JP2019036253A - Method for simulating coarse graining molecular dynamics of polymer material - Google Patents

Abstract

To accurately compare physical quantities due to deformation.SOLUTION: Provided is a method for comparing the performance of at least two kinds of polymer materials mutually differing in the interaction between a filler and a polymer using a computer. This simulation method includes: a step S1 for setting, on the basis of each polymer material, each of polymer material models mutually differing in the strength of interaction potential between a filler and a polymer to the computer; a step S2 in which the computer calculates the structural relaxation of each polymer material model on the basis of the interaction potential; and a step S3 for deforming each of the polymer material models after structural relaxation and calculating a physical quantity due to the deformation of each polymer material model. In the step S3 for calculating the structural relaxation, calculation is made of the structural relaxation under a condition where the pressure and temperature of each polymer material model and the number of particles constituting the filler and the polymer are mutually the same.SELECTED DRAWING: Figure 3

Description

  The present invention relates to a coarse-grained molecular dynamics simulation method for a polymer material, and more particularly, to compare the performance of at least two kinds of polymer materials having different filler-polymer interactions using a computer. Regarding the method.

  The following Patent Document 1 proposes a simulation method of a polymer material including a filler and a polymer using a computer. In the simulation method disclosed in Patent Document 1, first, a polymer material model for numerical calculation is set in a computer based on the polymer material. An interaction potential for applying a repulsive force or an attractive force is defined between the filler and the polymer. In the simulation method of Patent Document 1 below, the structural relaxation of the polymer material model is calculated based on the interaction potential.

  The interaction potential includes parameters for defining its strength. Decreasing the strength of the interaction potential weakens physical adsorption between the filler and the polymer. Also, increasing the strength of the interaction potential increases the physical adsorption between the filler and the polymer.

K. Hagita, H. Morita, H. Takano, `` Molecular dynamics simulation study of a fracture of filler-filled polymer nanocomposites '', Poymer, ELSEVIER, September 2, 2016, Vol. 99, p.368-375

  In the said nonpatent literature 1, the simulation regarding destruction of a polymeric material model is performed by setting the polymeric material model from which the intensity | strength of interaction potential differs mutually. However, in the simulation of Non-Patent Document 1, since the calculation method of the structural relaxation for the polymer material models whose interaction potential strengths are different from each other is not clearly shown, the physical quantity associated with the deformation of each polymer material model is determined. There was a problem that it was difficult to compare accurately.

  As a result of intensive studies, the inventors have found that the distribution of polymer to the filler changes unless the structural relaxation of polymer materials models with different interaction potential strengths is calculated appropriately. It was found that the internal stresses of the polymer material models differed greatly from each other. Then, it was found that the physical quantities associated with deformation cannot be compared with high accuracy in each polymer material model having greatly different internal stresses.

  The present invention has been devised in view of the actual situation as described above, and has as its main purpose to provide a coarse-grained molecular dynamics simulation method for polymer materials that can accurately compare physical quantities associated with deformation. Yes.

  The present invention is a method for comparing the performance of at least two types of polymer materials in which the interaction between the filler and the polymer is different from each other using a computer, and based on each of the polymer materials, A step of setting, in the computer, polymer material models having different interaction potential strengths with respect to the polymer, respectively, and the computer relaxes the structure of each of the polymer material models based on the interaction potential. And calculating the physical quantity associated with the deformation of each of the polymer material models by deforming each of the polymer material models after the structure relaxation, and calculating the structural relaxation. The calculating step constitutes the pressure and temperature of each polymer material model, and the filler and the polymer. Under conditions where the number of children is the same as each other, and calculates the structural relaxation.

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

  In the coarse-grained molecular dynamics simulation method for a polymer material according to the present invention, the physical quantity may include a parameter relating to pores of each polymer material model.

  In the coarse-grained molecular dynamics simulation method for the polymer material according to the present invention, the parameter relating to the pore is the total volume of the pore or the total of the pore with respect to the volume of each polymer material model It may be a volume ratio.

  In the coarse-grained molecular dynamics simulation method of the polymer material according to the present invention, the computer may further include a step of comparing the physical quantities of the polymer material models.

