JP7040152B2 - Simulation method for polymer materials - Google Patents

Description

The present invention relates to a simulation method for analyzing a polymer material.

In recent years, various simulation methods (numerical calculation) for evaluating the reaction of polymer materials such as rubber materials using a computer have been proposed. In the following Patent Documents 1 and 2, a coarse-grained model in which a polymer chain is modeled with a plurality of beads is created, and then the space unit and time unit of this model are used as the space unit and time unit of an all-atom model. It is associated with a unit.

Japanese Patent No. 6097130 Japanese Patent No. 6050903

In Patent Document 2, the coarse-grained model is associated with the all-atomic model by adjusting the length. As a result of diligent research, the inventors have found that in Patent Document 2, the effective density, which is the value obtained by dividing the Kuhn length of the coarse-grained model by the Packing length, deviates from that of the actual polymer chain. We found that the density of the coordinates of the all-atomic model, which can be obtained by converting the coordinates of the coarse-grained model of the thermal equilibrium state to the all-atomic model, can deviate from the equilibrium density of the all-atomic model. rice field. Therefore, there is room for further improvement in improving the calculation accuracy.

The present invention has been devised in view of the above circumstances, and an object of the present invention is to provide a simulation method of a polymer material capable of improving calculation accuracy.

The present invention is a method for analyzing a polymer material having a polymer chain using a computer, wherein the polymer chain is composed of a plurality of particles having a smaller number than the number of atoms constituting the polymer chain. Effective, which is the value obtained by dividing the Kuhn length of the coarsened molecular model by the packing length in the process of inputting the coarsened molecular model expressed using the method into the computer and in the calculation of structural relaxation based on molecular dynamics. The specific density approaches the effective density, which is the value obtained by dividing the Kuhn length of the polymer chain, the all-atomic model of the polymer chain, or the United atom model of the polymer chain by the Packing length. As described above, the step of defining the interaction between the adjacent particles of the coarsening molecular model and the computer calculates the structural relaxation for the coarsening molecular model in which the interaction is defined. It is characterized by including a step of performing.

In the method of simulating a polymer material according to the present invention, the interaction may affect the flexibility of the coarse-grained molecular model.

ここで、
Ｅ：相互作用ポテンシャル関数
Ｋ：相互作用パラメータ
θ：隣り合う３つの粒子がなす角度 In the method for simulating a polymer material according to the present invention, the interaction may be defined by the following formula (1).

here,
E: Interaction potential function K: Interaction parameter θ: Angle formed by three adjacent particles

In the method for simulating the polymer material according to the present invention, in the step of defining the interaction, a plurality of the roughened molecular models having different interaction parameters of the interaction are defined, and the polymer chain is described. A step of determining the interaction of the coarsened molecular model having an effective density close to the effective density of either the full atomic model of the polymer chain or the United atom model of the polymer chain. It may be included.

In the method for simulating a polymer material according to the present invention, the computer uses the first degree of bending after structural relaxation of the coarsened molecular model in which the interaction is defined, and the all-atom model or the United atom model. A step of calculating the ratio of the number of particles of the coarsened molecular model to the number of monomers of the polymer chain may be included based on the second degree of bending after structural relaxation.

In the method for simulating a polymer material of the present invention, the effective density of the coarsened molecular model is the polymer chain, the all-atom model of the polymer chain, or the all-atom model of the polymer chain at the time of calculation of structural relaxation based on molecular dynamics. It comprises defining the interaction between adjacent particles of the coarsening molecular model so as to approach the effective density of any of the United Atom models of the polymer chain. As a result, the unit of space (length) of the polymer chain, the whole atom model, or the United atom model can be associated with the unit of space (length) of the coarse-grained molecular model with high accuracy. It is possible to improve the calculation accuracy of the simulation using the coarse-grained model.

It is a perspective view which shows an example of the computer which performs the simulation method of a polymer material. It is a structural formula of polybutadiene. It is a conceptual diagram which shows an example of a coarse-grained molecular model. It is a partially enlarged view of the coarse-grained molecular model when it approximates an ideal chain. It is a flowchart which shows an example of the simulation method. It is a figure explaining an example of a bending potential. It is a flowchart which shows an example of the processing procedure of the interaction definition process. It is a conceptual diagram which shows an example of an all-atomic model. It is a flowchart which shows an example of the processing procedure of the 1st calculation process. It is a conceptual diagram which shows an example of a polymer material model in which an all-atomic model is arranged. It is a graph which shows the relationship between the effective density l _K / p of each whole atomic model, and the number of monomers. It is a flowchart which shows an example of the 2nd calculation process. It is a conceptual diagram which shows an example of a polymer material model in which a coarse-grained molecular model is arranged. It is an example of a graph showing the relationship between the effective density l _K / p of each coarse-grained molecular model, the interaction parameter K of the bending potential, and the number of particles N. It is a graph of the result of fitting the relationship between the number of Kuhn segments and the number of monomers of the all-atom model and the relationship between the number of Kuhn segments and the number of coarse-grained particles in the coarse-grained molecular model. It is a graph which shows the relationship between the number of Kuhn segments and the number of monomers of an all-atomic model.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
The polymer material simulation method (hereinafter, may be simply referred to as “simulation method”) is a method for analyzing a polymer material having a polymer chain using a computer. Examples of the polymer material include rubber, resin, elastomer and the like.

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

Examples of the polymer material include rubber, resin, elastomer and the like. In this embodiment, cis-1,4 polybutadiene (hereinafter, may be simply referred to as "polybutadiene") is exemplified as the polymer material. FIG. 2 is a structural formula of polybutadiene. In the polymer chain 4 constituting this polybutadiene, a monomer 5 {-[CH ₂ -CH = CH-CH ₂ ]-} composed of a methylene group (-CH _2- ) and a methine group (-CH-) is polymerized. It is composed of concatenated degrees. Further, a methyl group (-CH ₃ ) is linked to the end of the polymer material instead of the methylene group (-CH ₂ ). As the polymer material, a polymer material other than polybutadiene may be used.

In the simulation method of this embodiment, a coarse-grained molecular model expressing the polymer chain 4 is used. FIG. 3 is a conceptual diagram showing an example of a coarse-grained molecular model.

The coarse-grained molecular model 6 is configured to include a plurality of particles 7 and a binding chain 8 that connects the particles 7 and 7. In the coarse-grained molecular model 6, the polymer chain 4 is represented by using a plurality of particles 7 having a smaller number than the number of atoms constituting the polymer chain 4. The coarse-grained molecular model 6 of the present embodiment is exemplified by the Kremer-Grest model, but is not particularly limited, and is, for example, a model based on DPD (dissipative particle dynamics method). May be good. The particles 7 correspond to, for example, the monomer 5 of the polymer chain 4 shown in FIG.

The coarse-grained molecular model 6 may be, for example, an all-atomic model 11 (shown in FIG. 8) expressed based on the actual structure of the polymer chain 4 or a United atom model (hereinafter, simply referred to as “UA model”). It can handle a larger space and time than (there is.). On the other hand, the coarse-grained molecular model 6 uses a unit having a length different from that of the actual polymer chain 4 (shown in FIG. 2). Therefore, in order to treat the calculation result of the molecular dynamics calculation of the coarse-grained molecular model 6 as the actual motion of the polymer chain 4, the unit of the length of the coarse-grained molecular model 6 is the polymer chain 4. It is important to accurately convert to the unit of length of.

