JP6711201B2 - Polymer material simulation method - Google Patents

Description

The present invention relates to a method for simulating a polymer material that is useful for analyzing a polymer material.

In recent years, in order to develop a polymer material such as rubber, various simulation methods (numerical calculation) for evaluating the properties of the polymer material using a computer have been proposed (for example, see Patent Document 1 below). ..

In this kind of simulation method, first, a polymer material model in which a molecular chain model including a plurality of particle models is arranged in a space defined on a computer is defined. This polymer material model is subjected to relaxation calculation based on molecular dynamics. Then, the deformation calculation using the polymer material model is performed, and the performance of the polymer material is analyzed.

JP, 2013-195220, A

In actual polymer materials, it is known that molecular chains are broken when a large force is applied. However, in the simulation method as described above, there has been a problem that the polymer material cannot be accurately analyzed because the method of cutting the molecular chain model has not been established.

The present invention has been devised in view of the above circumstances, and its main object is to provide a method for simulating a polymer material, which enables accurate analysis of the polymer material.

The present invention is a simulation method for analyzing the breakage of a molecular chain of a polymer material by using a computer, wherein a plurality of particle models and a bond model connecting the particle models based on the molecular chain are used. Defining a molecular chain model including and in the computer, defining a polymer material model in which at least one of the molecular chain models is arranged in the space defined on the computer, and the computer in advance. A first molecular mechanics calculation for performing molecular mechanics calculation based on the polymer material model, including a cleavage calculation step for calculating the cleavage of the molecular chain model based on a predetermined condition. Regarding the step and the molecular chain model after the first molecular dynamics calculation step, there is a dissociated particle model part in which the distance between the particle models adjacent to each other via the bond model is larger than a predetermined first distance. If it is determined that the dissociated particle model portion exists, the quantum mechanical calculation is performed for the first region that is a non-whole region including the dissociated particle model portion. And a step of cutting between the particle models when the distance between the particle models is larger than a predetermined second distance in the first region after the quantum mechanical calculation step. And

In the simulation method of the polymer material according to the present invention, it is preferable that a potential close to a bond dissociation potential is defined as a bond potential between the particle models in the molecular mechanics calculation.

In the method for simulating the polymer material according to the present invention, the binding potential in the molecular mechanics calculation is within a range from a lower limit value of energy of the bond dissociation potential to 50% to 80% of an upper limit value of the energy. , Is preferably defined by a function approximating the bond dissociation potential.

In the polymer material simulation method according to the present invention, it is preferable that the bond dissociation potential be obtained by quantum mechanical calculation.

In the simulation method of the polymer material according to the present invention, the first distance is preferably smaller than the second distance.

In the method for simulating a polymer material according to the present invention, it is preferable that the second distance is defined based on a distance between particle models at an inflection point at which the energy increment is small for bond dissociation potential. ..

In the method for simulating a polymer material according to the present invention, it is preferable that the cutting calculation step further includes a second molecular dynamics calculation step of performing a molecular dynamics calculation on the first region.

In the simulation method of the polymer material according to the present invention, the cutting calculation step includes a step of calculating a physical quantity including the energy Et of the polymer material model, and the energy Et is calculated based on the following formula. Is desirable.
Et=Ea-Eb+Ec
here,
Ea: Energy of the polymer material model obtained in the first molecular mechanics calculation step Eb: Energy of the first region obtained in the second molecular mechanics calculation step Ec: Energy of the first region obtained in the quantum mechanics calculation step

In the simulation method of the polymer material according to the present invention, the cutting calculation step includes a step of calculating a physical quantity including a force Ft acting on the polymer material model, and the force Ft is calculated based on the following formula. It is desirable to be done.
Ft=Fa−Fb+Fc
here,
Fa: Force acting on the polymer material model obtained in the first molecular mechanics calculation step Fb: Force acting on the first region obtained in the second molecular mechanics calculation step Fc: No. determined in the quantum mechanics calculation step Force acting on one area

In the method for simulating a polymer material according to the present invention, the separated particle model unit includes a pair of first particle models adjacent to each other via the bond model, and the first region includes the first particle model in the first particle model. It is desirable to further include at least one second particle model adjacent to each other via the bond model.

In the polymer material simulation method according to the present invention, it is preferable that the first region further includes at least one third particle model adjacent to the second particle model via the bond model.

In the method for simulating a polymer material according to the present invention, the bond model between the first particle model and the second particle model defines a single bond between a pair of atoms forming the molecular chain. A bond bond model is included, and the bond model between the second particle model and the third particle model includes a double bond bond model defining a double bond between a pair of atoms constituting the molecular chain. Is desirable.

