JP6852551B2 - Simulation method for polymer materials - Google Patents

Description

The present invention relates to a method for simulating a polymer material, and more particularly to a method for analyzing the interaction between a polymer component contained in a polymer material and a filler using a computer.

In recent years, computer-based simulations have been carried out for the development of polymer materials containing fillers. In the simulation method of Patent Document 1 below, molecular dynamics calculation is performed using a filler model that models a filler and a molecular chain model that models a molecular chain of a polymer component, and the interaction between the two is estimated. Attempts have been made.

Japanese Unexamined Patent Publication No. 2014-203262

The filler model of Patent Document 1 is defined by a plurality of filler particle models arranged so as to form a uniform plane on a pair of surfaces constituting a cell which is a virtual space. In the simulation method using such a filler model, for example, the change in the interaction between the filler and the molecular chain due to the surface condition of the filler cannot be considered, and the interaction between the polymer component and the filler can be considered. There was a problem that it could not be analyzed accurately.

The present invention has been devised in view of the above circumstances, and an object of the present invention is to provide a method for simulating a polymer material capable of accurately analyzing the interaction between a polymer component and a filler. ..

The present invention is a method for analyzing the interaction between a polymer component contained in a polymer material and a filler using a computer, and provides a cell which is a virtual space corresponding to a part of the polymer material. , A step of inputting to the computer, a step of movably defining a molecular chain model in which the molecular chains of the polymer component are modeled using a plurality of polymer particle models, and a step of movably defining the molecular chains in the cell. Attractive and repulsive forces between the step of immovably defining a filler model that models the filler using a plurality of filler particle models, and between the polymer particle model and between the filler particle model and the polymer particle model. The filler model includes a step of defining the potential on which the is acting and a step of the computer performing a molecular dynamics calculation on the polymer particle model and the filler particle model, and the filler model includes a first filler model and a first filler model. The first filler model is defined to include two filler models, in which a plurality of the filler particle models are arranged so as to form an apparent plane, and the second filler model is the first filler. At least one of the filler particle models of the model is missing, and the second filler model is located on the center side of the cell so as to interact with the molecular chain model defined in the cell. It is characterized in that it is overlapped with the first filler model.

In the method for simulating a polymer material according to the present invention, the cell may include at least a pair of faces facing each other, and the filler particle model of the first filler model may be arranged on at least one of the faces. ..

In the method for simulating a polymer material according to the present invention, the filler particle model of the first filler model may be arranged on each of the pair of the surfaces.

In the method for simulating a polymer material according to the present invention, the second filler models are arranged facing each other in the thickness direction between the pair of the surfaces, and the distance between the pair of the second filler models is , It may be 3 times or more the inertial radius of the molecular chain model.

In the method for simulating a polymer material according to the present invention, the polymer material contains a functional group that enhances the affinity of the molecular chain for the filler, and the functional group is modeled by at least one functional group particle model. The step of performing the molecular dynamics calculation further includes a step of binding the functional group model to the filler model and a step of defining the potential between the functional group particle model and the polymer particle model. The molecular dynamics calculation may be performed on the polymer particle model, the filler particle model, and the functional group particle model.

In the method for simulating a polymer material according to the present invention, the functional group model may be arranged in the defective portion of the second filler model.

The filler model of the polymer material simulation method of the present invention is defined to include the first filler model and the second filler model. In the first filler model, a plurality of the filler particle models are arranged so as to form an apparent plane. The second filler model is one in which at least one of the filler particle models of the first filler model is missing. The second filler model is located on the center side of the cell and is superimposed on the first filler model so as to interact with the molecular chain model defined in the cell.

As a result of intensive research, the inventors have found that a functional group that replaces an atom of the filler exists on the surface of the filler, and the interaction between the filler and the molecular chain changes. In the simulation method of the present embodiment, the potential for the molecular chain model can be changed depending on the portion of the second filler model in which the filler particle model is deleted and the portion in which the filler particle model is not deleted. Therefore, the simulation method of the present invention accurately analyzes the interaction between the polymer component and the filler in consideration of the change in the interaction between the filler and the molecular chain due to the surface state of the filler and the like. It becomes possible to do.

It is a perspective view which shows an example of the computer for executing the simulation method of a polymer material. It is a structural formula of polyisoprene. It is a flowchart which shows an example of the processing procedure of the simulation method of a polymer material. It is a conceptual diagram which shows an example of a cell and a molecular chain model. It is a conceptual diagram which shows an example of a molecular chain model. It is a conceptual diagram which shows an example of a cell, a filler model and a molecular chain model. It is a perspective view which shows an example of the 1st filler model. It is a top view of the 1st filler model of FIG. It is a top view which shows an example of the 2nd filler model. It is a conceptual diagram which shows an example of a potential. It is a conceptual diagram which shows an example of a polymer material model. It is a flowchart which shows the processing procedure of the simulation method of the polymer material of another embodiment of this invention. It is a conceptual diagram which shows the 2nd filler model and the functional group model of another embodiment of this invention. It is a top view of the 2nd filler model and the functional group model of FIG.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
The method for simulating the polymer material of the present embodiment (hereinafter, may be simply referred to as “simulation method”) is for analyzing the interaction between the polymer component contained in the polymer material and the filler using a computer. This is the method.

