosslinking model 17.

  The cross-linking model 17 is for connecting the coarse-grained particles 15 and 15 of the polymer model 7. The bridge model 17 is set based on a predetermined bridge point. In the bridging model 17, a potential P <b> 10 with a full length set is defined. The potential P10 can be defined by the sum of the LJ potential and the FENE potential, for example, as in the prior art.

  Next, in the simulation 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 structure relaxation is performed in the same processing procedure as in step S6, and the filler model 6 and the polymer model 7 connected via the coupling agent model 8 and the polymer model 7 connected by the cross-linking model 17 are sufficient. It is calculated until it can be relaxed. Thereby, in the simulation method of the present embodiment, the polymer material model 10 that reproduces the crosslinked polymer material after the coupling reaction can be defined. The polymer material model 10 is stored in the computer 1.

  Next, in the simulation method of this embodiment, the computer 1 performs deformation calculation of the polymer material model 10 (step S10). The deformation calculation of the polymer material model 10 is performed, for example, in accordance with a procedure described in JP-A-2006-081297, one end of the polymer material model 10 (one surface 5a of the cell 4 shown in FIG. 5). The elongation of the polymer material model 10 is calculated so that the other ends of the polymer material model 10 (the other surface 5b of the cell 4 shown in FIG. 5) are 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. 11A is a conceptual diagram showing a part of the polymer material model 10 before the deformation calculation. FIG. 11B is a conceptual diagram showing a part of the polymer material model 10 after deformation calculation. In FIG. 11A and FIG. 11B, a plurality of small regions 25 partitioned into, for example, a cube are defined inside the cell 4. Before the deformation calculation of the polymer material model 10, any one of the filler model 6, the polymer model 7, and the coupling agent model 8 is arranged in each small region 25 by the above-described structural relaxation calculation.

  In step S <b> 10, the thermal motion of the filler model 6, the polymer model 7, and the coupling agent model 8 is calculated by the elongation calculation of the polymer material model 10. Such thermal motion is calculated based on the strain applied to the polymer material model 10, the potentials P1 to P10 shown in FIGS. 8 to 10 and the equation of motion. As a result, a small region 25 in which the filler model 6, the polymer 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 26 formed in the polymer material model 10. Such voids 26 reproduce the destruction of the polymer material model 10.

  As described above, in the simulation method of the present embodiment, the molecular structure of the coupling agent is modeled by the plurality of coarse-grained particles 19 each having a molecular weight of 30 to 550. The molecular weight of the polymerized particles 19 and the molecular weight of the polymer coarse-grained particles 15 can be approximated. Thereby, since the motion per coarse-grained particle and the kinetic energy per coarse-grained particle can be expressed with high accuracy, the destruction of the polymer material model 10 can be appropriately reproduced.

  Next, in the simulation method of the present embodiment, the computer 1 calculates the size of the holes 26 formed in the cell 4 (step S11). In step S11, the total volume of all the holes 26 formed in the cell 4 is calculated. The total volume of the holes 26 is stored in the computer 1.

  Next, in the simulation method of the present embodiment, the computer 1 evaluates the destruction of the polymer material based on the size of the holes 26 formed in the cell 4 (step S12). In step S12 of the present embodiment, when the size of the pores 26 formed in the cell 4 is smaller than a predetermined threshold value, the polymer material model 10 has excellent fracture resistance and wear resistance. It is evaluated that there is. About a threshold value, it sets suitably according to the fracture resistance and abrasion resistance calculated | required by polymeric material.

  In Step S12, when the size of the hole 26 is smaller than the threshold (“Y” in Step S12), the polymer material model 10 is evaluated as having the desired fracture resistance and wear resistance. be able to. For this reason, in the simulation method of the present embodiment, a polymer material is manufactured based on various conditions set in the polymer material model 10 (step S13). On the other hand, when the size of the hole 26 is equal to or larger than the threshold value in the step S12 (“N” in the step S12), it is evaluated that the polymer material model 10 does not have the desired fracture resistance and wear resistance. can do. For this reason, in the simulation method of the present embodiment, various conditions of the polymer material (for example, the molecular structure of the coupling agent) are changed (step S14), and steps S1 to S12 are performed again. Thereby, the simulation method of this embodiment can manufacture the polymeric material which is excellent in destruction resistance and abrasion resistance.

  As mentioned above, although especially preferable embodiment of this invention was explained in full detail, this invention is not limited to embodiment of illustration, It can deform | transform and implement in a various aspect.

  According to the processing procedure shown in FIG. 4, a coarse-grained molecular dynamics simulation of a polymer material containing a polymer, a filler, and a coupling agent was performed (Example, Comparative Example 1).

  In the examples, a first coupling agent model was defined in which the molecular structure of a first coupling agent having a molecular weight of 500 was modeled with coarse-grained particles having a molecular weight of 500. Furthermore, in the Examples, a second coupling agent model was defined in which the molecular structure of a second coupling agent having a molecular weight of 1000 was modeled with coarse-grained particles having a molecular weight of 500.

  Next, a first polymer material model in which a polymer model, a filler model, and a first coupling agent model are arranged inside a cell that is a virtual space corresponding to a part of the polymer material was defined. Furthermore, a second polymer material model in which a polymer model, a filler model, and a second coupling agent model are arranged inside the cell was defined. And the deformation calculation of the 1st polymer material model and the 2nd polymer material model was implemented, respectively, and destruction (wear resistance) of the polymer material was evaluated. The evaluation of wear resistance is indicated by an index with the first polymer material as 100. The larger the value, the better the wear resistance.