  In the coarse-grained molecular dynamics simulation method of the polymer material according to the present invention, the interaction potential may be a Leonard Jones potential, and the strength may be a potential depth ε of the Leonard Jones potential. .

  The coarse-grained molecular dynamics simulation method for a polymer material according to the present invention is based on each polymer material, and a polymer material model having different interaction potential strengths between the filler and the polymer is used as the polymer material model. It includes the process of setting each to a computer. Furthermore, in the coarse-grained molecular dynamics simulation method for a polymer material according to the present invention, the computer calculates a structure relaxation of each polymer material model based on the interaction potential, Each of the polymer material models is deformed, and a physical quantity associated with the deformation of each polymer material model is calculated.

  The step of calculating the structural relaxation calculates the structural relaxation under the condition that the pressure and temperature of each polymer material model and the number of particles constituting the filler and the polymer are the same. Yes. Thus, the coarse-grained molecular dynamics simulation method of the polymer material according to the present invention can approximate the internal stresses of the polymer material models after the structure relaxation to each other. The accompanying physical quantities can be accurately compared.

It is a perspective view which shows an example of the computer which performs the coarse-grained molecular dynamics simulation method of a polymeric material. It is a structural formula showing an example of a polymer. It is a flowchart which shows an example of the process sequence of the coarse-grained molecular dynamics simulation method of a polymeric material. It is a flowchart which shows an example of the process sequence of a model setting process. It is a conceptual diagram which shows an example of the cell by which the filler model and the polymer model are arrange | positioned. It is the A section enlarged view of FIG. 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 interaction potential of a filler model and a polymer model. It is a flowchart which shows an example of the process sequence of a relaxation process. It is a graph which shows the relationship between the volume fraction of a 2nd polymeric material model, and time. It is a graph which shows the relationship between the equilibrium internal stress of a 1st polymer material model, the internal stress of a 2nd polymer material model, and time. (A) is a conceptual diagram showing a part of a 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 graph which shows the relationship between the stress of an Example, and distortion. It is a graph which shows the relationship between the volume fraction of the void | hole of an Example, and distortion. It is a graph which shows the relationship between the internal stress of each polymer material model of a comparative example, and time. It is a graph which shows the relationship between the volume fraction of the hole of a comparative example, and time.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
In the coarse-grained molecular dynamics simulation method (hereinafter, simply referred to as “simulation method”) of the polymer material of the present embodiment, at least two types of interaction between the filler and the polymer are different from each other using a computer. The performances of two types of polymer materials (in this embodiment) are compared.

  FIG. 1 is a perspective view illustrating an example of a computer that executes a simulation method. The computer 1 includes a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with, for example, an arithmetic processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2. The storage device stores in advance software or the like for executing the simulation method of the present embodiment.

  As the filler, for example, silica, carbon black, alumina, or the like is employed. 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.

  In the simulation method of this embodiment, the first polymer material and the second polymer material are included in the polymer material model whose performance is compared. The first polymer material and the second polymer material are different from each other in the interaction between the filler and the polymer. The first polymer material of the present embodiment is classified as having a weaker interaction than the second polymer material, but may be a material having a stronger interaction than the second polymer material. Moreover, the case of physical adsorption is illustrated as interaction of this embodiment.

  Physical adsorption between the filler and the polymer is a phenomenon in which the polymer is adsorbed on the surface of the filler mainly by van der Waals interaction and electrostatic interaction acting between the filler and the polymer. It is expected that the higher the physical adsorption between the filler and the polymer, the better the fracture resistance of the polymer material. Such physical adsorption strength can be appropriately set in an actual polymer material by adjusting, for example, the chemical structure and molecular density of the molecule. On the other hand, in the polymer material model used for the simulation described later, for example, by adjusting the value set for the strength of the interaction potential between the filler and the polymer (potential depth), the strength of physical adsorption can be reduced. Can be defined.

  FIG. 3 is a flowchart illustrating an example of a processing procedure of the simulation method. In the simulation method of the present embodiment, first, polymer material models having different interaction potential strengths are set in the computer 1 based on the polymer material (model setting step S1). In the model setting step S1 of the present embodiment, a first polymer material model that models the first polymer material and a second polymer material model that models the second polymer material are respectively set. FIG. 4 is a flowchart showing an example of the processing procedure of the model setting step S1.