The method for simulating a polymer material according to the present invention includes a cleavage calculation step for calculating the cleavage of a molecular chain model defined based on the molecular chain of the polymer material. The cutting calculation step includes a first molecular dynamics calculation step for performing a molecular dynamics calculation based on a polymer material model and a molecular chain model after the first molecular dynamics calculation step between adjacent particle models via a bond model. And a determination step of determining whether or not there is a separated particle model portion whose distance is greater than a predetermined first distance.

If it is determined that the dissociated particle model part exists, the quantum mechanical calculation process for performing the quantum mechanical calculation for the first region that is the non-whole region including the dissociated particle model part, and the first region after the quantum mechanical calculation process And, when the distance between the particle models is larger than the second predetermined distance, the step of cutting between them is further included.

The detached particle model portion is a portion in the molecular chain model that is likely to be cut between particle models. Quantum mechanical calculation with higher calculation accuracy than molecular mechanics calculation is performed for the first region including the dissociated particle model unit. Therefore, in the simulation method of the present invention, the breakage between particle models can be approximated to the breakage of an actual molecular chain, and a polymeric material can be analyzed with high accuracy.

Further, the presence/absence of the dissociated particle model unit is determined based on the molecular mechanics calculation that requires a shorter calculation time than the quantum mechanics calculation. Therefore, it is not necessary to perform the quantum mechanical calculation for the entire area of the polymer material model. Therefore, the simulation method of the present invention can reduce the calculation time.

It is a perspective view of the computer which performs the simulation method of this embodiment. It is a structural formula of polyisoprene. It is a flow chart which shows an example of the processing procedure of the simulation method of this embodiment. It is a conceptual diagram of the molecular chain model of this embodiment. It is a flow chart which shows an example of a processing procedure of a molecular chain model setting process. (A)-(c) is a partial view of a molecular chain model explaining the 1st potential. It is a conceptual diagram of a polymer material model. It is a flow chart which shows an example of the processing procedure of the cutting calculation process of this embodiment. It is a side view explaining the extension simulation of a polymer material model. It is a flow chart which shows an example of a processing procedure of a potential definition process of this embodiment. It is a figure which shows an example of the molecular model used for calculating|requiring a bond dissociation potential. It is a graph which shows a bond dissociation potential. It is a graph which shows a bond dissociation potential and a bond potential. It is a flow chart which shows an example of the processing procedure of a quantum mechanical calculation process. It is a figure which shows a 1st area|region. It is a graph which showed the stress of the polymeric material of an example, and the relation of the extension rate of a polymeric material model. 5 is a graph showing the relationship between the number of cuts between particle models of Example 1 and the elongation rate of a polymer material model. 3 is a graph showing the relationship between the stress of the polymer material of Example 1 and the elongation rate of the polymer material model.

An embodiment of the present invention will be described below with reference to the drawings.
The polymer material simulation method of the present embodiment (hereinafter, also simply referred to as “simulation method”) is a method for analyzing the breakage of the molecular chain of the polymer material using a computer.

FIG. 1 is a perspective view of a computer that executes the simulation method of this embodiment. The computer 1 is configured to include 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. In addition, a processing procedure (program) 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. The polymer material of the present embodiment is cis-1,4 polyisoprene (hereinafter, simply referred to as “polyisoprene”). FIG. 2 is a structural formula of polyisoprene.

Molecular chain 2A constituting the polyisoprene methine group (e.g., -CH =,> C =) , methylene group _(-CH 2 -), and a monomer isoprene constituted by a methyl group (-CH ₃₎ (Isoprene molecule) 3 is connected at a polymerization degree n. A polymer material other than polyisoprene may be used as the polymer material.

FIG. 3 is a flowchart showing an example of the processing procedure of the simulation method of this embodiment. In the simulation method of this embodiment, first, a molecular chain model is defined in the computer 1 based on the molecular chain 2A shown in FIG. 2 (molecular chain model setting step S1). FIG. 4 is a conceptual diagram of the molecular chain model 5 of this embodiment.

The molecular chain model 5 is configured as an all atom model. The molecular chain model 5 of the present embodiment is set as polyisoprene in which one sulfur atom is crosslinked. The molecular chain model 5 is configured to include a plurality of particle models 6 and a bond model 7 that connects the particle models 6 and 6.

The particle model 6 and the bond model 7 are linked based on the unit structure of the monomer 3 of the molecular chain 2A shown in FIG. Thereby, the monomer model 9 is set. The monomer model 9 is linked based on the molecular weight (degree of polymerization) Mn. Thereby, the molecular chain model 5 is set. FIG. 5 is a flowchart showing an example of the processing procedure of the molecular chain model setting step S1.