FIG. 1 is a perspective view showing an example of a computer for executing 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, a storage device such as an arithmetic processing unit (CPU), a ROM, a work memory, and a magnetic disk, and disk drive devices 1a1 and 1a2. Further, the storage device stores in advance a processing procedure (program) for executing the simulation method of the present embodiment.

The polymer material contains at least one kind of polymer component, and in this embodiment, one kind of polymer component. Examples of the polymer component are natural rubber, isoprene rubber, butadiene rubber, styrene butadiene rubber and the like. Examples of the polymer component of the present embodiment include isoprene rubber (cis-1,4 polyisoprene (hereinafter, may be simply referred to as "polyisoprene")). FIG. 2 is a structural formula of polyisoprene.

The molecular chain 2 constituting polyisoprene is an isoprene monomer composed of a methine group or the like (for example, −CH =,> C =), a methylene group (−CH ₂ −), and a methyl group (−CH _3). (Isoprene molecule) 3 is linked at a degree of polymerization n. As the polymer material, a polymer material other than polyisoprene may be used.

An example of the filler is graphite (carbon black), silica, or the like. An example of the filler of the present embodiment is graphite. In addition, the polymer chain contains a functional group that enhances the affinity of the molecular chain for the filler. Examples of functional groups are aldehydes, ketones, carboxylic acids, or carboxylic acid salts. Examples of the functional group of the present embodiment include aldehydes and ketones.

FIG. 3 is a flowchart showing an example of the processing procedure of the simulation method. In the simulation method of the present embodiment, first, the cell 4, which is a virtual space corresponding to a part of the polymer material, is input to the computer 1 (step S1). FIG. 4 is a conceptual diagram showing an example of a cell and a molecular chain model.

The cell 4 of the present embodiment has at least a pair of faces 5, 5 facing each other, and in the present embodiment, three pairs of faces 5, 5 facing each other, and is defined as a rectangular parallelepiped. Periodic boundary conditions are defined on each of the surfaces 5 and 5. By using such a cell 4, in the molecular dynamics calculation described later, for example, with respect to the molecular chain model 6 described later, which models the molecular chain 2 (shown in FIG. 2) of the polymer component, one side surface. It can be calculated so that a part of the molecular chain model 6 exiting from 5a enters from the other surface 5b. Therefore, it can be treated as if the surface 5a on one side and the surface 5b on the other side are continuous (connected).

Each length L1 (L1a, L1b, L1c) of one side of the cell 4 can be appropriately set. The length L1 of this embodiment is preferably three times or more the radius of inertia (not shown), which is an amount indicating the spread of the molecular chain model 6 described later. As a result, in the molecular dynamics calculation described later, the cell 4 can prevent the occurrence of collision with its own image due to the periodic boundary condition, so that the spatial spread of the molecular chain model 6 can be appropriately calculated. Further, the size of the cell 4 is set to a stable volume at, for example, 1 atm. 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 molecular chain model 6 that models the molecular chain of the polymer component is defined in the cell 4 (step S2). The molecular chain model 6 of this embodiment is configured as an all-atom model. The molecular chain model 6 may be defined as, for example, a coarse-grained model (Kremer-Grest model or the like).

The molecular chain model 6 is modeled using a plurality of polymer particle models 7 and is defined to be movable within the cell 4. Movable means that the molecular chain model 6 can move in the cell 4 based on the molecular dynamics calculation described later. The molecular chain model 6 of the present embodiment includes a plurality of polymer particle models 7 and a binding chain model 8 that binds between the adjacent polymer particle models 7 and 7. FIG. 5 is a conceptual diagram showing an example of a molecular chain model.

The polymer particle model 7 and the bound chain model 8 are linked based on the unit structure forming the monomer 3 of the molecular chain 2 shown in FIG. As a result, the monomer model 11 is set. The molecular chain model 6 of this embodiment is defined by only one monomer model 11. As a result, in the simulation method of the present embodiment, the chain length of the polymer particle model 7 to be calculated can be significantly shortened in the molecular dynamics calculation described later, so that the calculation time required for structural relaxation can be shortened. Moreover, since the molecular chain model 6 is defined based on the unit structure forming the monomer 3, it is possible to suppress a decrease in calculation accuracy. The molecular chain model 6 may be defined by connecting the monomer models 11 based on the molecular weight (degree of polymerization) Mn in order to further improve the calculation accuracy.