  In the model setting step S1 of the present embodiment, first, a cell that is a virtual space corresponding to a part of the polymer material is defined in the computer 1 (step S11). The cell 4 is defined for each polymer material model 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)). FIG. 5 is a conceptual diagram showing an example of the cell 4 in which the filler model 6 and the polymer model 7 are arranged.

  The cell 4 has at least a pair of surfaces 5 and 5 facing each other, and in this embodiment, three pairs of surfaces 5 and 5 facing each other, and is defined as a rectangular parallelepiped or a cube (in this example, 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, it is possible to appropriately calculate the spatial spread of the polymer model 7 while 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.

  FIG. 6 is an enlarged view of part A in FIG. In the cell 4, for example, a plurality of small regions 9 divided into cubes are defined. Each small area 9 is set with a node 9t. Such a small region 9 is used to track the small particles 12 (shown in FIG. 9) of the filler model 6 and the coarse-grained particles 15 (shown in FIG. 9) of the polymer model 7 in the molecular dynamics calculation described later. Used for. The length L2 of one side of the small region 9 is preferably set to about 0.1 to 5 times the diameter of the coarse-grained particles 15, for example. The cell 4 is stored in the computer 1.

  Next, in the model setting step S1 of the present embodiment, a filler model 6 in which a filler is modeled is defined inside the cell 4 shown in FIG. 5 (step S12). In step S12 of this embodiment, a filler model 6 is defined for each cell 4 of each polymer material model 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)). Is done.

  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 primary particle of the filler in the electron beam transmission image of an actual polymer material. Thereby, the filler model 6 can accurately represent the shape of the actual filler. FIG. 7 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. The small particles 12 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 small particles 12.

  Each filler particle model 11 may be defined with a constraint condition that fixes the relative position between the adjacent small particles 12 and 12, or a bond chain model (not shown) that constrains between the adjacent small particles 12 and 12. 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 the shape of the filler model 6 can be approximated to the shape of the actual filler.

  A bond chain model (not shown) that constrains between small particles 12 and 12 is, 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) and can be defined by the sum of the Leonard Jones potential and the FENE potential. The constants defined for each potential can be set as appropriate based on the above paper.

  Of the plurality of small particles 12 constituting the filler particle model 11, the small particles 12 constituting the outer surface of the filler particle model 11 may be provided with a functional group model (not shown) that models a functional group, for example. Good. 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 model setting step S1 of the present embodiment, a polymer model 7 in which a polymer is modeled is defined inside the cell 4 shown in FIG. 5 (step S13). In step S13 of this embodiment, a polymer model 7 is defined for each cell 4 of each polymer material model 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)). Is done.

  In step S13 of 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 S13, the polymer model 7 can be defined, avoiding the overlap with the filler model 6.

  FIG. 8 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 the polymer shown in FIG. 2 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 particles 15 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 15.

  FIG. 9 is a conceptual diagram illustrating an example of the interaction potential of the filler model 6 and the polymer model 7. The bond chain model 16 is defined by an interaction potential P1 in which a full length is set between the coarse-grained particles 15 and 15. The interaction potential P1 can be defined as appropriate. For example, the interaction potential P1 can be defined by the sum of the Leonard Jones potential and the FENE potential, as in the conventional case. The constants defined for each potential can be set as appropriate 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 model setting step S1 of the present embodiment, an interaction potential is defined in the adjacent filler model 6 and polymer model 7 (step S14). In step S14 of the present embodiment, the interaction potential is defined in each polymer material model 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)).

In step S14 of this embodiment, as shown in FIG. 9, the following interaction potentials P2 to P4 are defined in the small particles 12 of the filler model 6 or the coarse-grained particles 15 of the polymer model 7.
Interaction potential P2: small particle 12 of filler model 6 and
Interaction potential P3 with the coarse particle 15 of the polymer model 7 and the small particle 12 of the filler model 6
Between the coarse-grained particles 15 of the polymer model 7 and the interaction potential P4: the small particles 12 of the filler model 6
Between the coarse-grained particles 15 of the polymer model 7

  The interaction potentials P2 to P4 can be defined by the Leonard Jones potential as in the conventional case. About the constant of interaction potential P2-P4, it can set suitably based on the said paper. These interaction potentials P2 to P4 are stored in the computer 1.