  In Comparative Example 1, a first coupling agent model was defined in which the molecular structure of the first coupling agent having a molecular weight of 500 was modeled with coarse-grained particles having a molecular weight of 50. Further, in Comparative Example 1, a second coupling agent model was defined in which the molecular structure of the second coupling agent having a molecular weight of 1000 was modeled with coarse-grained particles having a molecular weight of 50. Next, a first polymer material model in which a polymer model, a filler model, and a first coupling agent model are arranged inside a cell that is a virtual space corresponding to a part of the polymer material, a polymer model, A filler model and a second polymer material model in which a second coupling agent model is arranged are defined. And the deformation calculation of the 1st polymer material model and the 2nd polymer material model was implemented, respectively, and destruction (wear resistance) of the polymer material was evaluated. The evaluation of wear resistance is indicated by an index with the first polymer material as 100. The larger the value, the better the wear resistance.

  For comparison, an all-atom molecular dynamics simulation of a polymer material including a polymer, a filler, and a coupling agent was performed (Comparative Example 2). In Comparative Example 2, the all-atom model of the first coupling agent and the all-atom model of the second coupling agent were defined. Next, a first polymer material model in which a polymer all-atom model, a filler all-atom model, and a first coupling agent all-atom model are arranged inside the cell, and a polymer all-atom model, filler And a second polymer material model in which all atom models of the second coupling agent are arranged. And the deformation calculation of the 1st polymer material model and the 2nd polymer material model was implemented, respectively, and destruction (wear resistance) of the polymer material was evaluated. The evaluation of wear resistance is indicated by an index with the first polymer material as 100. The larger the value, the better the wear resistance.

In order to confirm the simulation accuracy of Examples, Comparative Examples 1 and 2, a first rubber compounded with a first coupling agent and a second rubber compounded with a second coupling agent were produced. . And the volume loss amount of the 1st rubber | gum and the 2nd rubber | gum was measured using the LAT tester (Laboratory Abrasion and Skid Tester), and the reciprocal number was calculated | required. The result is an index with the volume loss amount of the first rubber of the example as 100, and the larger the value, the better the wear resistance. The common specifications are as follows.
Polymer: Polystyrene Filler: Silicon dioxide First coupling agent: Silane coupling agent (TESPD)
Second coupling agent: alkyl group of silane coupling agent (TESPD),
Modified so that the molecular weight is about 2 times. Filler model:
Number of filler particle models: 15
Volume fraction: 0.18
Polymer model:
Number of coarse-grained particles constituting one polymer model: 1000
Number of polymer models: 1000
Coupling agent model:
Number of coupling agent models: 2500
Cross-linking model:
Number of cross-linking models: 10,000
All-atom molecular dynamics simulation:
Force field: GAFF
Temperature: Adjust temperature using Langevin heat bath Computer CPU: Xeon (registered trademark) 2.26 GHz (24 cores) manufactured by intel
The test results are shown in Table 1.

  As a result of the test, the improvement in wear resistance of the second polymer material model relative to the first polymer material model of the example approximated the increase in wear resistance of the second tire relative to the first tire of the experimental example. On the other hand, the improvement in wear resistance of the second polymer material model relative to the first polymer material model in the comparative example did not approximate the increase in wear resistance of the second tire relative to the first tire in the experimental example. Therefore, the example was able to carry out a stable and highly accurate simulation as compared with the comparative example. In addition, the example was able to evaluate the wear resistance of the polymer material safely and at a lower cost than the experimental example in which the prototype tire was actually run.

  In Comparative Example 2, since the all-atom molecular dynamics simulation with a large calculation load was performed, the calculation could not be completed even after 10,000 hours had passed. Therefore, the embodiment was able to carry out a stable and accurate simulation in a short time.

S4 Defining the coupling agent model

Claims (4)

A polymer model including a polymer, a filler, and a coupling agent for binding the filler to the polymer, a polymer model modeling the polymer, a filler model modeling the filler, and the coupling agent A method for performing coarse-grained molecular dynamics simulation using a polymer material model including a modeled coupling agent model using a computer ,
Defining a cell in the computer that is a virtual space corresponding to a portion of the polymeric material;
Disposing the polymer model, the filler model, and the coupling agent model inside the cell to define the polymer material model in the computer,
The polymer model is obtained by modeling the molecular structure of the polymer with a plurality of coarse-grained particles each having a molecular weight of 30 to 550,
The coupling agent model, the molecular structure of the coupling agent, in which each modeled by a plurality of coarse-grained particles having a molecular weight of 30 to 550,
Coarse-grained molecular dynamics simulation method for polymer materials.   The coarse-grained molecular dynamics simulation method for a polymer material according to claim 1, wherein the molecular weight of the coarse-grained particles of the coupling agent is the same as the molecular weight of the coarse-grained particles of the polymer. The computer performs deformation calculation of the polymer material model, and based on the pore size of the cell in which the polymer model, the filler model, and the coupling agent model are not disposed, The method for coarse-grained molecular dynamics simulation of a polymer material according to claim 1, further comprising a step of evaluating destruction of the molecular material. Prior to the step of calculating deformation of the polymer material model, the computer calculates structural relaxation of the polymer material model;
After calculating the structural relaxation of the polymer material model, the computer connects the filler model and the polymer model through the coupling agent model and connects the adjacent polymer models. The coarse-grained molecular dynamics simulation method for a polymer material according to claim 3, further comprising the step of defining a crosslinking model and recalculating the structural relaxation of the polymer material model.

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