The polymer particle model 7 is treated as a mass point of the equation of motion in the molecular dynamics calculation described later. That is, in the polymer particle model 7, parameters such as mass, diameter, charge, or initial coordinates are defined. The polymer particle model 7 of the present embodiment includes a carbon particle model 7C that models the carbon atom of the molecular chain 2 shown in FIG. 2 and a hydrogen particle model 7H that models a hydrogen atom.

The binding chain model 8 includes a main chain 8a and a side chain 8b. The main chain 8a is for connecting the carbon particle models 7C and 7C. The side chain 8b is for connecting between the carbon particle model 7C and the hydrogen particle model 7H. Further, the bond chain model 8 includes a single bond model 8A that defines a single bond between a pair of atoms and a double bond model 8B that defines a double bond between a pair of atoms.

A potential P1 on which attractive and repulsive forces act is defined between the polymer particle models 7 and 7 adjacent to each other via the binding chain model 8. Potentials P1 with different values are defined in the single bond model 8A and the double bond model 8B, respectively.

The potential P1 can be appropriately defined as in the conventional case. The potential P1 of this embodiment is described in Paper 1 (Stephen L. Mayo, Barry D. Olafson, and William A. Goddard III, "DREIDING: A Generic Force Field for Molecular Simulations", J. Chem Phys. Vol.94, No. Based on .26, 8897-8909, 1990), it is set according to the structure of the molecular chain 2 shown in FIG.

The number of molecular chain models 6 defined in the cell 4 can be appropriately set. It is desirable that the number of molecular chain models 6 of the present embodiment be adjusted so that the densities of all the molecular chain models 6 arranged in the cell 4 match the densities of polyisoprene. The molecular chain model 6 is stored in the computer 1.

Next, in the simulation method of the present embodiment, a filler model in which the filler is modeled is defined in the cell 4 (step S3). FIG. 6 is a conceptual diagram showing an example of the cell 4, the filler model 13, and the molecular chain model 6.

The filler model 13 is modeled using a plurality of filler particle models 14 and is defined as immovable within the cell 4. Here, "immovable" means that the filler model 13 cannot move in the cell 4 based on the molecular dynamics calculation described later. In the present embodiment, the filler model 13 is defined as immovable by fixing the coordinate values in the cell 4 of the filler particle model 14.

The filler model 13 is defined to include a first filler model 13A and a second filler model 13B.

FIG. 7 is a perspective view showing an example of the first filler model 13A. FIG. 8 is a plan view of the first filler model 13A of FIG. In the first filler model 13A, a plurality of filler particle models 14 are arranged so as to form an apparent plane. In the present embodiment, each filler particle model 14 is defined as immovable in the cell 4, and the adjacent filler particle models 14 and 14 are not connected to each other. It should be noted that the apparent flat surface allows irregularities formed by the adjacent filler particle model 14. As shown in FIG. 6, the filler particle model 14 of the present embodiment is arranged on at least one surface 5 of the cell 4, and in the present embodiment, each of the pair of surfaces 5 and 5.

Parameters such as mass, diameter, charge, or initial coordinates are defined in the filler particle model 14 of the present embodiment. The particle size of the filler particle model 14 can be set as appropriate. In the present embodiment, the particle size of the filler particle model 14 is set to be the same as or slightly larger than the particle size of the polymer particle model 7. Since the filler particle model 14 is defined as immovable in the cell 4, it is not necessary to calculate the time evolution in the molecular dynamics calculation described later. Therefore, the calculation time of the molecular dynamics calculation can be shortened as compared with the case where the filler particle model 14 is treated as a mass point of the equation of motion.

As shown in FIG. 8, the filler particle model 14 is regularly arranged on the surface 5 (shown in FIG. 6) of the cell 4. The first filler model 13A of the present embodiment is defined by arranging a plurality of units 16 including the filler particle model 14 so as to form an apparent plane. The unit 16 of this embodiment is composed of a filler particle model 14 arranged at the apex of a hexagon based on the structure of a filler (graphite in this embodiment).

A method of defining the filler particle model 14 as immovable in the cell 4 can be appropriately adopted. In the present embodiment, the filler particle model 14 is defined as immovable by fixing the coordinates of each filler particle model 14 in the cell 4. As a result, the filler particle model 14 can be easily defined as immovable, and the calculation time in the molecular dynamics calculation described later can be shortened.

In the first filler model 13A, the gap formed between the adjacent filler particle models 14 and 14 is set to be smaller than the particle size of the polymer particle model 7. As a result, the first filler model 13A can prevent the infiltration of the polymer particle model 7, and therefore, in the molecular dynamics calculation described later, an unrealistic calculation such that the molecular chain model 6 invades the inside of the filler model 13 is performed. Can be prevented.