In the molecular chain model setting step S1 of the present embodiment, first, as shown in FIG. 4, the particle model 6 is set (step S11). The particle model 6 is treated as a mass point of the equation of motion in the simulation based on the molecular dynamics calculation, the molecular mechanics calculation, and the quantum mechanics calculation described later. That is, in the particle model 6, parameters such as mass, diameter, electric charge, or initial coordinates are defined.

The particle model 6 of the present embodiment is a carbon particle model 6C that models carbon atoms of the molecular chain 2A shown in FIG. 2, a hydrogen particle model 6H that models hydrogen atoms, and a sulfur particle that models sulfur atoms. Model 6S is included. These particle models 6 are stored in the computer 1.

Next, in the molecular chain model setting step S1, the bond model 7 is set (step S12). The bond model 7 binds between the particle models 6 and 6. The bond model 7 of this embodiment includes a main chain 7a and a side chain 7b. The main chain 7a connects the carbon particle models 6C and 6C. The side chain 7b connects between the carbon particle model 6C and the hydrogen particle model 6H and between the carbon particle model 6C and the sulfur particle model 6S. Further, the bond model 7 includes a single bond bond model 10A that defines a single bond between a pair of atoms and a double bond bond model 10B that defines a double bond between a pair of atoms. In the single bond bond model 10A and the double bond bond model 10B, different potentials are defined based on the following equations (1) to (3).

Next, in the molecular chain model setting step S1, a potential that causes an interaction (including repulsive force and attractive force) between the particle models 6 and 6 adjacent to each other via the bond model 7 is defined (step S13). As shown in FIG. 4, the potential includes the first potential P1 defined between the particle models 6 and 6 adjacent to each other via the bond model 7 and the particle models 6 and 6 adjacent to each other without the bond model 7. A second potential P2 defined in between is defined.

6A to 6C are partial views of the molecular chain model 5 for explaining the first potential P1. As shown in FIGS. 6A and 6B, the molecular chain model 5 has a bond distance (bond length) r which is a bond length between the particle models 6 and 6 and a bond model 7. A bond angle θ, which is an angle formed by three continuous particle models 6, is defined. Further, as shown in FIG. 6C, in the molecular chain model 5, one plane 8A formed by three adjacent particle models 6 in the four particle models 6 continuous via the bond model 7 and the other A dihedral angle φ that is an angle formed by the plane 8B of is defined. The bond distance r, the bond angle θ, and the dihedral angle φ change according to an external force or an internal force acting on the molecular chain model 5.

ここで、各定数及び変数は、次のとおりである。
ｒ：結合距離（結合長）
ｒ₀：平衡距離（平衡長）
ｋ₁、ｋ₂：ばね定数
θ：結合角
θ₀：平衡角度
ｋ₃：二面角ポテンシャルの強度
Ｎ−1：二面角ポテンシャル多項式の次数
φ：二面角
Ａ_n：二面角定数
なお、結合距離ｒ及び平衡距離ｒ₀は、各粒子モデル６の中心（図示省略）間の距離として定義される。 The bond distance r, the bond angle θ, and the dihedral angle φ are the bond potential U _bond (r) defined by the following formula (1), the bond angle potential U _angle (θ) defined by the following formula (2), and , _Is set by the bond dihedral angle potential U _torsion (φ) defined by the following equation (3).

Here, each constant and variable are as follows.
r: bond distance (bond length)
r ₀ : Equilibrium distance (equilibrium length)
k ₁ , k ₂ : spring constant θ: bond angle θ ₀ : equilibrium angle k ₃ : strength of dihedral potential N−1: order of dihedral potential polynomial φ: dihedral angle A _n : dihedral constant , The bond distance r and the equilibrium distance r ₀ are defined as the distance between the centers (not shown) of each particle model 6.

Each constant of each bond potential U _bond (r), bond angle potential U _angle (θ), and bond dihedral angle potential U _torsion (φ) can be appropriately set. Note that these potentials are preferably set according to the structure of the molecular chain Mc based on the paper (J. Phys. Chem. 94, 8897 (1990)).

ここで、各定数及び変数は、次のとおりである。
E：結合ポテンシャル（ボンドポテンシャル）
ForceC：平衡位置近傍の曲率
Dlim：結合解離エネルギーに相当
R：結合距離（結合長）
R_M：平衡距離（平衡長） The binding potential is not limited to the above formula (1). For example, the binding potential may be defined by a Morse type function defined by the following equation (4).