  Next, in the model setting step S1 of the present embodiment, the filler and the polymer are changed for each polymer material model 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)). The strengths of the interaction potentials are made different from each other (step S15). In step S15, the strength of the interaction potential P4 defined between the small particles 12 of the filler model 6 and the coarse-grained particles 15 of the polymer model 7 is made different for each polymer material model 10.

In step S15 of the present embodiment, Leonard defined as the interaction potential P4 for each polymer material model 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)). Jones potentials have different depths ε. As described above, since the first polymer material of the present embodiment is classified as having lower physical adsorption than the second polymer material, the interaction potential P4 (that is, Leonard) of the first polymer material model 10A is classified. The potential depth ε of the Jones potential) is set to be smaller than the potential depth ε of the interaction potential P4 of the second polymer material model. Thereby, in model setting process S1, the polymer material model 10 from which the intensity | strength of the interaction potential between a filler and a polymer mutually differs can be each set. Each polymer material model 10 is stored in the computer 1. Note that the potential depth ε of the interaction potential P4 of the first polymer material model 10A and the second polymer material model can be set as appropriate, and is set as follows in the present embodiment. The
Depth of potential of first polymer material model ε: 0.5
Depth of potential of second polymer material model ε: 2.0

  Next, in the simulation method of the present embodiment, the computer 1 uses the polymer material models 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown) based on the interaction potential. )) Structural relaxation is calculated (relaxation step S2). In the relaxation step S2 of the present embodiment, the structural relaxation of each polymer material model 10 is calculated based on the coarse-grained molecular dynamics calculation.

  In the coarse-grained molecular dynamics calculation of this embodiment, Newton's equation of motion is applied, for example, assuming that the filler model 6 and the polymer model 7 follow classical mechanics for a predetermined time for the cell 4. Then, the movements of the filler model 6 and the polymer model 7 at each time are tracked for each unit time of the simulation. The calculation of structural relaxation can be processed using COGNAC or VSOP included in a soft material synthesis simulator (J-OCTA) manufactured by JSOL Corporation.

  By the way, in the conventional simulation method, the volume and temperature of each polymer material model 10 and the number of particles constituting the filler and the polymer (the small particles 12 of the filler model 6 and the polymer model) The structural relaxation of each polymer material model 10 was calculated under the condition that the coarse-grained particles 15) of 7 are constant (ie, NVT). Each polymer material model 10 has the same volume, temperature, and number of particles. For this reason, in the structure relaxation calculation of the conventional simulation method, in each polymer material model 10, the distribution of the polymer with respect to the filler (that is, the distribution of the coarse-grained particles 15 of the polymer model 7 with respect to the filler model 6) changes, respectively. The internal stress of each polymer material model 10 is different. When deformation calculation is performed using each of the polymer material models 10 having different internal stresses, there is a problem in that physical quantities associated with deformation cannot be accurately compared.

  In the relaxation step S2 of this embodiment, the pressure, temperature, filler, and polymer of each polymer material model 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)) are used. Structural relaxation is calculated under the condition that the number of constituent particles (small particles 12 of filler model 6 and coarse-grained particles 15 of polymer model 7) are the same. FIG. 10 is a flowchart illustrating an example of the processing procedure of the relaxation step S2.

  In the relaxation step S2 of the present embodiment, first, from the polymer material model 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)) set in the model setting step S1, One polymer material model 10 (hereinafter, simply referred to as “reference polymer material model”) is selected (step S21). The reference polymer material model of the present embodiment is exemplified by the case where the first polymer material model 10A is selected, but is not limited to such a mode. For example, the second polymer material model May be selected.

  Next, in the relaxation step S2 of this embodiment, structural relaxation is calculated for the selected one polymer material model (reference polymer material model) 10 as in the conventional simulation method (step S22). In step S22, with respect to the reference polymer material model (first polymer material model 10A), the volume and temperature of the polymer material model 10 and the number of particles constituting the filler and polymer (of the small particles 12 of the filler model 6). The structural relaxation is calculated under the condition that the number and the number of coarse-grained particles 15 of the polymer model 7) are constant (ie, NVT ensemble).