FIG. 9 is a plan view showing an example of the second filler model 13B. The second filler model 13B lacks at least one of the filler particle models 14 of the first filler model 13A shown in FIG. In this embodiment, for example, the filler particle model 14 is deleted based on the number and types of functional groups bonded to the filler. The filler particle model 14 may be randomly deleted. The number and types of functional groups can be determined by, for example, experiments.

As shown in FIG. 6, the second filler model 13B is overlapped with the first filler model 13A so as to be located on the center side of the cell 4 with respect to the first filler model 13A. As a result, the filler model 13 of the present embodiment is composed of two layers in which the first filler model 13A and the second filler model 13B overlap. Since the second filler model 13B is located on the center side of the cell 4 with respect to the first filler model 13A, the molecular chain model 6 has priority over the first filler model 13A in the molecular dynamics calculation described later. Can be calculated to interact with. With such a second filler model 13B and the first filler model 13A, the unevenness formed on the surface of the filler can be expressed.

Between the first filler model 13A and the second filler model 13B in the thickness direction between the pair of surfaces 5 and 5 on which the filler model 13 is arranged (hereinafter, may be simply referred to as the "thickness direction"). The distance L2 can be set as appropriate. The distance L2 of the present embodiment can be set based on, for example, the interwall distance of graphite in order to accurately analyze the interaction between the polymer component and the filler. The distance L2 is defined as the distance between the centers 14c of the filler particle models 14 and 14.

The second filler model 13B is superposed on the first filler models 13A and 13A arranged on each of the pair of surfaces 5 and 5 of the cell 4. As a result, the second filler models 13B are arranged facing each other in the thickness direction (in the present embodiment, the Z-axis direction). The distance L3 in the thickness direction between the pair of second filler models 13B and 13B can be appropriately set. The distance L3 of the present embodiment is set in the molecular chain model 6 in order to efficiently calculate the structural relaxation of the molecular chain model 6 and the interaction between the molecular chain model 6 and the filler model 13 in the molecular dynamics calculation described later. It is desirable to set it to 3 times or more of the inertial radius (not shown). The distance L3 is defined as the distance between the centers 14c of the filler particle models 14 and 14. The filler model 13 is stored in the computer 1.

Next, in the simulation method of the present embodiment, between the polymer particle models 7 and 7 (that is, between the polymer particle models 7 and 7 adjacent to each other without passing through the binding chain model 8), and between the filler particle model 14 and the polymer particle model. The potential on which attractive and repulsive forces act is defined between 7 and 7 (step S4). FIG. 10 is a conceptual diagram showing an example of the potential.

First, the potential P2 between the polymer particle models 7 and 7 _{is defined by the LJ potential ULJ} (r _ij ) of the following formula (1).

ここで、各定数及び変数は、Lennard-Jones ポテンシャルのパラメータであり、次のとおりである。
ｒ_ij：ポリマー粒子モデル７、７間の距離
ε：ポリマー粒子モデル７、７間に定義されるＬＪポテンシャルの強度
σ：ポリマー粒子モデル７の直径に相当
ｒ_c：カットオフ距離（＝２．５σ）
なお、距離ｒ_ijは、各ポリマー粒子モデル７、７の中心７ｃ間の距離として定義される。

Here, each constant and variable is a parameter of the Lennard-Jones potential and is as follows.
r _ij : Distance between polymer particle models 7 and 7 ε: Strength of LJ potential defined between polymer particle models 7 and 7 σ: Corresponds to the diameter of polymer particle model 7 r _c : Cutoff distance (= 2.5σ) )
The distance r _ij is defined as the distance between the centers 7c of each of the polymer particle models 7 and 7.

In the above formula (1), the potential P2 generates repulsive force and attractive force only when _{the distance r ij} between the polymer particle models 7 and 7 is less than the cutoff distance r _{c. When the distance r ij} between the polymer particle models 7 and 7 is equal to or greater than the cutoff distance r _c , the potential P2 becomes zero and no repulsive force or attractive force is generated.

In this embodiment, different potentials P2 are set between the carbon particle models 7C and 7C, between the hydrogen particle models 7H and 7H, and between the carbon particle model 7C and the hydrogen particle model 7H. Each potential P2 has a different constant in the above equation (1). Each constant can be appropriately set based on, for example, the above-mentioned Article 1. The potential P2 is stored in the computer 1.

Next, the potential P3 between the filler particle model 14 and the polymer particle model 7 is defined by _{the LJ potential ULJ} (r _ij ) of the above formula (1), similarly to the potential P2 between the polymer particle models 7 and 7. Will be done. With such a potential P3, the attractive and repulsive forces acting between the filler particle model 14 and the polymer particle model 7 can be defined. The values of each constant and each variable of the potential P3 can be set as appropriate, but it is desirable that they are set based on the above-mentioned Article 2.