However, in the coarse-grained molecular model 6 that does not handle the coordinates of individual atoms, such as the Kremer-Grest model and the model based on DPD (Dissipated Particle Dynamics), the thickness of the polymer chain 4 is taken into consideration. Therefore, even if the unit of space (length) is converted so as to match the flexibility of the polymer chain 4, as in Patent Document 2, the effective density of the coarse-grained molecular model 6 is still high. It does not necessarily match that of the polymer chain 4, the all-atom model 11, or the UA model.

Here, the "effective density" is expressed as a value l _K / p obtained by dividing the Kuhn length l _K defined by the following equation (2) by the Packing length p defined by the following equation (3). The amount. This can be approximately treated as an amount proportional to the number of polymer chains 4 per range (volume) of the tubular space in which one polymer chain 4 in the rubber region can move.

ここで、
Ｌ：粗視化分子モデル又は高分子鎖（全原子モデル又はＵＡモデル）の全長
Ｒ_g：粗視化分子モデル又は高分子鎖（全原子モデル又はＵＡモデル）の慣性半径

here,
L: Overall length of coarse-grained molecular model or polymer chain (all-atom model or UA model) R _g : Inertial radius of coarse-grained molecular model or polymer chain (all-atom model or UA model)

ここで、
Ｍ：粗視化分子モデル又は高分子鎖（全原子モデル又はＵＡモデル）の質量
Ｒ_g：粗視化分子モデル又は高分子鎖（全原子モデル又はＵＡモデル）の慣性半径
ρ：粗視化分子モデル又は高分子鎖（全原子モデル又はＵＡモデル）の密度
Ｎ_A：アボガドロ数

here,
M: Mass of coarse-grained molecular model or polymer chain (all-atom model or UA model) R _g : Inertial radius of coarse-grained molecular model or polymer chain (all-atom model or UA model) ρ: Crude molecule Density of model or polymer chain (all-atom model or UA model) NA: _Abogadro number

FIG. 4 is a partially enlarged view of a coarse-grained molecular model when approximated to an ideal chain. The Kuhn length l _K in the above formula (1) is a quantity having a unit of length, and is the rigidity of the polymer chain 4 (shown in FIG. 2) (that is, the difficulty of bending, which is the opposite concept to the flexibility). ) Is a parameter. As shown in FIG. 4, the Kuhn length _lK is the particle 7'when the polymer chain 4 is close to the ideal chain 6'known in polymer physics, that is, so that the radius of inertia is reproduced. Connected particles when coarse-grained molecular model 6 is approximated as a straight line in which (called Kuhn segment) are connected in random directions (at the binding chain 8'of the ideal chain) at regular intervals. Corresponds to the distance between 7'(Kuhn segments).

On the other hand, the packing length p in the above formula (2) is a quantity having a unit of length, and is defined as a ratio between the volume occupied by one polymer chain and the root mean square of the distance between the ends. This packing length p can be approximately treated as an amount proportional to the thickness of the tubular space 15 in which one polymer chain 4 in the rubber region can move. In the above formula (2) and the above formula (3), the root mean square of the distance between the ends of the polymer chain 4 is estimated as 6 times the root mean square of the radius of inertia.

When the deviation (deviation) of the effective density _lK / p between the coarse-grained molecular model 6 and the polymer chain 4, the all-atom model 11 or the UA model becomes large, the length of the coarse-grained molecular model 6 becomes long. When conversion is performed between the unit of grain and the unit of length of the polymer chain 4 (shown in FIG. 2), the deviation in density (that is, the deviation from the equilibrium density) becomes large. For example, when the method of Patent Document 2 described above is used to obtain the conversion constant of the coarse-grained molecular model 6 and the polymer chain 4 in time units, all the coordinates are overlapped with the structurally relaxed coordinates of the coarse-grained model. When the coordinates of the atomic model are set to create the structurally relaxed coordinates of the all-atomic model, the density of the obtained coordinates deviates from the equilibrium density (that is, the structural relaxation becomes insufficient). When such a combination of the coarse-grained molecular model 6 and the polymer chain 4, the all-atomic model 11 or the UA model is used, it becomes impossible to accurately obtain the conversion constant in units of time.

In the simulation method of the present embodiment, when the structural relaxation is calculated, the effective density l _K / p of the roughened molecular model 6 is the all atoms of the polymer chain 4 (shown in FIG. 2) and the polymer chain 4. Between adjacent particles 7 and 7 of the coarse-grained molecular model 6 so as to approach the effective density l _K / p of the model 11 (shown in FIG. 8) or the UA model of the polymer chain 4 (not shown). The structural relaxation is calculated by defining the interaction with. FIG. 5 is a flowchart showing an example of the simulation method. In the simulation method of the present embodiment, the effective density l _K / p of the coarse-grained molecular model 6 approaches the effective density l _K / p of the all-atomic model 11 (shown in FIG. 8). An embodiment in which the structural relaxation of the coarse-grained molecular model 6 is calculated is exemplified, but the present invention is not limited to such an embodiment. For example, the structural relaxation of the coarse-grained molecular model 6 may be calculated to approach the effective density l _K / p of the UA model, or the effective density l _K / p of the polymer chain 4 is known. In some cases, structural relaxation of the coarse-grained molecular model 6 may be calculated to approach this known effective density l _K / p.

In the simulation method of the present embodiment, first, the coarse-grained molecular model 6 shown in FIG. 3 is input to the computer 1 (step S1).

When the polymer chain 4 (shown in FIG. 2) is polybutadiene, Article 1 (Kurt Kremer & Gary S. Grest, "Dynamics of entangled linear polymer melts: A molecular-dynamics simulation", J. Chem Phys. Vol. Based on .92, No.8, 15 April 1990), for example, 1.55 polymers 5 are used as structural units, and the structural units are replaced with one particle 7. As a result, a plurality of (for example, 10 to 5000) particles 7 are set in the coarse-grained molecular model 6.

The particle 7 is treated as a mass point of the equation of motion in the molecular dynamics calculation. That is, parameters such as mass, diameter, charge or initial coordinates are defined for the particle 7. Each of these parameters is stored in the computer 1 as numerical information.

The bond chain 8 is configured as a bond potential that defines an equilibrium length between the particles 7 and 7. Here, the "equilibrium length" is the bond distance between the particles 7 and 7. The equilibrium length is defined as the distance between the centers 7a, 7a of the adjacent particles 7, 7. Further, it is desirable that the binding potential of the binding chain 8 is set based on, for example, the above-mentioned Article 1. Such coarse-grained molecular model 6 is numerical data for handling a polymer material by molecular dynamics calculation, and is input to the computer 1.

Next, in the simulation method of the present embodiment, the interaction is defined in the computer 1 between the adjacent particles of the coarse-grained molecular model 6 (interaction definition step S2). As mentioned above, the interaction is that the effective density l _K / p of the coarse-grained molecular model 6 is the effect of the polymer chain 4 (shown in FIG. 2) when calculating the structural relaxation based on molecular dynamics. This is to bring the density closer to the target density l _K / p.

As for the interaction, the effective density l _K / p of the coarse-grained molecular model 6 is the effective density of the polymer chain 4, the all-atomic model 11 or the UA model (in this embodiment, the all-atomic model 11). It is not particularly limited as long as it approaches l _K / p. As the interaction of the present embodiment, an interaction that affects the flexibility of the coarse-grained molecular model 6 (hereinafter, may be simply referred to as “flexibility”) is adopted.

The bending potential is not particularly limited as long as it affects the bending property of the coarse-grained molecular model 6. FIG. 6 is a diagram illustrating an example of bending potential. The bending potential of this embodiment is defined by the following equation (1).