Here, each constant and variable are as follows.
E: Bond potential
ForceC: Curvature near the equilibrium position
Dlim: Equivalent to bond dissociation energy
R: Bond distance (bond length)
R _M : Equilibrium distance (equilibrium length)

In the above formula (4), each constant and variable can be set appropriately. By being defined by such a Morse type function, it is possible to prevent the bond potential from being calculated excessively large when the bond distance becomes large, so that the accuracy of simulation can be improved.

As described above, the second potential P2 is defined between the particle models 6 and 6 adjacent to each other without the bond model 7 interposed therebetween. The second potential P2 of the present embodiment is the LJ potential U _LJ (r _ij ) defined by the following equation (5).

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：粒子モデル間の距離
ε：粒子モデル間に定義されるＬＪポテンシャルの強度
σ：粒子モデルの直径に相当
なお、距離ｒ_ijは、各粒子モデル６、６の中心（図示省略）間の距離として定義される。

Here, each constant and variable are parameters of the Lennard-Jones potential, and are as follows.
r _ij : Distance between particle models ε: Strength of LJ potential defined between particle models σ: Corresponding to diameter of particle model Note that the distance r _ij is between the centers (not shown) of each particle model 6, 6. Defined as a distance.

In the second potential P2, the repulsive force acting between the particle models 6 increases as the distance r _ij between the particle models becomes smaller than σ. Further, the second potential P2 becomes minimum when the distance r _ij between the particle models becomes 2 ^1/6 σ, and no repulsive force or attractive force acts between the particle models 6 and 6. Furthermore, when the distance r _ij between the particle models becomes larger than 2 ^1/6 σ, the second potential P2 has an attractive force acting between the particle models 6 and 6. Thus, the second potential P2 can define the repulsive force and attractive force according to the distance r _ij between the particle models.

In the present embodiment, between the sulfur particle models 6S and 6S, between the carbon particle models 6C and 6C, between the carbon particle model 6C and the hydrogen particle model 6H, between the sulfur particle model 6S and the carbon particle model 6C, and sulfur Different second potentials P2 are set between the particle model 6S and the hydrogen particle model 6H. The constants of the above equation (5) are different for each second potential P2. In addition, each constant can be appropriately set based on, for example, a paper (J. Phys. Chem. 94, 8897 (1990)).

Next, in the simulation method of this embodiment, a polymer material model is defined in the computer 1 (step S2). FIG. 7 is a conceptual diagram of a polymer material model. The polymer material model 16 is defined on the computer 1, and is defined by arranging at least one molecular chain model 5 in a space (cell) 17 corresponding to a part of the polymer material.

The space 17 of the present embodiment is defined as a rectangular parallelepiped having three pairs of flat surfaces 17a and 17b facing each other. Periodic boundary conditions are defined in each of the planes 17a and 17b. Thereby, in the space 17, it can be calculated that, for example, a part of the molecular chain model 5 that has exited from the one plane 17a enters from the other plane 17b. Therefore, the one flat surface 17a and the opposite flat surface 17b can be treated as being continuous (connected).

The lengths L1, L2, L3 of one side of the space 17 can be set appropriately. The length L1 of this embodiment is preferably twice or more the radius of gyration (not shown) of the molecular chain model 5. The radius of gyration is an amount indicating the spread of the molecular chain model 5. In such a space 17, in the molecular dynamics calculation, the collision with the self image due to the periodic boundary condition is unlikely to occur, so that the spatial expansion of the molecular chain model 5 can be appropriately calculated. Further, the size of the space 17 is set to a stable volume at 1 atmospheric pressure, for example. Such space 17 can define the volume of at least a portion of the polymeric material. Further, the number of molecular chain models 5 arranged in the space 17 can be set appropriately. It is desirable that the number of the molecular chain models 5 of the present embodiment is set to, for example, 1 or more, preferably 30 or more.

In the present embodiment, relaxation calculation by molecular dynamics (MD) calculation is performed using the space 17 in which the molecular chain model 5 is arranged. Thereby, the polymer material model 16 is set.

In the molecular dynamics calculation of the present embodiment, for example, Newton's equation of motion is applied assuming that the molecular chain model 5 follows classical mechanics for a predetermined time in the space 17. Then, the movement of the particle model 6 at each time is tracked for each unit time step. Such structural relaxation calculation can be processed using, for example, COGNAC included in the soft material comprehensive simulator (OCTA).