The potential P3 is defined in each filler particle model 14 of the first filler model 13A and each filler particle model 14 of the second filler model 13B, respectively. In the present embodiment, the potential P3 defined in each filler particle model 14 of the first filler model 13A and the potential P3 defined in each filler particle model 14 of the second filler model 13B are constants and variables. It is set to be the same. Therefore, since the second filler model 13B is located closer to the center of the cell 4 (that is, near the polymer particle model 7) than the first filler model 13A, the repulsive force or attractive force of the potential P3 can be set to the polymer particle model. It can act preferentially on 7.

Further, in the filler model 13, in the portion 17 where the filler particle model 14 of the second filler model 13B is not deficient (hereinafter, may be simply referred to as “non-defective portion”) 17, the thickness direction (in the present embodiment, the present embodiment). In the Z-axis direction), both the potential P3 of the filler particle model 14 of the first filler model 13A and the potential P3 of the filler particle model 14 of the second filler model 13B can act on the polymer particle model 7. On the other hand, in the portion 18 where the filler particle model 14 of the second filler model 13B is deficient (hereinafter, may be simply referred to as a “defective portion”) 18, the filler particle model 14 of the first filler model 13A is formed in the thickness direction. Only the potential P3 of can act on the polymer particle model 7.

As described above, in the simulation method of the present embodiment, the strength of the potential P3 with respect to the molecular chain model 6 can be changed between the non-defective portion 17 and the defective portion 18. The potential P3 is stored in the computer 1.

Next, in the simulation method of the present embodiment, the computer 1 performs the molecular dynamics calculation for the polymer particle model 7 and the filler particle model 14 (step S5).

In the molecular dynamics calculation of the present embodiment, for example, Newton's equation of motion is applied to cell 4 assuming that the molecular chain model 6 follows classical mechanics for a predetermined time. Then, the movement of the polymer particle model 7 at each time is tracked for each unit time step.

In the molecular dynamics calculation, the pressure and temperature are kept constant, or the volume and temperature are kept constant in the cell 4. As a result, in step S5, the artificial initial arrangement of the molecular chain model 6 can be accurately relaxed by approximating the molecular motion of the actual polymer material. As a result, the polymer material model 10 is set. The calculation of structural relaxation can be performed using, for example, COGNAC included in the soft material comprehensive simulator (J-OCTA) manufactured by JSOL Corporation, as in the conventional case.

In the simulation method of the present embodiment, since the filler model 13 is defined as immovable, only the initial arrangement of the molecular chain model 6 is relaxed. As a result, the simulation method of the present embodiment reduces the calculation time as compared with the case where the relaxation calculation is performed for both the molecular chain model 6 and the filler model defined as movable (not shown), for example. Can be shortened. Further, since the molecular chain model 6 of the present embodiment is defined by only one monomer model 11, the calculation time can be significantly shortened. FIG. 11 is a conceptual diagram showing an example of the polymer material model 10.

As described above, in the simulation method of the present embodiment, the strength of the potential P3 between the molecular chain model 6 and the filler model 13 can be changed by the non-defective portion 17 and the defective portion 18 of the filler model 13. .. As a result, in step S5 of the present embodiment, the molecular chain model takes into consideration the change in the interaction between the filler and the molecular chain due to the surface state of the filler (for example, the presence of a functional group replacing the atom of the filler) and the like. 6 can be relaxed.

Further, in the filler model 13, even if the molecular chain model 6 invades the defective portion 18 of the second filler model 13B, the intrusion of the molecular chain model 6 can be prevented by the first filler model 13A having no defective portion. This makes it possible to prevent unrealistic calculations such that the molecular chain model 6 penetrates into the filler model 13.

Next, as shown in FIG. 3, in the simulation method of the present embodiment, the computer 1 determines whether or not the initial arrangement of the molecular chain model 6 can be sufficiently relaxed (step S6). The criteria for determining mitigation can be appropriately set as in the conventional case.

If it is determined in step S6 that the initial arrangement of the molecular chain model 6 has been sufficiently relaxed (“Y” in step S6), the next step S7 is carried out. On the other hand, if it is determined in step S6 that the initial arrangement of the molecular chain model 6 has not been sufficiently relaxed (“N” in step S6), one unit step is advanced (step S8), steps S5 and Step S6 is carried out again. As a result, in the simulation method of the present embodiment, as shown in FIG. 11, the equilibrium state (state in which the structure is relaxed) of the molecular chain model 6 can be reliably calculated. The unit step is set to, for example, 0.5 to 2.0 fs.