  In step S22, the initial arrangement of the filler model 6 and the polymer model 7 is sufficient in the reference polymer material model (in this example, the first polymer material model 10A) based on the same procedure as the conventional simulation method. Calculated until relaxed. Thereby, in process S22, the equilibrium state (state in which the structure was relaxed) of filler model 6 and polymer model 7 can be calculated reliably. The structure-relaxed reference polymer material model is stored in the computer 1.

  Next, in the relaxation step S2 of this embodiment, another polymer material model 10 (in this example, the second polymer material model (not shown)) for which structural relaxation has not been calculated is selected (step S23). The structural relaxation of the selected polymer material model 10 is calculated (step S24).

  In step S24, the pressure of the reference polymer material model (first polymer material model 10A in this example) is selected for the selected polymer material model 10 (second polymer material model (not shown) in this example). Structure relaxation under the same conditions as the number of particles constituting the filler and polymer (number of small particles 12 of filler model 6 and number of coarse-grained particles 15 of polymer model 7). Is calculated.

  As described above, in the model setting step S1, each polymer material model 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)) has a volume, temperature, and number of particles. They are set the same. Therefore, in step S24, the selected polymer material model 10 (in this example, the second polymer material model) is different from the reference polymer material model (in this example, the first polymer material model 10A). By calculating the structural relaxation while changing the volume, the pressure and temperature of the reference polymer material model and the number of particles constituting the filler and polymer are made the same.

  FIG. 11 is a graph showing the relationship between the volume ratio (volume fraction) of the second polymer material model (not shown) to the volume of the first polymer material model 10A and time. FIG. 12 is a graph showing the relationship between the equilibrium internal stress of the first polymer material model, the internal stress of the second polymer material model (not shown), and time. In this embodiment, the strength of the interaction potential P4 of the selected polymer material model 10 (in this example, the second polymer material model) is the reference polymer material model (in this example, the first polymer material model). It is larger than the strength of the interaction potential P4 of 10A). In such a case, in step S24, as shown in FIG. 11, the volume of the selected polymer material model (second polymer material model) is set as the reference polymer material model (first polymer material model 10A). The structural relaxation is calculated to be smaller than the volume of. Thereby, the distribution of the polymer with respect to the filler of the selected polymer material model 10 (second polymer material model) is different from the distribution of the polymer with respect to the filler of the reference polymer material model (first polymer material model 10A). However, as shown in FIG. 12, the internal stress of the selected polymer material model (second polymer material model (not shown)) is expressed as a reference polymer material model (first polymer material model 10A). It is possible to approximate the internal stress of

  In step S24, calculation is performed until the initial arrangement of the filler model 6 and the polymer model 7 is sufficiently relaxed in the selected polymer material model 10 (in this example, the second polymer material model (not shown)). Is done. The pressure control of the selected polymer material model 10 is performed based on, for example, Andersen pressure control, Parrinello-Rahman pressure control, or the like. Thereby, in process S24, based on the said conditions, the equilibrium state (state in which the structure was relaxed) of the filler model 6 and the polymer model 7 can be calculated reliably. The structure-relaxed polymer material model 10 (second polymer material model) is stored in the computer 1.

  Next, in the relaxation step S2 of this embodiment, the structural relaxation of all the polymer material models 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)) has been calculated. It is determined whether or not (step S25). When the structural relaxation of all the polymer material models 10 is calculated in step S25 (“Y” in step S25), the next step S3 (shown in FIG. 3) is performed. On the other hand, when it is determined in Step S25 that the structure relaxation of all the polymer material models 10 has not been calculated (“N” in Step S25), Steps S23 to S25 are performed again. Thus, in the relaxation step S2, the pressure and temperature of each polymer material model 10 and the number of particles constituting the filler and polymer (the number of small particles 12 of the filler model 6 and the coarse-grained polymer model 7). The structural relaxation can be calculated under the condition that the number of particles 15) is the same. The internal stress of each polymer material model 10 after the relaxation calculation can be approximated.