ここで、
Ｅ：相互作用ポテンシャル関数（屈曲ポテンシャル）
Ｋ：相互作用パラメータ
θ：隣り合う３つの粒子がなす角度

here,
E: Interaction potential function (flexion potential)
K: Interaction parameter θ: Angle formed by three adjacent particles

In the above equation (1), when the interaction parameter K is positive, the bending potential E (θ) increases as the angle θ formed by the three adjacent particles 7 decreases. On the other hand, when the interaction parameter K is negative, the tendency is the opposite of the positive case. By adjusting the value of the interaction parameter K in this way, the bending potential E (θ) can be appropriately set. With such a bending potential E (θ), it is possible to set a coarse-grained molecular model 6 that is easy to bend and a coarse-grained molecular model 6 that is hard to bend.

The effective density l _K / p of the coarse-grained molecular model 6 is reduced to the effective density l _K / p of the polymer chain 4, the all-atomic model 11 or the UA model (in this embodiment, the all-atomic model 11). Appropriate determination of the interaction parameter K is important for effective close proximity. In the interaction definition step S2 of the present embodiment, a plurality of coarse-grained molecular models having different interaction parameters K are defined, and among these coarse-grained molecular models, the polymer chain 4, the all-atom model 11 or the UA The interaction 10 of the coarse-grained molecular model 6 with an effective density that closely resembles the effective density of the model (in this embodiment, the all-atom model 11) is determined.

Further, in the interaction definition step S2 of the present embodiment, the above-mentioned interaction 10 is determined, and the number of particles of the coarse-grained molecular model 6 (shown in FIG. 3) and the polymer chain 4 (shown in FIG. 2) are determined. The ratio to the number of monomers is also calculated. FIG. 7 is a flowchart showing an example of the processing procedure of the interaction definition step S2.

In the interaction definition step S2 of the present embodiment, first, the effective density l _K / p of the all-atomic model 11 is acquired (first calculation step S21). FIG. 8 is a conceptual diagram showing an example of an all-atomic model.

The all-atomic model 11 is represented by an atomic model 12 that models an atom based on the actual structure of the polymer chain 4 (shown in FIG. 2). In the molecular dynamics calculation using the all-atomic model 11, a unit of length based on the actual polymer chain 4 is used. Therefore, by obtaining the effective density l _K / p of the all-atomic model 11, the effective density l _K / p of the polymer chain 4 can be obtained.

In the first calculation step S21 of the present embodiment, the effective density l _K / p of the all-atomic model 11 is obtained, and the number of Kuhn segments of the all-atomic model 11 is obtained. The number of Kuhn segments is used to calculate the ratio between the number of particles in the coarse-grained molecular model 6 (shown in FIG. 3) and the number of monomers in the polymer chain 4 (shown in FIG. 2). FIG. 9 is a flowchart showing an example of the processing procedure of the first calculation step S21.

In the first calculation step S21 of the present embodiment, first, a plurality of all-atomic models 11 (shown in FIG. 8) having different numbers of monomers are set (step S41). As shown in FIG. 8, the all-atomic model 11 includes a plurality of atomic models 12 and bonds 13 that bond the atomic models 12 to each other. The monomer model 14 is set by connecting the atomic model 12 with the bond 13 based on the unit structure representing the monomer 5 of the polymer chain 4 shown in FIG. The monomer model 14 is linked based on a predetermined number of monomers (that is, molecular weight (degree of polymerization)). As a result, a plurality of all-atomic models 11 having different numbers of monomers are set.

The number of monomers is set within a range in which the structural relaxation calculation can be completed in a realistic calculation time based on the type of polymer material and the performance of the computer 1 that performs the molecular dynamics calculation described later. Is desirable. It is desirable to exclude an extremely small value for the number of monomers in order to maintain the calculation accuracy. As an example of the number of monomers, it can be selected from 10 to 60. The number of monomers is not limited to this.

The atomic model 12 is treated as a mass point of the equation of motion in a simulation based on the molecular dynamics calculation described later. That is, parameters such as mass, diameter, charge, or initial coordinates are defined in the atomic model 12. The atomic model 12 of the present embodiment includes a carbon atom model 12C that models the carbon atom of the polymer chain 4 (shown in FIG. 2) and a hydrogen atom model 12H that models the hydrogen atom of the polymer chain 4. I'm out.

The bond 13 constrains between the atomic models 12 and 12. The bond 13 of the present embodiment includes a main chain 13A connecting the carbon atom models 12C and 12C, and a side chain 13B connecting the carbon atom model 12C and the hydrogen atom model 12H. These main chain 13A and side chain 13B are treated as, for example, a spring in which an equilibrium length and a spring constant are defined.

The all-atomic model 11 has a bond length which is a bond length between each atomic model 12 and 12, a bond angle which is an angle formed by three continuous atomic models 12 via a bond 13, and a bond angle which is continuous through a bond 13. In the four atomic models 12 to be used, the two-sided angles and the like created by the three adjacent atomic models 12 are defined. As a result, the all-atomic model 11 has three-dimensional structure. In the all-atomic model 11, the bond length, bond angle and dihedral angle are changed by receiving an external force or an internal force according to the convention. This allows the all-atomic model 11 to change its three-dimensional structure.

Bond length, bond angle and dihedral angle can be defined, for example, by the potential (GAFF) set based on Article 2 (J. Comput. Chem. 25, 1157-1174 (2004)). It is desirable that the potential is set according to the structure of the polymer chain 4. Such an all-atomic model 11 can be created by using material property simulation software (for example, J-OCTA manufactured by JSOL Co., Ltd.). Each all-atomic model 11 is numerical data that can be handled by the computer 1 and is input to the computer 1.

Next, in the first calculation step S21 of the present embodiment, the initial arrangement of each all-atomic model 11 having a different number of monomers is determined (step S42). In step S42, a polymer material model in which the all-atomic model 11 is arranged is set in a predetermined space. FIG. 10 is a conceptual diagram showing an example of the polymer material model 18 in which the all-atomic model 11 is arranged.

In step S42 of the present embodiment, all atomic models 11 having different numbers of monomers are arranged in independently provided spaces 16. Thereby, in step S42, the polymer material model 18 in which the initial arrangement of each all-atomic model 11 is determined is defined. A plurality of all-atomic models 11 having the same number of monomers are arranged in each polymer material model 18. The all-atomic model 11 is preferably arranged in space 16 based on the Monte Carlo method.

The space 16 corresponds to the microstructure portion of the polymer material to be analyzed. The space 16 of the present embodiment is defined as a cube having three pairs of planes 17, 17 facing each other. Periodic boundary conditions are defined for each plane 17. Therefore, it can be treated as if one plane 17 and the other plane 17 are continuous (connected).

The number of all-atomic models 11 arranged in each space 16 is appropriately set based on the number of monomers and the size of the space 16. As the number of all-atomic models 11, it is desirable to select a number in which the periodic boundary length at equilibrium can be three times or more the inertial radius at equilibrium from the viewpoint of preventing entanglement between all-atomic models. In the present embodiment, the number is preferably 20 or more, and preferably 200 or less.

The length La of one side of the space 16 is preferably set so that the initial density of the atomic model 12 in the system is, for example, 0.001 g / cm ³ .

Next, in the first calculation step S21 of the present embodiment, in the polymer material model 18 in which the initial arrangement of the all-atomic model 11 is determined, the atomic models 12 and 12 of the adjacent all-atomic models 11 and 11 are mutual to each other. The action potential P1 is defined (step S43).

The interaction potential P1 of the present embodiment is the LJ potential _ULJ (r _ij ) and is defined by the following equation (4). Such interaction potentials can define repulsive and attractive forces depending on the distance r _ij between the atomic models 12 and 12.