Next, as shown in FIG. 3, in the simulation method of the present embodiment, the computer 1 evaluates the strength of the interaction between the filler model 13 and the molecular chain model 6 shown in FIG. The interaction between the component and the filler is analyzed (step S7).

In step S7 of the present embodiment, first, the molecular dynamics calculation for a predetermined time (for example, 2 to 10 ns) is calculated for each unit step for the polymer particle model 7 and the filler particle model 14. .. In each unit step, the coordinates of the polymer particle model 7 of each molecular chain model 6 are stored in the computer 1.

As described above, in the simulation method of the present embodiment, the strength of the potential P3 between the molecular chain model 6 and the filler model 13 can be changed by the non-defective portion 17 and the defective portion 18 of the filler model 13. .. As a result, in the molecular dynamics calculation in step S7 of the present embodiment, changes in the interaction between the filler and the molecular chain due to the surface state of the filler (for example, the presence of a functional group replacing the atom of the filler) and the like are taken into consideration. Therefore, the interaction between the molecular chain model 6 and the filler model 13 can be calculated with high accuracy.

Further, in the filler model 13, even if the molecular chain model 6 invades the defective portion 18 of the second filler model 13B, the intrusion of the molecular chain model 6 can be prevented by the first filler model 13A having no defective portion. This makes it possible to prevent unrealistic calculations such that the molecular chain model 6 penetrates into the filler model 13.

Next, in step S7, the strength of the interaction between the filler model 13 and the molecular chain model 6 is evaluated based on the coordinate values of the polymer particle model 7 stored in the computer 1. The strength of the interaction can be evaluated as appropriate. In this embodiment, the strength of the interaction between the filler model 13 and the molecular chain model 6 is evaluated based on the mean square displacement (MSD) of the polymer particle model 7 of the molecular chain model 6. In the present embodiment, the mean square displacement is calculated only for the carbon particle model 7C among the polymer particle models 7. The mean square displacement is defined by the following equation (2).

MSD = <| r (τ) -r (0) | ² > ... (2)
The symbols are as follows.
r (0): Coordinate value of polymer particle model at arbitrary time r (τ): Coordinate value of polymer particle model after time τ from arbitrary time <>: Ensemble average

In the above formula (2), the above | r (τ) −r (0) | is the distance traveled by the polymer particle model 7 in the time width τ. For the squared value of this distance | r (τ) −r (0) |, the mean square displacement in the time width τ can be obtained by taking the ensemble average with respect to the polymer particle model 7 to be evaluated. It is assumed that the coordinate values r (τ) and r (0) are specified by the center 7c of each polymer particle model 7. Note that "τ" is a time parameter used in the simulation.

The mean square displacement is a value obtained by averaging the square of the distance traveled by each polymer particle model 7 in the time width τ with the polymer particle model 7 to be evaluated. By examining the value of such mean square displacement, the momentum of the polymer particle model 7 can be grasped.

When the mean square displacement is small, it indicates that the momentum of the polymer particle model 7 is small. Therefore, it can be evaluated that the interaction between the filler model 13 and the molecular chain model 6 is strong. As a result, in step S7, it can be estimated that the interaction between the polymer component and the filler is large.

On the other hand, when the mean square displacement is large, it indicates that the momentum of the polymer particle model 7 is large. Therefore, it can be evaluated that the interaction between the filler model 13 and the molecular chain model 6 is weak. As a result, in step S7, it can be estimated that the interaction between the polymer component and the filler is small. As described above, in step S7, the strength of the interaction between the filler model 13 and the molecular chain model 6 and the interaction between the polymer component and the filler are easily and accurately evaluated based on the mean square displacement. be able to.

The evaluation of the strength of the interaction between the filler model 13 and the molecular chain model 6 is based on the change in the interaction between the filler and the molecular chain due to the surface state of the filler (for example, the presence of a functional group replacing the atom of the filler). It is done based on the result of molecular dynamics calculation considering. Therefore, in step S7, the interaction between the polymer component and the filler can be accurately analyzed based on the strength of the interaction between the filler model 13 and the molecular chain model 6. The analysis result of the interaction between the polymer component and the filler can be useful for the development of the polymer material.

In the embodiments so far, changes in the interaction between the filler and the molecular chain have been considered by the non-defective portion 17 and the defective portion 18 of the filler model 13 shown in FIG. 10, but the present invention is not limited to such an embodiment. .. For example, not only the non-defective portion 17 and the defective portion 18 of the filler model 13, but also a functional group model in which a functional group is modeled may be used to consider changes in the interaction between the filler and the molecular chain.

FIG. 12 is a flowchart showing a processing procedure of the simulation method of another embodiment of the present invention. FIG. 13 is a conceptual diagram showing a second filler model 13B and a functional group model 21 according to another embodiment of the present invention. FIG. 14 is a plan view of the second filler model 13B and the functional group model 21 of FIG. In this embodiment, the same configurations as those in the previous embodiment are designated by the same reference numerals, and the description thereof may be omitted.