In the molecular dynamics calculation, the pressure and temperature are kept constant, or the volume and temperature are kept constant in the space 17. Further, the molecular dynamics calculation is performed until it can be considered that the artificial initial arrangement of the molecular chain model 5 is sufficiently eliminated. Thus, in step S2, the initial movement of the molecular chain model 5 can be accurately relaxed by approximating the actual molecular motion of the polymer material. The polymer material model 16 is defined through such relaxation calculation. The polymer material model 16 is stored in the computer 1.

Next, in the simulation method of the present embodiment, the computer 1 calculates the breakage of the molecular chain model 5 based on a predetermined condition (cutting calculation step S3). In the cutting calculation step S3 of this embodiment, an extension simulation is performed in which the polymer material model 16 shown in FIG. 7 is extended in one axis direction (for example, the Z axis direction).

In the extension simulation of the present embodiment, the extension of the polymer material model 16 is calculated for each unit time step using molecular mechanics calculation (Molecular Mechanics: MM) and quantum mechanics calculation (Quantum Mechanics: QM). Then, by advancing the unit time step, the polymer material model 16 extended to a predetermined length (upper limit value) is calculated. By the extension of the polymer material model 16, the molecular chain model 5 is separated from the particle models 6, 6. The state in which the molecular chain model 5 is cut is calculated as the particle models 6 are separated from each other. Molecular mechanics calculations can be calculated by the above software similar to molecular dynamics calculations.

In the quantum mechanical calculation, it is assumed that the molecular chain model 5 follows the interaction based on the atomic nucleus and the electron, and the electronic state and movement of the particle model 6 are traced at each unit time step of the simulation. Therefore, the quantum mechanical calculation has higher calculation accuracy than the molecular mechanical calculation. Such quantum mechanical calculation can be processed using Gaussian03, which is a quantum chemical calculation program manufactured by Gaussian, or Gaussian09.

In the present embodiment, the elongation simulation is performed on the entire region of the polymer material model 16 by using molecular mechanics calculation. Then, the cutting of the molecular chain model 5 is calculated in detail by using quantum mechanical calculation only for the portion of the molecular chain model 5 that is likely to be cut between the particle models 6 and 6. Therefore, in the cutting calculation step S3 of the present embodiment, for example, the calculation time can be significantly shortened as compared with the case where the quantum mechanical calculation is performed on the entire region of the polymer material model 16. FIG. 8 is a flowchart showing an example of the processing procedure of the disconnection calculation step S3 of this embodiment.

In the cutting calculation step S3 of the present embodiment, first, initial conditions for carrying out the extension simulation of the polymer material model 16 are set (step S31). FIG. 9 is a side view for explaining the extension simulation of the polymer material model 16. As the initial conditions, the lengths L1, L2, and L3 of the polymer material model 16 at each unit time step are defined based on the Poisson's ratio of the polymer material model 16. As a result, in the cutting calculation step S3, it is possible to perform a simulation in which the polymer material model is elongated in one axis direction (for example, the Z axis direction) based on the Poisson's ratio of the polymer material model 16.

The uniaxial extension speed Va of the polymer material model 16 can be appropriately set according to the polymer material to be analyzed and the simulation conditions. The extension speed Va of this embodiment is set to, for example, 50 m/sec to 200 m/sec. Thereby, in the cutting calculation step S3 of the present embodiment, it is possible to calculate the state in which the polymer material is stretched at high speed. These initial conditions are stored in the computer 1.

Next, in the cutting calculation step S3 of the present embodiment, the bond potential Pn used in the molecular mechanics calculation is defined (bond potential defining step S32). The bond potential Pn (shown in FIG. 4) is defined between the particle models 6 and 6 adjacent to each other via the bond model 7 in the molecular chain model 5. As the bond potential Pn of this embodiment, a potential Pn that is close to the bond dissociation potential Pu (not shown) is defined. The bond dissociation potential Pu is a potential between the particle models 6 calculated by using quantum mechanical calculation. Since such a binding potential Pn approximates the potential in quantum mechanical calculation, the difference between the result of molecular mechanical calculation and the result of quantum mechanical calculation can be minimized.

The bond dissociation potential Pu (not shown) differs depending on the type of particle model 6 to be bonded. In the present embodiment, between the sulfur particle models 6S and 6S, between the carbon particle models 6C and 6C, between the carbon particle model 6C and the hydrogen particle model 6H, between the sulfur particle model 6S and the carbon particle model 6C, and sulfur Different bond dissociation potentials Pu are obtained between the particle model 6S and the hydrogen particle model 6H.