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：原子モデル間の距離
ｒ_c：カットオフ距離
ε：原子モデル間に定義されるＬＪポテンシャルの強度
σ：原子モデルの直径に相当
なお、距離ｒ_ij及びカットオフ距離ｒ_cは、各原子モデル１２、１２の中心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 atomic models r _c : Cutoff distance ε: Intensity of LJ potential defined between atomic models σ: Corresponds to the diameter of the atomic model Note that the distance r _ij and the cutoff distance r _c are each atom. It is defined as the distance between the centers of models 12 and 12.

The interaction potentials are the first potential set between the carbon atom models 12C and 12C (shown in FIG. 8), the second potential set between the hydrogen atom models 12H and 12H (shown in FIG. 8), and carbon. It contains a third potential set between the atomic model 12C and the hydrogen atom model 12H. Each constant in the above equation (4) can be appropriately set based on the above-mentioned paper 1. The polymer material model 18 in which the initial arrangement of these all-atomic models 11 is determined is input to the computer 1.

Next, in the first calculation step S21 of the present embodiment, the structural relaxation of the initially arranged all-atomic model 11 is calculated (step S44). In step S44, molecular dynamics calculations are performed for each polymer material model 18 (shown in FIG. 10) for which the initial arrangement of the all-atomic model 11 has been determined. For the molecular dynamics calculation, Newton's equation of motion is applied, for example, assuming that all atomic models 11 arranged for a predetermined time in the space 16 shown in FIG. 10 follow classical mechanics. Then, the movements of all the atomic models 12 at each time are tracked and stored in the computer 1. Further, the conditions for molecular dynamics calculation are, for example, that the number, volume, and temperature of the atomic models 12 in the system are constant. Such molecular dynamics calculations can be performed using, for example, the molecular dynamics calculation program LAMMPS.

In step S44, molecular dynamics calculations are performed until the initial arrangement of the all-atomic model 11 is sufficiently relaxed. The criteria for determining the structural relaxation of the initial arrangement can be appropriately set as long as the criteria can be considered that the artificial initial arrangement of the all-atomic model 11 is sufficiently excluded. In step S44, it is desirable that the final size of the space 16 be set to, for example, an equilibrium volume of 1 atm by structural relaxation calculation.

Next, in the first calculation step S21 of the present embodiment, it is determined whether or not the structural relaxation of all all-atomic models (that is, all all-atomic models having different numbers of monomers) 11 has been calculated (step S45). .. When it is determined in step S45 that the structural relaxation of all atomic models 11 has been calculated (“Y” in step S45), the next step S46 is carried out. On the other hand, when it is determined that the structural relaxation calculation of all the all-atomic models 11 has not been completed (“N” in step S45), the all-atomic model 11 for which the structural relaxation has not been calculated (that is, shown in FIG. 10). The polymer material model 18) is selected (step S47), and steps S44 to S45 are carried out. As a result, the thermal equilibrium state (structural relaxation state) of all the all-atomic models 11 is calculated.

Next, in the first calculation step S21 of the present embodiment, the total length L (not shown) of the all-atomic model 11 is calculated (step S46). In step S46, the total length L is calculated for all structurally relaxed all-atomic models (that is, all all-atomic models with different numbers of monomers) 11. The total length L can be obtained, for example, by a deformation calculation for forcibly stretching the all-atomic model 11 in the main chain direction based on the method of Patent Document 1. The total length L of each all-atomic model 11 is input to the computer 1.

Next, in the first calculation step S21 of the present embodiment, the inertial radius R _g of the all-atomic model 11 is calculated (step S48). In step S48, the inertial radius R _g is calculated for all structurally relaxed all-atomic models (that is, all all-atomic models with different numbers of monomers) 11. The inertial radius R _g of the all-atomic model 11 is, for example, the coordinates of the atomic model 12 of the all-atomic model 11 obtained by the molecular dynamics calculation in step S44 based on the equation 2.5 described in the above-mentioned paper 1. Calculated from the value. The inertial radius of each all-atomic model 11 is input to the computer 1.

Next, in the first calculation step S21 of the present embodiment, the density ρ of the all-atomic model 11 is calculated (step S49). The density ρ can be calculated as appropriate.

In step S49 of the present embodiment, the density ρ of the structurally relaxed polymer material model 18 (shown in FIG. 10) is calculated for all atomic models 11 having different degrees of polymerization (that is, different numbers of monomers). The calculated density ρ is stored in the computer 1.

Next, in the first calculation step S21 of the present embodiment, the second bending degree of the all-atomic model 11 is calculated (step S50). The second degree of bending of this embodiment is the number of Kuhn segments of the all-atomic model 11 after structural relaxation. In step S50, the number of Kuhn segments is calculated for all structurally relaxed all-atomic models (that is, all all-atomic models with different numbers of monomers) 11. The number of Kuhn segments is one of the parameters of the ideal chain known in polymer physics, and is calculated by the following equation (5).

ここで、
Ｎ_kuhn：Kuhnセグメント数
Ｌ：全原子モデルの全長
Ｒ_g：全原子モデルの慣性半径

here,
N _kuhn : Number of Kuhn segments L: Overall length of all-atomic model R _g : Inertial radius of all-atomic model

In the above formula (5), for example, unlike the above-mentioned Patent Document 1 which uses the ensemble average of the lengths of the inter-terminal vector V1 (shown in FIG. 8) of the all-atomic model 11, the all-atomic model obtained in step S48 is used. The Kuhn segment number N _kuhn is obtained by using the inertial radius R _g and the total length L of the all-atomic model obtained in step S46. As a result, in the present embodiment, the influence of the high motility of the atomic model 12 on the terminal side of the all-atomic model 11 can be reduced, so that the number of Kuhn segments N _kuhn can be obtained accurately.

In the above equation (5), the larger the value of the number of Kuhn segments N _kuhn , the more compactly the all-atomic model 11 becomes a folded shape. On the other hand, the smaller the value of the number of Kuhn segments N _kuhn , the smaller the bending of the all-atomic model 11, and the shape becomes a linear and continuous extension. Therefore, the number of Kuhn segments N _kuhn is used as a parameter indicating the degree of bending of the all-atomic model. The number of Kuhn segments N _kuhn is stored in the computer 1.

Next, in the first calculation step S21 of the present embodiment, the effective density l _K / p of the all-atomic model 11 is calculated (step S51). In this embodiment, the effective density l _K / p of the all-atomic model 11 (which has a long chain length limit) with little dependence on the degree of polymerization is calculated.

In step S51 of the present embodiment, first, the effective densities l _K / p of the structurally relaxed all-atomic model 11 having different degrees of polymerization (that is, different numbers of monomers) are calculated. As described above, the effective density l _K / p is the value l _K / p obtained by dividing the Kuhn length l _K defined by the above equation (2) by the Packing length p defined by the above equation (3). You can get it at.

The total length L obtained in step S46 is substituted into the total length L of the all-atomic model 11 of the above formula (2). The inertial radius R _g obtained in step S48 is substituted into the inertial radius R _g of the all-atomic model 11 of the above equations (2) and (3). The total mass of the atomic models 12 constituting one all-atomic model 11 is substituted into the mass M of the all-atomic model 11 of the above equation (3). The density ρ of the all-atomic model 11 obtained in step S49 is substituted into the density ρ of the all-atomic model 11 of the above equation (3). Thereby, in step S51, the effective density l _K / p of each all-atomic model 11 can be calculated. FIG. 11 is a graph showing the relationship between the effective density l _K / p of each all-atomic model and the number of monomers.