  Next, in the simulation method of the present embodiment, the computer 1 uses each polymer material model 10 after the structure relaxation (in this example, the first polymer material model 10A and the second polymer material model (not shown)). Each is deformed, and the physical quantity associated with the deformation of each polymer material model 10 is calculated (step S3).

  In step S3, as shown in FIG. 5, each polymer material model 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)) is placed in a predetermined direction. A pulling uniaxial tensile test is calculated. The direction in which the polymer material model 10 is pulled can be selected as appropriate. In this example, the polymer material model 10 is pulled in the z-axis direction.

  The deformation calculation of the polymer material model 10 is performed, for example, in accordance with the procedure described in the patent document (Japanese Patent Laid-Open No. 2006-81297), in one end of the polymer material model 10 (shown in FIG. 5) in the z-axis direction. The extension of the polymer material model 10 is such that the one surface 5a) of the cell 4 and the other end of the polymer material model 10 (the other surface 5b of the cell 4 shown in FIG. 5) are separated from each other. Calculated. The elongation calculation of the polymer material model 10 is calculated based on the molecular dynamics calculation.

  FIG. 13A is a conceptual diagram showing a part of the polymer material model 10 before deformation calculation. FIG. 13B is a conceptual diagram showing a part of the polymer material model 10 after deformation calculation. Before the deformation calculation of the polymer material model 10, either the filler model 6 (not shown) or the polymer model 7 is arranged in each small region 9 inside the cell 4 by the above-described structural relaxation calculation. Yes.

  In step S <b> 3, the thermal motion of the filler model 6 and the polymer model 7 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 interaction potentials P1 to P4 shown in FIG. 9, and the equation of motion. Thereby, as shown in FIG. 13B, a small region 9 in which the filler model 6, the polymer model 7, and the coupling agent model 8 are not formed is formed in the cell 4. Such a small region 9 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.

  The deformation condition can be appropriately set as long as the holes 26 can be formed in at least a part of the region where the polymer model 7 is disposed. As an example of the deformation condition, the strain applied to the polymer material model 10 is about 0.1 to 0.3, and the deformation speed V1 per strain (shown in FIG. 5) is about 1000 to 10000τ. .

  In step S3, a unit of molecular dynamics calculation from the start of deformation to the end of deformation of each polymer material model 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)). For each step (MD step), a physical quantity associated with the deformation of each polymer material model 10 is calculated. As physical quantity, it can employ | adopt suitably. The physical quantity of the present embodiment includes the stress of the polymer material model 10. In step S3, the stress component in the extension direction of the polymer material model 10 is calculated for each strain applied to the polymer material model 10. Thereby, in the simulation method of this embodiment, the stress-strain curve which shows the relationship between the stress and distortion of each polymer material model 10 is acquirable.

  Furthermore, the physical quantities of the present embodiment include parameters related to the holes 26 of each polymer material model 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)). . Regarding the parameters related to the holes 26, for example, the total volume of the holes 26 formed in the entire system of the polymer material model 10 and the ratio of the total volume of the holes 26 to the volume of each polymer material model 10 (hereinafter, For example, it may be simply referred to as “a void volume fraction”). In step S3, the total volume of the holes 26 formed in the entire system of the polymer material model 10 is calculated for each strain applied to the polymer material model 10. Thereby, in the simulation method of this embodiment, the graph which shows the relationship between the parameter (in this example, the volume fraction of a void | hole) of each polymer material model 10 and a distortion | strain can be acquired. . The volume fraction of the holes 26 may be a ratio of the volume of the holes 26 to the volume change amount of the polymer material model 10 (cell 4) due to the strain generated by the deformation calculation.

  In step S3 of the present embodiment, each of the polymer material models 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)) in which the internal stresses after the structure relaxation are approximated to each other. Since the deformation is calculated, the physical quantity scales of the respective polymer material models 10 can be aligned with each other. Therefore, in the simulation method of the present embodiment, the deformation of each polymer material model 10 in consideration of the interaction between the filler and the polymer can be calculated with the physical quantity scale aligned. It is possible to accurately compare physical quantities associated with deformation. The physical quantity of each polymer material model 10 is stored in the computer 1.