In the bond potential defining step S32 of this embodiment, the bond dissociation potential Pu is obtained by quantum mechanical calculation using a molecular model including a pair of particle models 6, 6. FIG. 10 is a flowchart showing an example of the processing procedure of the binding potential defining step S32 of this embodiment. FIG. 11 is a diagram showing a molecular model 11 used to determine the bond dissociation potential Pu.

In the binding potential defining step S32 of this embodiment, first, the molecular model 11 is set (step S321). For the molecular model 11, all combinations of the pair of particle models 6 and 6 in the molecular chain model 5 are set. In this embodiment, the sulfur particle models 6S and 6S are combined with the molecular model 11A, the carbon particle models 6C and 6C are combined with each other (not shown), and the carbon particle model 6C and the hydrogen particle model 6H are combined with each other ( (Not shown), a molecular model (not shown) in which the sulfur particle model 6S and the carbon particle model 6C are connected, and a molecular model (not shown) in which the sulfur particle model 6S and the hydrogen particle model 6H are connected are set. In FIG. 11, the molecular model 11A in which the sulfur particle models 6S and 6S are combined is representatively shown.

The molecular model 11 of the present embodiment includes a pair of particle models 6 and 6 (sulfur particle models 6S and 6S in the present embodiment) and a bond model 7 that connects the particle models 6 and 6. Each particle model 6 has a number of hydrogens obtained by subtracting the number of bonds (for example, 1) of the particle model 6 from the valence of the atom modeled by the particle model 6 (for example, in the case of sulfur atom: 2). The particle model 6H (for example, one) is connected via the bond model 7. Thereby, the molecular model 11 can maintain a stable structure in quantum mechanical calculation. Based on such a method, each of the above molecular models 11 is set. These molecular models 11 are stored in the computer 1.

Next, in the binding potential defining step S32 of the present embodiment, the theory and basis functions used for the quantum mechanical calculation are defined between the particle models 6, 6 of each molecular model 11 (step S322). As the theory defined in this embodiment, for example, the density functional method (functional: B3LYP) is defined. As the basis function, for example, a basis function (6-31G(d)) is defined. The theory and basis functions used for these quantum mechanical calculations can be defined by using the above-mentioned program for quantum mechanical calculations. These theories and basis functions are stored in the computer 1.

Next, in the bond potential defining step S32 of the present embodiment, the bond dissociation potential Pu between the particle models 6 and 6 is obtained by a simulation that performs quantum mechanical calculation using the molecular model 11 (step S323).

As shown in FIG. 11, in the molecular model 11, the equilibrium distance r ₀ of the particle models 6 and 6 is determined by the balance of the interaction based on the nucleus and the electron, based on the above theory and basis function. In step S323 of the present embodiment, for example, from the state where the particle models 6 and 6 are in contact with each other until the distance r between the particle models 6 and 6 becomes larger than the equilibrium distance r ₀ (for example, 4.5 Å). In the meantime, quantum mechanical calculation is performed in which the particle models 6 and 6 are separated by 0.1 Å for each unit step. In addition, in the quantum mechanical calculation of the present embodiment, the total energy of the molecular model 11 is calculated for each unit step based on the unrestricted density functional method. Then, the bond dissociation potential Pu can be obtained based on the relationship between the distance r between the particle models 6 and the total energy of the molecular model 11. FIG. 12 is a graph showing the bond dissociation potential Pu. The equilibrium distance r ₀ and the distance r are defined as the distance between the centers 6c, 6c (shown in FIG. 11) of the particle models 6, 6. Further, in FIG. 12, the potential energy is relative energy with the minimum energy being 0.

In the graph of FIG. 12, the bond dissociation potential Pu depends on the repulsive force between the particle models 6 and 6 as the distance r between the particle models 6 and 6 becomes smaller than the equilibrium distance r ₀ (2.1 in this embodiment). growing. Further, the bond dissociation potential Pu has the minimum energy when the distance r becomes 2.1, and no repulsive force or attractive force acts between the particle models 6 and 6. Furthermore, the bond dissociation potential Pu becomes larger due to the attractive force between the particle models 6 when the distance r becomes larger than the equilibrium distance r ₀ . Thus, the bond dissociation potential Pu can define repulsive force and attractive force according to the distance r.

The bond dissociation potential Pu has an inflection point 13 where the increment of the potential energy of the molecular model 11 becomes small in a region where the distance r between the particle models 6 is larger than the equilibrium distance r ₀ . The inflection point 13 is a pair of regions close to the bond dissociation potential Pu in the region where the distance r is expected to be larger than the inflection point 13 and the region where the distance r is expected to be smaller than the inflection point 13. It can be specified by the intersection of the straight lines 15a and 15b.