Next, in step S51, an approximate curve 21 with an effective density l _K / p of each all-atomic model is obtained. As the approximate curve 21, for example, _lK / p = c1 × (1-M / c2) can be used. The variables c1 and c2 are fitting parameters. Next, in step S51, the long chain length limit l _K / p _∞ with an effective density is obtained as the value of the molecular weight ∞ of the approximate curve 21 (the value of the variable c1 of the approximate curve 21). The long chain length limit l _K / p _∞ of effective density is stored in computer 1.

Next, in the interaction definition step S2 of the present embodiment, the effective densities l _K / p of a plurality of coarse-grained molecular models 6 having different interaction parameters K are acquired (second calculation step S22). In the second calculation step S22 of the present embodiment, the effective density l _K / p of the coarse-grained molecular model 6 is obtained, and the number of Kuhn segments of the coarse-grained molecular model 6 is obtained. FIG. 12 is a flowchart showing an example of the second calculation step S22.

In the second calculation step S22 of the present embodiment, first, a plurality of coarse-grained molecular models 6 having different number of particles (chain length) are set (step S61). As shown in FIG. 3, the coarse-grained molecular model 6 includes a plurality of particles 7 and a binding chain 8 that binds the particles 7 and 7.

In the second calculation step S22 of the present embodiment, a plurality of coarse-grained molecular models 6 having different number of particles are set by connecting the particles 7 based on a plurality of different number of particles (chain length). The plurality of different number of particles can be appropriately set based on the type of the polymer material, the performance of the computer 1 for performing the molecular dynamics calculation described later, and the like. The number of particles is preferably selected from, for example, 5 to 1000. The number of particles is not limited to this. These coarse-grained molecular models 6 are numerical data for handling polymer materials in molecular dynamics calculations, and are input to the computer 1.

Next, in the second calculation step S22 of the present embodiment, a plurality of coarse-grained molecular models 6 having different interaction parameters K are defined (step S62). As shown in FIG. 6, the interaction 10 of the present embodiment is the bending potential E (θ) defined by the above equation (1). In step S62, a plurality of different interaction parameters K are defined by defining bending potentials E (θ) between adjacent particles 7 and 7 of the coarse-grained molecular model 6 based on a plurality of different interaction parameters K. Coarse-grained molecular model 6 is defined.

The plurality of different interaction parameters K can be appropriately set based on, for example, the effective density l _K / p in the range that the polymer chain 4 can take. The interaction parameter K of the present embodiment is selected from the range of 0 to 1.5, for example, when the effective density l _K / p of the polymer chain 4 is about 2.5 to 7.0. desirable.

In step S62, a plurality of coarse-grained molecular models 6 having different interaction parameters K are set for each coarse-grained molecular model 6 having a different number of particles set in step S61. That is, in step S62, the number of types of the number of particles N (for example, two types (N = 50, 100 shown in FIG. 14)) and the number of types of interaction (for example, three types (shown in FIG. 14)). A coarse-grained molecular model 6 with a number of types (eg, 6 types) multiplied by K = 0.8, 1.2, 1.6)) is set. Each coarse-grained molecular model 6 having a different number of particles and interaction is stored in the computer 1.

Next, in the second calculation step S22 of the present embodiment, the initial arrangement of the coarse-grained molecular models 6 having different particle numbers and interactions is determined (step S63). In step S63, a polymer material model in which each coarse-grained molecular model 6 is arranged in a predetermined space is set. FIG. 13 is a conceptual diagram showing an example of the polymer material model 20 in which the coarse-grained molecular model 6 is arranged.

In step S63 of the present embodiment, each coarse-grained molecular model 6 having a different number of particles and interaction is arranged in an independently provided space 16. Thereby, in step S63, the polymer material model 20 in which the initial arrangement of each coarse-grained molecular model 6 is determined is defined. In each polymer material model 20, a plurality of coarse-grained molecular models 6 having the same number of particles and the same interaction are arranged in the space 16. The coarse-grained molecular model 6 is preferably placed in space 16 based on the Monte Carlo method.

The space 16 corresponds to the microstructure portion of the polymer material to be analyzed, and is set in the same manner as the space 16 shown in FIG. The number of coarse-grained molecular models 6 arranged in each space 16 is appropriately set based on the number of particles and the size of the space 16. The number of coarse-grained molecular models 6 arranged in the space 16 is preferably 50 or more, and preferably 2000 or less.

In step S63, in each polymer material model 20, the interaction potential P2 is defined between the particles 7 and 7 of the adjacent coarse-grained molecular models 6 and 6, respectively. The interaction potential P2 of the present embodiment is an LJ (Lennard-Jones) potential and is defined by the above equation (4). In the above equation (4), "between atomic models" is replaced with "between particles".

It is desirable that the intensity ε of the interaction potential P2, the distance σ on which the interaction potential P2 acts, and the cutoff distance _rc are set based on, for example, the above-mentioned paper 2. The polymer material model 20 in which the initial arrangement of these coarse-grained molecular models 6 is determined is input to the computer 1.

Next, in the second calculation step S22 of the present embodiment, the structural relaxation of the initially arranged coarse-grained molecular model 6 is calculated (step S64). In step S64, molecular dynamics calculations are performed for each polymer material model 20 (shown in FIG. 13) for which the initial arrangement of the coarse-grained molecular model 6 has been determined. In step S64, the movements of all the particles 7 at each time are tracked and stored in the computer 1. In step S64, molecular dynamics calculations are performed until the initial arrangement of the coarse-grained molecular model 6 is sufficiently relaxed. The criteria for determining the structural relaxation of the initial arrangement can be appropriately set as long as it can be considered that the artificial initial arrangement of the coarse-grained molecular model 6 is sufficiently excluded.

Next, in the second calculation step S22 of the present embodiment, whether or not the structural relaxation of all the coarse-grained molecular models (that is, all the coarse-grained molecular models having different particle numbers and interactions) 6 has been calculated. It is determined (step S65). If it is determined in step S65 that the structural relaxation of all coarse-grained molecular models 6 has been calculated (“Y” in step S65), the next step S66 is carried out. On the other hand, when it is determined that the structural relaxation calculation of all the coarse-grained molecular models 6 has not been completed (“N” in step S65), the coarse-grained molecular model 6 for which structural relaxation has not been calculated (that is, that is). The polymer material model 20) shown in FIG. 13) is selected (step S67), and steps S64 to S65 are carried out. As a result, the thermal equilibrium state (structural relaxation state) of all coarse-grained molecular models 6 is calculated.

Next, in the second calculation step S22 of the present embodiment, the total length L (not shown) of the coarse-grained molecular model 6 is calculated (step S66). In step S66, the total length L is calculated for each of the structurally relaxed coarse-grained molecular models (that is, all coarse-grained molecular models with different particle numbers and interactions) 6. In the present embodiment, the total length L is obtained by multiplying the equilibrium internuclear distance of the adjacent particles in the coarse-grained molecular model 6 by the number of particles. The equilibrium internuclear distance is obtained based on the result of the above molecular dynamics calculation. The total length L of the coarse-grained molecular model 6 is input to the computer 1, respectively.

Next, in the second calculation step S22 of the present embodiment, the inertial radius R _g of the coarse-grained molecular model 6 is calculated (step S68). In step S68, the inertial radius R _g is calculated for all structurally relaxed coarse-grained molecular models (that is, all coarse-grained molecular models with different particle numbers and interactions) 6. The inertial radius of the all-atom model 11 is, for example, the coordinate value of the particle 7 of the coarse-grained molecular model 6 obtained by the molecular dynamics calculation in step S64 based on the equation 2.5 described in the above paper 1. Calculated from. The inertial radius of each coarse-grained molecular model 6 is input to the computer 1.