In the simulation method of this embodiment, the functional group model 21 is bound to the filler model 13 prior to the step S5 of performing the molecular dynamics calculation (step S9). The functional group model 21 is a model of a functional group with at least one functional group particle model 22. The functional group model 21 includes, for example, an aldehyde model 21A that models an aldehyde (-CHO) and a ketone model 21B that models a ketone (-CO-).

As described above, the functional groups are present on the surface of the filler in place of the atoms of the filler, causing a change in the interaction between the filler and the molecular chain. Therefore, the functional group model 21 of the present embodiment is arranged in the defective portion 18 of the second filler model 13B. The functional group model 21 arranged in the defect portion 18 is connected to the filler particle model 14 of the adjacent second filler model 13B.

The functional group particle model 22 is treated as a mass point of the equation of motion in the molecular dynamics calculation. That is, in the polymer particle model 7, parameters such as mass, diameter, charge, or initial coordinates are defined. As shown in FIG. 13, the functional group particle model 22 of the present embodiment includes a carbon particle model 22c, a hydrogen particle model 22h, and an oxygen particle model 22o.

The connection between the functional group particle models 22 and 22 and the connection between the functional group particle model 22 and the filler particle model 14 can be appropriately defined. The connection between the functional group particle models 22 and 22 and the connection between the functional group particle model 22 and the filler particle model 14 of the present embodiment are defined in the same manner as the connection between the polymer particle models 7 and 7. The functional group model 21 is stored in the computer 1.

Next, in the simulation method of this embodiment, the potential P4 in which attractive and repulsive forces act between the functional group particle model 22 and the polymer particle model 7 and between the functional group particle model 22 and the filler particle model 14. Is defined (step S10). This potential P4 is defined by _{the LJ potential ULJ} (r _ij ) of the above equation (1). The values of each constant and each variable of the potential P4 can be set as appropriate, but it is desirable that they are set based on the above-mentioned Article 1.

In the step S5 of performing the molecular dynamics calculation of this embodiment, the computer 1 performs the molecular dynamics calculation for the polymer particle model 7, the filler particle model 14, and the functional group particle model 22 (step S5). The details of the molecular dynamics calculation are as described in the previous embodiment.

In the step S7 for evaluating the strength of the interaction between the filler model 13 and the molecular chain model 6 in this embodiment, first, as in the previous embodiment, the polymer particle model 7, the filler particle model 14, and the functional group Molecular dynamics calculations are performed on the particle model 22. Then, the strength of the interaction between the filler model 13 and the molecular chain model 6 is evaluated based on the coordinate values of the polymer particle model 7. The method for evaluating the strength of the interaction is as described in the previous embodiment.

In this embodiment, not only the potential P3 (shown in FIG. 10) changed by the non-defective portion 17 and the defective portion 18 of the filler model 13, but also the potential P4 between the functional group particle model 22 and the polymer particle model 7 (shown in FIG. 10). (Shown in FIG. 13) also acts on the molecular chain model 6. As a result, in the simulation method of the present embodiment, the change in the interaction between the filler and the molecular chain due to the presence of the functional group replacing the atom of the filler can be considered, so that the molecular chain model 6 and the filler model 13 can be used. Interaction (interaction between polymer component and filler) can be calculated more accurately.

In the previous embodiments, the filler particle model 14 of the first filler model 13A and the filler particle model 14 of the second filler model 13B are not coupled to each other in the thickness direction (in the present embodiment, the Z-axis direction). However, the filler particle model 14 of the first filler model 13A and the filler particle model 14 of the second filler model 13B may be bonded to each other. This makes it possible to accurately define the filler model 13 that models silica having a three-dimensional network structure.

Although the particularly preferable embodiments of the present invention have been described in detail above, the present invention is not limited to the illustrated embodiments and can be modified into various embodiments.

According to the processing procedure shown in FIG. 3, a molecular chain model and a two-layer filler model including a first filler model and a second filler model were defined in a cell which is a virtual space (Examples 1 and 2). ). Further, according to the treatment procedure shown in FIG. 12, a functional group model was further defined in addition to the molecular chain model and the two-layer filler model (Examples 3 to 4). In Examples 5 to 6, pressure control for keeping the pressure constant was omitted in the molecular dynamics calculation.

Further, for comparison, a two-layer filler model including a second filler model having no defect in the filler particle model was defined (Comparative Example 1). Further, a molecular chain model and a one-layer filler model including only the second filler model were defined in the cell which is a virtual space (Comparative Example 2 and Comparative Example 3).