In the region Tb where the distance r is smaller than the inflection point 13, the increment of the potential energy of the molecular model 11 is larger than in the region Ta where the distance r between the particle models 6 and 6 is larger than the inflection point 13. This indicates that in the region Tb smaller than the inflection point 13, the bond between the particle models 6 is firmly maintained. Further, in the region Ta where the distance r is larger than the inflection point 13, the particle models 6 and 6 are broken or the bond order is decreased, and the increment of the potential energy of the molecular model 11 is small. Therefore, the inflection point 13 can be considered as the boundary between the bond and the dissociation between the particle models 6, 6.

In step S323, quantum mechanical calculation is performed for each of the above-described molecular models 11. Thereby, the bond dissociation potential Pu between the sulfur particle models 6S and 6S, the bond dissociation potential Pu between the carbon particle models 6C and 6C, the bond dissociation potential Pu between the carbon particle model 6C and the hydrogen particle model 6H, and the sulfur particle model The bond dissociation potential Pu between 6S and the carbon particle model 6C and the bond dissociation potential Pu between the sulfur particle model 6S and the hydrogen particle model 6H are obtained. Each bond dissociation potential Pu is stored in the computer 1.

Next, in the bond potential defining step S32 of the present embodiment, a potential (bond potential) Pn that approximates the bond dissociation potential Pu is obtained (step S324). FIG. 13 is a graph showing the bond dissociation potential Pu and the bond potential Pn. In step S324 of this embodiment, a harmonic oscillator-type function based on Hooke's law is approximated to the bond dissociation potential Pu. As a result, the coupling potential Pn is obtained. The harmonic oscillator type function is defined by the following equation (6).

ここで、
Ｖ：分子モデルのエネルギー
ｋ：バネ定数
ｒ：粒子モデル間の距離
ｒ₀：粒子モデル間の平衡距離

here,
V: Energy of molecular model k: Spring constant r: Distance between particle models r ₀ : Equilibrium distance between particle models

The harmonic oscillator type function of the above equation (6) is a quadratic function indicating the relationship between the distance r between the particle models 6 and 6 and the energy of the molecular model. In the present embodiment, in the region Tb (shown in FIG. 12) where the distance r is smaller than the inflection point 13, the harmonic oscillator type function is approximated to the bond dissociation potential Pu to obtain the bond potential Pn. .. Therefore, the bond potential Pn of the present embodiment is close to the bond dissociation potential Pu before the particle models 6 and 6 are broken or the bond order is reduced.

As a method of approximating the harmonic oscillator type function to the bond dissociation potential Pu, for example, the least square method can be used. With such a coupling potential Pn, the complex bond dissociation potential Pu can be expressed by a simple harmonic oscillator type function.

In step S324, in the range from the lower limit value of the energy of bond dissociation potential Pu (energy of molecular model 11) (that is, equilibrium distance r ₀ ) to 50% to 80% of the upper limit value of energy, a harmonic oscillator type It is desirable to approximate the function to the bond dissociation potential Pu. As a result, the bond potential Pn can be accurately approximated to the bond dissociation potential Pu in the region Tb (shown in FIG. 12) where the distance r ₀ is smaller than the inflection point 13.

In the range approximated to the harmonic oscillator type function, when the upper limit of the energy of the bond dissociation potential Pu exceeds 80%, the region Ta (shown in FIG. 12) having a distance larger than the inflection point 13 is included. , There is a risk of approximating a harmonic oscillator type function. On the contrary, when the energy of the bond dissociation potential Pu is less than 50% of the upper limit value, the range of approximation to the bond dissociation potential Pu becomes small, and the bond dissociation potential Pu may not be accurately approximated. From such a viewpoint, it is more preferably 70% or less of the upper limit value of the energy of the bond dissociation potential Pu, and more preferably 60% or more in the range approximated to the harmonic oscillator type function.

In step S324, the bond dissociation potential Pu between the sulfur particle models 6S and 6S, the bond dissociation potential Pu between the carbon particle models 6C and 6C, the bond dissociation potential Pu between the carbon particle model 6C and the hydrogen particle model 6H, and the sulfur particles The bond potential Pn is calculated for the bond dissociation potential Pu between the model 6S and the carbon particle model 6C and the bond dissociation potential Pu between the sulfur particle model 6S and the hydrogen particle model 6H.

In step S324, a bond potential Pn is defined between the particle models 6 and 6 adjacent to each other via the bond model 7 in the molecular chain model 5 shown in FIG. 4, instead of the first potential P1. In addition, in the single bond bond model 10A and the double bond bond model 10B, different bond potentials Pn are defined according to their bond strengths. The second potential P2 defined between the particle models 6 and 6 adjacent to each other without the bond model 7 is maintained.