Next, in the second calculation step S22 of the present embodiment, the first degree of bending of the coarse-grained molecular model 6 is obtained (step S69). The first degree of bending of this embodiment is the number of Kuhn segments of the coarse-grained molecular model 6 after structural relaxation. In step S69, the number of Kuhn segments of all structurally relaxed coarse-grained molecular models (ie, all coarse-grained molecular models with different particle numbers and interactions) 6 is calculated. As described above, the number of Kuhn segments is calculated by the above equation (5) using the inertial radius R _g of the coarse-grained molecular model and the total length L of the coarse-grained molecular model. The number of Kuhn segments N _kuhn of the coarse-grained molecular model 6 is stored in the computer 1.

Next, in the second calculation step S22 of the present embodiment, the effective density l _K / p of the coarse-grained molecular model is calculated (step S70). In this embodiment, for each interaction (interaction parameter K), the effective density l _K / p of the coarse-grained molecular model 6 with less polymerization degree dependence (that is, the long chain length limit) is calculated. ..

In step S70 of the present embodiment, first, the effective density l _K / p of all coarse-grained molecular models (that is, all coarse-grained molecular models having different particle numbers and interactions) 6 is calculated. .. As described above, the effective density l _K / p is the value l _K / p obtained by dividing the Kuhn length l _K defined by the above equation (2) by the Packing length p defined by the above equation (3). You can get it at.

The total length L obtained in step S66 is substituted into the total length L of the coarse-grained molecular model 6 of the above formula (2). The inertial radius R _g obtained in step S68 is substituted into the inertial radius R _g of the coarse-grained molecular model 6 of the above equations (2) and (3). The total mass of the particles 7 constituting one coarse-grained molecular model 6 is substituted into the mass M of the coarse-grained molecular model 6 of the above formula (3). For example, 0.85 mass / σ ³ is substituted into the density ρ of the coarse-grained molecular model 6 of the above equation (3). Thereby, in step S70, the effective density l _K / p of each coarse-grained molecular model 6 can be calculated.

In step S70 of the present embodiment, the effective density l _K / p of the coarse-grained molecular model in which the number of particles N is different is obtained for each interaction (interaction parameter K). FIG. 14 is an example of a graph showing the relationship between the effective density l _K / p of each coarse-grained molecular model, the interaction parameter K of the bending potential, and the number of particles N. In FIG. 14, for three coarse-grained molecular models with different interaction parameters K, the effective density of two types of particle numbers (chain lengths) N is l _K / p (number of particles N = 50 is a long-dotted chain line, number of particles). N = 100 is shown by a two-dot chain line) and the estimated value l _K / p (solid line) of the long chain length limit of effective density is shown.

Next, in step S70, the coarse-grained molecular model 6 is obtained for a graph in which the effective density l _K / p of the coarse-grained molecular model in which the number of particles N is different for each interaction (interaction parameter K) is obtained. Approximate curves 28 of the effective density l _K / p of are obtained respectively. As the approximate curve 28, for example, _lK / p = c1 × (1-M / c2) × exp (c3 × K) can be used. The variables c1, c2 and c3 are fitting parameters. Next, in step S70, the effective density l _K in the long chain length limit of the coarse-grained molecular model 6 is set as the value of the molecular weight ∞ of the approximate curve 28 (c1 × exp (c3 × K) in the above equation). / P _∞ is acquired as a function of the interaction (interaction parameter K). Then, all the parameter values of the obtained approximate curve of the effective density l _K / p _∞ are stored in the computer 1.

Next, in the interaction definition step S2 of the present embodiment, an effective density l _K / p (l _K / p _∞ shown in FIG. 11) of the polymer chain (all-atomic model 11) is approximated. The interaction of the coarse-grained molecular model 6 with the density l _K / p (l _K / p _∞ shown in FIG. 14) is determined (step S23). In step S23, first, the effective density l _K / p _∞ of the all-atomic model 11 shown in FIG. 11 and the coarse grain of the long chain length limit as a function of the interaction (interaction parameter K) shown in FIG. The effective density l _K / p _∞ of the visualization molecular model 6 is compared. Then, the interaction (interaction parameter K) of the coarse-grained molecular model 6 having a density l _K / p close to the effective density l _K / p of the all-atomic model 11 is determined.

In the interaction definition step S2 of the present embodiment, a plurality of coarse-grained molecular models 6 having different interaction parameters K are defined, and the effective density l _K / p of each coarse-grained molecular model 6 is calculated. There is. Therefore, the interaction (interaction parameter K) of the coarse-grained molecular model having an effective density l _K / p close to the effective density l _K / p of the polymer chain 4 can be determined. The interaction parameter K is determined in the above equation l _K / p = c1 × (1-M / c2) × exp (c3 × K) used for fitting, and l _K / p _∞ of the all-atomic model 11. Can be calculated by K = ln (l _K / p _∞ / c1) / c3 using.

Further, in the interaction definition step S2 of the present embodiment, the effective density l _K / p (l _K / p _∞ shown in FIG. 11) of the all-atomic model 11 having a small degree of polymerization dependence (long chain length limit). ) And the effective density l _K / p (l _K / p _∞ shown in FIG. 14) of the coarse-grained molecular model 6 with less dependence on the degree of polymerization (long chain length limit) are compared. As a result, in the interaction definition step S2, the effective density of the coarse-grained molecular model 6 is determined regardless of the degree of polymerization of the all-atom model 11 and the degree of polymerization of the coarse-grained molecular model 6. It is possible to determine the interaction parameter K that can approach the effective density of chain 4. The determined interaction (interaction parameter K) of the coarse-grained molecular model 6 is stored in the computer 1.

Next, in the interaction definition step S2 of the present embodiment, the ratio between the number of particles of the coarse-grained molecular model 6 (shown in FIG. 3) and the number of monomers of the polymer chain 4 (shown in FIG. 2) is calculated. (Step S24). In step S24, the first degree of bending of the coarse-vision molecular model 6 in which the interaction is defined after structural relaxation and the second degree of bending of the all-atom model 11 or the United atom model (not shown) after structural relaxation are obtained. Based on this, the ratio of the number of particles of the coarse-grained molecular model 3 to the number of monomers of the polymer chain 4 (the number of monomers of the polymer chain 4 per one particle 7 of the coarse-vision molecular model 6) is obtained. There is.

The first degree of bending is the number of Kuhn segments of the coarse-grained molecular model 6 acquired in step S69. In step S24, first, among all the coarse-grained molecular models 6, only a plurality of coarse-grained molecular models 6 having the interaction parameter K determined in step S23 are targeted, and the number of Kuhn segments and the number of particles are determined. The relationship is acquired.

On the other hand, the second degree of bending is the number of Kuhn segments of the all-atomic model 11 acquired in step S50. In step S24, the relationship between the number of Kuhn segments and the number of monomers of the all-atomic model 11 is acquired.

Next, in step S24, the relationship between the number of Kuhn segments and the number of monomers in the all-atom model 11 and the relationship between the number of Kuhn segments and the number of particles in the coarse-grained molecular model 6 are fitted. FIG. 15 shows the ratio of the number of Kuhn segments to the number of monomers (N _Kuhn / N _FA ) and Kuhn segments after fitting the number of Kuhn segments of the total atomic model 11 and the number of Kuhn segments of the coarse-grained molecular model 6. It is a graph which shows the correspondence relation of the ratio (N _Kuhn / N _CG ) of the number and the number of particles.

In step S24 of the present embodiment, the relationship between the number of Kuhn segments in the coarse-grained molecular model 6 and the number of particles N _CG , and the relationship between the number of Kuhn segments in the all-atom model 11 and the number of monomers N _FA are fitted. Will be done. As a result, considering the dependence of the chain length (number of particles N _CG , number of monomers N _FA ), the number of particles in the coarse-grained molecular model 6 such that the same chain length and the same spatial spread are obtained. The ratio of the polymer chain 4 to the number of monomers can be calculated.