  Next, in the simulation method of the present embodiment, the computer 1 compares the physical quantities of the respective polymer material models 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)). (Step S4). In step S4, the parameters relating to stress and vacancies are compared for each polymer material model 10. Thereby, in the simulation method of the present embodiment, the performance (for example, fracture characteristics, etc.) of polymer materials having different interactions (physical adsorption in this example) between the filler and the polymer can be evaluated. Therefore, it is useful for the development of polymer materials. Further, in the simulation method of the present embodiment, it is possible to present the direction of development of a polymer material by a parameter study in which various interactions are set and the physical quantity of the polymer material model 10 is evaluated.

  Next, in the simulation method of the present embodiment, the computer 1 has a good physical quantity for each polymer material model 10 (in this example, the first polymer material model 10A and the second polymer material model (not shown)). It is determined whether or not a high polymer material model 10 exists (step S5). In step S5, whether or not the physical quantity of each polymer material model 10 is good is determined based on a predetermined threshold value. In this embodiment, when the stress of each polymer material model 10 is larger than the threshold value, it is determined that the fracture resistance is excellent. Furthermore, in this embodiment, when the parameter regarding the pore 26 of each polymer material model 10 is smaller than the threshold value, it is determined that the fracture resistance is excellent. In addition, about a threshold value, it can set suitably according to the destructive performance etc. which are calculated | required by the polymeric material, for example.

  In Step S5, when it is determined that there is a polymer material model 10 having a good physical quantity (“Y” in Step S5), a high value is determined based on various conditions set for the polymer material model 10 having a good physical quantity. A molecular material is manufactured (step S6). On the other hand, when it is determined in step S5 that the polymer material model 10 having a good physical quantity does not exist (“N” in step S5), the interaction between the filler and the polymer (physical adsorption in this example) is changed. (Step S7), Steps S2 to S5 are performed again. Thereby, the simulation method of this embodiment can develop the polymeric material which is excellent in fracture resistance based on interaction with a filler and a polymer.

  In the simulation method of the present embodiment, the filler model 6 and the polymer model 7 are defined inside the cell 4 shown in FIG. 5, but the present invention is not limited to such a mode. For example, a coupling agent model (not shown) that models a coupling agent for bonding a filler to a polymer may be further defined inside the cell 4.

  In the polymer material model 10, a cross-linking model (not shown) for connecting adjacent polymer models 7 may be defined. In this case, it is desirable to connect the coarse-grained particles 15 and 15 of the polymer model 7 with a crosslinking model based on a predetermined crosslinking point. Thereby, in the simulation method of this embodiment, the physical quantity accompanying the deformation | transformation of the bridge | crosslinked polymeric material model 10 can be compared accurately.

  Further, the coupling material model can be defined by, for example, a plurality of coarse-grained particles and a bond chain model that connects adjacent coarse-grained particles, as in the polymer model 7. At least a part of the filler model 6 and the polymer model 7 are connected via a coupling agent model. Thereby, in the simulation method of this embodiment, the physical quantity accompanying a deformation | transformation can be compared accurately about the polymeric material model 10 after a coupling reaction.

  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.

  Based on the processing procedure shown in FIG. 3, polymer material models having different interaction potential strengths between the filler and the polymer were set (Examples and Comparative Examples). As the polymer material model, the first polymer material model and the second polymer material model described above were set. In Examples and Comparative Examples, the structure relaxation of each polymer material model was calculated, and the physical quantity associated with the deformation of each polymer material model after the structure relaxation was calculated.

  The step of calculating the structural relaxation of each example is performed under the conditions in which the pressure and temperature of each polymer material model and the number of particles constituting the filler and the polymer are the same as each other. Was calculated. On the other hand, in the comparative example, the volume and temperature of each polymer material model, and the number of particles constituting the filler and polymer are constant, as in the simulation method of the patent document (Japanese Patent Laid-Open No. 2006-81297). Below, the structural relaxation of each polymer material model was calculated.