Then, a molecular dynamics calculation (5ns) was carried out using a computer for the molecular chain model, the filler model, and the functional group model of Examples 1 to 6 and Comparative Examples 1 to 3, and the filler and the molecule were subjected to the calculation. The strength of the interaction with the chain was evaluated. The strength of the interaction is indicated by an index with the value of the mean square displacement of Example 2 as 100. The larger the number, the stronger the interaction. The common specifications are as follows.

Cell: Each length of one side L1: 3.68 to 3.83 nm
Polymer component: Polyisoprene (Density: 0.9-1.0 g / cm ³ )
Molecular chain model:
Quantity: The density of all molecular chain models placed in the cell,
Adjusted to match the above density of polyisoprene
Distance between second filler models L3 / radius of inertia Rg: 10
Filler: Graphite (carbon black)
Functional groups: Aldehydes, ketones The results of the test are shown in the table.

It is generally known that the more activated the surface of graphite (that is, the larger the number of functional group models or the proportion of defects), the stronger the interaction (interfacial adhesive force) (for example, "carbon"). Black Handbook (3rd Edition) ", Carbon Black Association, 1995, p. 216). In Examples 1 and 2, the larger the percentage of defects in the filler particle model of the second filler model, the stronger the interaction between the filler and the molecular chain. Further, in Examples 3 to 4 and Examples 5 to 6, as the number of functional group models and the rate of deletion of the filler particle model of the second filler model increase, the interaction between the filler and the molecular chain increases. I got stronger. Therefore, from the results of Examples 1 to 6, the simulation method of the present invention was able to accurately analyze the interaction between the polymer component and the filler.

Further, in Examples 1 to 4, since the pressure is controlled to keep the pressure constant, the number of functional group models and the second filler are as compared with those of Examples 5 and 6 in which the pressure is not controlled. The change in the strength of the interaction due to the percentage of defects in the model filler particle model could be defined accurately.

On the other hand, in Comparative Example 1, since the number of functional group models and the defect ratio of the filler particle model of the second filler model are "0", the potential between the filler model and the molecular chain model acts uniformly. However, the change in the interaction between the filler and the molecular chain could not be considered. Therefore, in Comparative Example 1, the interaction between the polymer component and the filler could not be analyzed accurately.

Further, in Comparative Example 2 and Comparative Example 3 in which a one-layer filler model including only the second filler model was defined, the molecular chain model penetrated into the defective portion, and the molecular chain model protruded from the defective portion onto the cell surface. .. Therefore, in Comparative Example 2 and Comparative Example 3, the interaction between the polymer component and the filler could not be analyzed.

4 cell 6 molecular chain model 13 filler model 13A 1st filler model 13B 2nd filler model 14 filler particle model

Claims (6)

It is a method for analyzing the interaction between a polymer component contained in a polymer material and a filler using a computer.
A process of inputting a cell, which is a virtual space corresponding to a part of the polymer material, into the computer,
In the cell, a step of movably defining a molecular chain model that models the molecular chain of the polymer component using a plurality of polymer particle models, and
A step of defining a filler model in which the filler is modeled by using a plurality of filler particle models in the cell, and a step of immovably defining the filler model.
A step of defining the potential for attractive and repulsive forces to act between the polymer particle models and between the filler particle model and the polymer particle model.
The computer includes a step of performing a molecular dynamics calculation on the polymer particle model and the filler particle model.
The filler model is defined to include a first filler model and a second filler model.
In the first filler model, a plurality of the filler particle models are arranged so as to form an apparent plane.
The second filler model lacks at least one of the filler particle models of the first filler model.
The second filler model is a method for simulating a polymer material located on the center side of the cell and superposed on the first filler model so as to interact with the molecular chain model defined in the cell. .. The cell contains at least a pair of faces facing each other.
The method for simulating a polymer material according to claim 1, wherein the filler particle model of the first filler model is arranged on at least one of the surfaces. The method for simulating a polymer material according to claim 2, wherein the filler particle model of the first filler model is arranged on each of the pair of the surfaces. The second filler model is arranged facing each other in the thickness direction between the pair of the surfaces.
The method for simulating a polymer material according to claim 3, wherein the distance between the pair of the second filler models is three times or more the radius of inertia of the molecular chain model. The polymeric material contains functional groups that enhance the affinity of the molecular chain for the filler.
A step of binding the functional group model in which the functional group is modeled by at least one functional group particle model to the filler model, and
A step of defining the potential is further included between the functional group particle model and the polymer particle model.
The high level according to any one of claims 1 to 4, wherein the step of performing the molecular dynamics calculation is performed on the polymer particle model, the filler particle model, and the functional group particle model. Method of simulating molecular materials. The method for simulating a polymer material according to claim 5, wherein the functional group model is arranged in the defective portion of the second filler model.

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