In step S24, the relationship between the number of Kuhn segments of the coarse-grained molecular model 6 and the number of particles N _CG is fitted by the smooth curve 25 (shown by the broken line) shown in FIG. In FIG. 15, in order to visualize the dependence of the chain length, the ratio of the number of Kuhn segments to the chain length (N _Kuhn / N _CG and N _Kuhn / N _FA ) is used as the vertical axis. The curve is defined by the following equation (6). Since such a curve 25 uses three fitting parameters a, b, and c, it can be fitted accurately in consideration of the dependence of the chain length (particularly, the influence of high terminal motility).

ここで、
Ｎ_kuhn：Kuhnのセグメント数
Ｎ_CG：粗視化分子モデルの粒子数
ａ、ｂ、ｃ：フィッティングパラメータ

here,
N _kuhn : Number of Kuhn segments N _CG : Number of particles in the coarse-grained molecular model a, b, c: Fitting parameters

Next, in step S24, the relationship between the number of Kuhn segments N _kuhn of the all-atomic model 11 and the number of monomers N _FA is fitted to the curve 25 based on the following equation (7). In the following equation (7), since the single fitting parameter d is used, the relationship of the all-atomic model 11 having a larger statistical error than the coarse-grained molecular model 6 can be accurately fitted to the curve 25.

ここで、
Ｎ_FA：全原子モデルのモノマー数
Ｎ_CG：粗視化分子モデルの粒子数
ｄ：フィッティングパラメータ

here,
N _FA : Number of monomers in the total atomic model N _CG : Number of particles in the coarse-grained molecular model d: Fitting parameters

As for the fitting method and the statistical error used for fitting, the same method as described in Patent Document (Patent No. 6050903) is used. In the example of the graph shown in FIG. 15, the ratio of the number of particles of the roughened molecular model 6 to the number of monomers of the polymer chain 4 (that is, the number of monomers per particle 7) is 1.2. be. The ratio of the number of particles of such coarse-grained molecular model 6 (shown in FIG. 3) to the number of monomers of the polymer chain 4 (shown in FIG. 2) is input to the computer 1.

In step S24 of the present embodiment, the number of Kuhn segments of the all-atom model 11 (shown in FIG. 5) and the number of Kuhn segments of the coarse-grained molecular model 6 (shown in FIG. 3) are fitted to be substantially the same as each other. Since the all-atom model 11 and the coarse-grained molecular model 6 that form the shape can be associated with each other, the ratio between the number of particles in the coarse-grained molecular model 6 and the number of monomers in the polymer chain 4 should be calculated accurately. Can be done. Further, in the present embodiment, since a plurality of Kuhn segments of the all-atomic model 11 and a plurality of Kuhn segments of the coarse-grained molecular model 6 are obtained, fitting can be performed with high accuracy.

Further, in step S24 of the present embodiment, the relationship between the number of Kuhn segments and the number of particles is acquired only for a plurality of coarse-grained molecular models 6 having the interaction parameter K determined in step S23. As a result, it is possible to fit with the number of Kuhn segments of the all-atom model 11 and the coarse-grained molecular model 6 whose effective densities l _K / p are close to each other. The ratio of the molecular chain 4 to the number of monomers can be calculated accurately.

Next, in the simulation method of the present embodiment, the computer 1 calculates the structural relaxation for the coarse-grained molecular model 6 in which the interaction is defined (step S3). In step S3, first, as shown in FIG. 13, a polymer material model 20 in which a plurality of coarse-grained molecular models 6 in which interactions are defined are arranged in a space 16 is set. The number of coarse-grained molecular models 6 is preferably set within the above range, for example.

Next, in step S3 of the present embodiment, in the polymer material model 18, the interaction potential P2 is defined between the particles 7 and 7 of the adjacent coarse-grained molecular models 6 and 6, respectively. The interaction potential P2 is as described above. Then, in step S3, structural relaxation based on molecular dynamics is calculated for the coarse-grained molecular model 6 in which the interaction is defined.

As described above, the simulation method of the present embodiment has an effective density _lK / of the coarse-grained molecular model 6 based on the interaction defined between the adjacent particles 7 and 7 of the coarse-grained molecular model 6. p can be brought closer to the effective density l _K / p of the polymer chain 4 (shown in FIG. 2). Thereby, from the coordinates of the polymer material model 20 after the structural relaxation calculation, the coarse visualization is performed based on the ratio of the number of particles of the coarse visualization molecular model 6 and the number of monomers of the polymer chain 4 obtained in step S24. The density of the polymer material model 18 in which the all-atom model 11 obtained by replacing the particles 7 of the molecular model 6 with the monomer of the polymer chain 4 is arranged is actually high without additional structural relaxation calculation. It can be approximated to the density of the molecular chain 4. Further, since the additional structural relaxation calculation is not required, the inertial radius of the all-atomic model 11 can be approximated to the inertial radius of the actual polymer chain 4. That is, since the structural relaxation similar to the actual polymer chain 4 can be performed by using the polymer material model 20 in which the coarse-vision molecular model 6 is arranged, the density of the polymer material model 18 after the structural relaxation calculation is performed. Can be approximated to the actual density of the polymer chain 4. In the simulation method of this embodiment, the calculation accuracy can be improved.

Further, in the coarsening molecular model 6 of the present embodiment, the ratio of the number of particles of the coarsening molecular model 6 obtained in step S24 to the number of monomers of the polymer chain 4 (that is, per particle 7). Since the monomer of the polymer chain 4 is replaced with one particle 7 based on the number of monomers), the unit of the length of the coarse-vision molecular model 6 is changed to the unit of the length of the polymer chain 4. It can be converted accurately. Therefore, the simulation method of the present embodiment can improve the calculation accuracy.

The coarsened molecular model 6 in which the interaction is defined can be used, for example, in the time conversion step of Patent Document (Japanese Patent Laid-Open No. 6050903) from the polymer material model 20 after the structural relaxation calculation in step S24. Based on the ratio of the obtained number of particles of the coarsened molecular model 6 to the number of monomers of the polymer chain 4, the particles of the coarsened molecular model 6 are replaced with the monomers of the polymer chain 4 to form a polymer material model. By creating 18, the structurally relaxed coordinates of the long chain length all-atom model required for time unit conversion can be created with high accuracy. Therefore, the time unit of the coarsened molecular model 6 can be used for the polymer chain. Useful for more accurate conversion in time units.

Next, in the simulation method of the present embodiment, as shown in FIG. 5, whether the computer 1 has good simulation results (that is, has desired performance) using the polymer material model (not shown). It is determined whether or not (step S4). In step S4, for example, after the deformation calculation using the polymer material model 20 after structural relaxation in step S3, the unit of length of the coarse-grained molecular model 6 (shown in FIG. 3) is changed to the polymer chain 4 (FIG. 3). The physical properties of the polymer chain 4 are evaluated based on the result of accurate conversion into the unit of length (shown in 2).

When it is determined in step S4 that the simulation result is good (“Y” in step S4), the polymer material is manufactured based on the simulated polymer material model (not shown) (step S5). ). On the other hand, when it is determined that the simulation result is not good (“N” in step S4), the structure and conditions of the polymer chain 4 (shown in FIG. 2) are changed (step S6), and steps S1 to step S1 to step are changed. S4 is carried out again. Thereby, in the simulation method of the present embodiment, it is possible to produce a polymer material having desired performance without actually making a prototype of the polymer material.