In the deformation calculation of the example, the tensile calculation in the z-axis direction was performed based on the following friction coefficient and deformation speed. In the deformation calculation of the comparative example, after the tensile calculation in the z-axis direction is performed based on the following initial friction coefficient and initial deformation speed, the friction coefficient is set to be the same as the friction coefficient in the above paper, and the polymer A relaxation calculation of 900τ was performed with the volume of the material model fixed. The common specifications of the examples and comparative examples are as follows.
cell:
Side length L1: 350σ
Side length L2 of small region: 1.5σ
Filler model:
Volume fraction: 16.2%
Number of filler particle models: 1973
Diameter of filler particle model: 28.2σ
Small particles constituting one filler particle model: 16,589 polymer models:
Number: 100,000
Coarse-grained particles constituting one polymer model: 1000 Crosslink density: 0.007245 (1 / σ ³ )
Coupling agent model:
Coarse-grained particles constituting one coupling agent model: 1
Coupling agent model per filler particle model: 80 deformation calculations:
Distortion: 0.15
Example:
Friction coefficient: Same as the friction coefficient in the above paper
Deformation speed: 6300τ / strain
Comparative example:
Initial friction coefficient: 10 times the above paper
Initial deformation speed: 6.3τ / strain

  As shown in FIG. 12, in the example, the internal stress of each polymer material model after the structure relaxation could be approximated to each other. FIG. 14 is a graph showing the relationship between stress and strain in the example. FIG. 15 is a graph showing the relationship between the void volume fraction and strain in the example. The volume fraction was calculated as the ratio of the void volume to the volumetric deformation of the cell due to strain of 0.15. As shown in FIG. 14, the second polymer material model was calculated to have a greater stress than the first polymer material model. As shown in FIG. 15, in the second polymer material model, the void volume fraction was calculated to be smaller at 5 to 10% strain than the first polymer material model. In this way, since the examples were able to align the physical quantity scales of each polymer material model with each other, the deformation of each polymer material model considering the interaction (physical adsorption) between the filler and the polymer was calculated. I was able to. Therefore, the Example was able to compare the physical quantity accompanying the deformation of each polymer material model with high accuracy.

  FIG. 16 is a graph showing the relationship between internal stress and time of each polymer material model of the comparative example. FIG. 17 is a graph showing the relationship between the volume fraction of holes in the comparative example and time. As shown in FIG. 16, in the comparative example, the internal stress of each polymer material model after the structure relaxation was greatly different from each other. Therefore, in the comparative example, the physical quantity scales of the respective polymer material models could not be aligned with each other. Thereby, since the comparative example could not calculate the deformation of each polymer material model considering the interaction (physical adsorption) between the filler and the polymer, the physical quantity of the first polymer material model as shown in FIG. (Volume volume fraction) and the physical quantity (hole volume fraction) of the second polymer material model were substantially the same. Therefore, the comparative example cannot accurately compare the physical quantities associated with the deformation of each polymer material model.

S1 A step of setting a polymer material model having different interaction potential strengths S2 A step of calculating a structural relaxation of each polymer material model S3 A step of calculating a physical quantity associated with the deformation of each polymer material model

Claims (6)

A method for comparing the performance of at least two types of polymer materials having different interactions between a filler and a polymer using a computer,
A step of setting, in the computer, polymer material models having different interaction potential strengths between the filler and the polymer based on the polymer materials, respectively,
The computer calculating a structural relaxation of each polymer material model based on the interaction potential;
The computer deforming each polymer material model after structure relaxation, and calculating a physical quantity associated with the deformation of each polymer material model,
The step of calculating the structural relaxation calculates the structural relaxation under the conditions that the pressure and temperature of each polymer material model and the number of particles constituting the filler and the polymer are the same.
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 physical quantity includes a stress of each polymer material model.   3. The coarse-grained molecular dynamics simulation method for a polymer material according to claim 1, wherein the physical quantity includes a parameter related to a pore of each polymer material model.   The coarse-grained molecular power of the polymer material according to claim 3, wherein the parameter relating to the pores is a total volume of the pores or a ratio of the total volume of the pores to a volume of each polymer material model. Simulation method.   The coarse-grained molecular dynamics simulation method for a polymer material according to any one of claims 1 to 4, wherein the computer further includes a step of comparing the physical quantities of the polymer material models. The interaction potential is a Leonard Jones potential,
The coarse-grained molecular dynamics simulation method for a polymer material according to claim 1, wherein the strength is a potential depth ε of the Leonard Jones potential.

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