In the interaction definition step S2 of the present embodiment, the interaction 10 of the coarse-grained molecular model 6 is defined, the number of particles of the coarse-grained molecular model 6 (shown in FIG. 3), and the polymer chain 4 (FIG. 2). The ratio to the number of monomers (shown in) has been calculated, but is not limited to such an embodiment. For example, in the interaction definition step S2, only the interaction 10 of the coarse-grained molecular model 6 may be defined. In such a simulation method, the monomer of the polymer chain 4 is replaced with one particle 7 based on the ratio of the number of particles of the coarsening molecular model 6 to the number of monomers of the polymer chain 4. Even if the molecular model 6 is not used, the structural relaxation similar to the actual polymer chain 4 is possible in the step S3 for calculating the structural relaxation of the coarse-visualized molecular model 6 in which the interaction is defined. Therefore, in such a simulation method, the calculation time can be shortened while improving the calculation accuracy.

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

According to the processing procedure shown in FIG. 5, a coarsening molecular model modeling a polymer chain (cis-1.4 polybutadiene) is input to a computer, and coarsening is performed when calculating structural relaxation based on molecular dynamics. Interactions were defined between adjacent particles of the coarse-grained molecular model so that the effective density of the molecular model approaches the effective density of the polymer chains (Examples).

In the step of defining the interactions of the examples, a plurality of coarse-grained molecular models with different interaction parameters are defined based on the processing procedure shown in FIG. 7 to approximate the effective density of the polymer chains. The interaction of coarse-grained molecular models with effective densities was determined.

In the first calculation step of obtaining the effective density l _K / p of the whole atomic model in the step of defining the interaction of the examples, the number of monomers (molecular weight) is different based on the processing procedure shown in FIG. A plurality of all-atomic models (in this embodiment, the first all-atomic model to the third all-atomic model) were set, and the effective density l _K / p of the all-atomic model was obtained. FIG. 11 is a graph showing the relationship between the effective density l _K / p of each all-atomic model and the number of monomers. FIG. 16 is a graph showing the relationship between the number of Kuhn segments (N _Kuhn / N _FA ) and the number of monomers in the total atomic model. In the molecular dynamics calculation, the initial density of the space was set to 0.001 g / cm ³ , the temperature was set to 360 K, and the pressure was set to 1 atm. The number of monomers of each all-atomic model, the number of all-atomic models arranged in space, and the like are as follows.
First all-atomic model:
Number of monomers: 20, Number in space: 50 Second all-atomic model:
Number of monomers: 30, Number in space: 75 Third all-atomic model:
Number of monomers: 40, number in space: 75

In the second calculation step of obtaining the effective density l _K / p of the coarse-grained molecular model in the step of defining the interaction of the examples, the number of particles (chain length) is based on the processing procedure shown in FIG. ) And a plurality of coarse-grained molecular models (in this embodiment, the first coarse-grained model to the sixth coarse-grained model) having different interactions (interaction parameter K) are set, and the all-atom model is effective. The density l _K / p was obtained. FIG. 14 is a graph showing the relationship between the effective density l _K / p of each coarse-grained molecular model, the interaction parameter K of the bending potential, and the number of particles N. The number of particles (molecular weight), interaction (interaction parameter K), and the number of coarse-grained models arranged in space of each coarse-grained model are as follows.
First coarse-grained model:
Number of particles: 50, interaction parameter K: 0.8, number of particles in space: 200 Second coarse-grained model:
Number of particles: 50, interaction parameter K: 1.2, number of particles in space: 200 Third coarse-grained model:
Number of particles: 50, interaction parameter K: 1.6, number of particles in space: 200 4th coarse-grained model:
Number of particles: 100, interaction parameter K: 0.8, number of particles in space: 100 5th coarse-grained model:
Number of particles: 100, interaction parameter K: 1.2, number of particles in space: 100 6th coarse-grained model:
Number of particles: 200, interaction parameter K: 1.6, number of particles in space: 100

In the step of defining the interaction of the examples, the effective density l _K / p (density l _K / p _∞ shown in FIG. 14) of the coarse-grained molecular model acquired for each interaction (interaction parameter K). ), The interaction (interaction parameter K) of the coarse-grained molecular model having a density l _K / p (density l _K / p _∞ ) close to the effective density l _K / p _∞ of the all-atomic model. It has been determined. Then, based on the determined interaction parameter K, the interaction is defined between the adjacent particles of the coarse-grained molecular model shown in FIG. 3, and the polymer material model in which 100 particles are arranged in the space is defined. rice field. Then, the structural relaxation was calculated for the coarse-grained molecular model placed in the polymer material model, and the density of the polymer material model after the structural relaxation calculation was calculated.

For comparison, a coarse-grained molecular model modeling a polymer chain (cis-1.4 polybutadiene) was input to the computer (comparative example). The coarse-grained molecular model of the comparative example does not define the interactions that affect flexibility as in the examples. Then, a polymer material model in which 100 coarse-visualized molecular models of the comparative example were arranged in the space was defined. Then, the structural relaxation was calculated for the coarse-grained molecular model placed in the polymer material model, and the density of the polymer material model after the structural relaxation calculation was calculated.

The density of the polymer material model of the comparative example was twice as small as the density after performing additional structural relaxation calculations from the coordinates until the density became constant. The radius of inertia after equilibration was 20% smaller than the value expected at equilibrium. On the other hand, the density of the polymer material model of the example had a difference of less than 1% as compared with the density after the additional structural relaxation calculation. Therefore, in the examples, it was confirmed that the additional structural relaxation calculation can be omitted. Moreover, the calculation cost of the example was substantially the same as the calculation cost of the comparative example. Therefore, the examples were able to improve the calculation accuracy while maintaining the calculation cost as compared with the comparative example.

S1 Step to input coarse-grained molecular model S2 Step to define interaction S3 Step to calculate structural relaxation

Claims (5)

A method for analyzing polymer materials having polymer chains using a computer.
A step of inputting a coarse-grained molecular model expressing the polymer chain using a plurality of particles smaller than the number of atoms constituting the polymer chain to the computer.
At the time of calculation of structural relaxation based on molecular dynamics, the effective density, which is the value obtained by dividing the Kuhn length of the coarsened molecular model by the Packing length, is the polymer chain, the all-atomic model of the polymer chain, Alternatively, the interaction between adjacent particles of the coarsening molecular model is approached so as to approach an effective density which is the value obtained by dividing the Kuhn length of any of the United atom models of the polymer chain by the packing length. The process of defining and
The computer comprises a step of calculating the structural relaxation for the coarse-grained molecular model in which the interaction is defined.
Simulation method for polymer materials. The method for simulating a polymer material according to claim 1, wherein the interaction affects the flexibility of the coarse-grained molecular model. The interaction is the method for simulating a polymer material according to claim 2, which is defined by the following formula (1).

here,
E: Interaction potential function K: Interaction parameter θ: Angle formed by three adjacent particles In the step of defining the interaction, a plurality of coarse-grained molecular models having different interaction parameters of the interaction are defined, and the polymer chain, the all-atomic model of the polymer chain, or the polymer is defined. The high according to any one of claims 1 to 3, comprising determining the interaction of the coarse-grained molecular model having an effective density close to the effective density of any of the United Atom models of the chain. Method of simulating molecular materials. The computer is based on the first degree of flexion after structural relaxation of the coarse-grained molecular model for which the interaction is defined and the second degree of flexion after structural relaxation of the all-atom model or the United Atom model. The method for simulating a polymer material according to any one of claims 1 to 4, which comprises a step of calculating the ratio between the number of particles of the coarse-grained molecular model and the number of monomers of the polymer chain.

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