Next, in the cutting calculation step S3 of the present embodiment, a deformation calculation for expanding the polymer material model 16 (shown in FIG. 7) is executed (expansion step S33). In this embodiment, the deformation of the polymer material model 16 is calculated based on the Poisson's ratio set as the initial condition.

In the stretching step S33, the polymer material model 16 stretched in the uniaxial direction is calculated at the current unit time step. By the extension of the polymer material model 16, the molecular chain model 5 shown in FIG. 7 is also uniaxially stretched, and the distance r (shown in FIG. 4) between the particle models 6 and 6 adjacent to each other via the bond model 7 At least part of it gets bigger.

Next, in the cutting calculation step S3 of the present embodiment, molecular mechanics calculation (Molecular Mechanics: MM) is performed based on the polymer material model 16 deformed in the extension step S33 (first molecular mechanics calculation step S34). .. In the first molecular dynamics calculation step S34, a physical quantity including the energy Ea of the polymer material model 16 and the force Fa acting on the polymer material model 16 is calculated. The physical quantity including the energy Ea and the force Fa is stored in the computer 1.

Next, in the cutting calculation step S3 of the present embodiment, for the molecular chain model 5 after the first molecular dynamics calculation step S34, the distance r between the particle models 6 and 6 adjacent to each other via the bond model 7 (shown in FIG. 4). ), it is determined whether or not there is a separated particle model unit 21 (not shown) that is larger than the first distance La set in advance (step S35).

In step S35, the distance r between the particle models 6 and 6 adjacent to each other through the bond model 7 is calculated for all the molecular chain models 5 arranged in the space 17. In step S35, the distance between the particle models 6 and 6 not constrained by the bond model 7 is not calculated. The distance r between the particle models 6 and 6 adjacent to each other via the bond model 7 is larger than the first distance La. The pair of particle models 6 and 6 (hereinafter, simply referred to as “first particle models 23A and 23A”). Is determined as the separated particle model unit 21 (not shown).

The first distance La of this embodiment is set to be smaller than the distance r(Ln) between the particle models 6 and 6 at the inflection point 13 of the bond dissociation potential Pu shown in FIG. Further, the first distance La is set to be larger than the equilibrium distance r ₀ of the particle models 6, 6. As described above, the inflection point 13 can be considered as a boundary point between coupling and dissociation between the particle models 6, 6. Therefore, it can be considered that the separated particle model unit 21 (not shown) in which the distance r is larger than the first distance La has a high possibility of cutting between the particle models 6, 6. Therefore, in step S35, it is possible to determine the presence/absence of the disengaged particle model portion 21 that is highly likely to be cut between the particle models 6, 6.

Further, the first distance La can be appropriately set as long as it is a value smaller than the distance r at the inflection point 13. In the present embodiment, as shown in FIG. 13, the distance r at the intersection 18 between the bond dissociation potential Pu and the bond potential Pn is obtained as the first distance La. This makes it possible to accurately determine the presence or absence of the dissociated particle model unit 21 based on the molecular mechanics calculation that can reduce the calculation time as compared with the quantum mechanics calculation.

When it is determined that the dissociated particle model unit 21 exists in step S35 (“Y” in step S35), the next quantum mechanical calculation step S36 is performed on the dissociated particle model unit 21. On the other hand, when it is determined that the separated particle model unit 21 does not exist (“N” in step S35), step S40 described below is performed.

Next, in the cutting calculation step S3 of the present embodiment, quantum mechanical calculation is performed on the first region 22 including the separated particle model unit 21 (quantum mechanical calculation step S36). FIG. 14 is a flowchart showing an example of the processing procedure of the quantum mechanical calculation step S36. FIG. 15 is a diagram showing the first region 22.

In the quantum mechanical calculation step S36 of the present embodiment, first, the first region 22 including the separated particle model unit 21 is set (step S361). The first region 22 is a non-whole region in which only the dissociated particle model portion 21 is extracted from the molecular chain model 5 (shown in FIG. 4) of the polymer material model 16. When the polymer material model 16 has a plurality of separated particle model parts 21, all the separated particle model parts 21 are included in the first region 22.

In addition, to each first particle model 23A of the separated particle model unit 21, from the valence of the atom modeled by the first particle model 23A (for example, in the case of carbon atom: 4), the first particle model 23A is bonded. The number of hydrogen particle models 6H (for example, 3) reduced by the number (for example, 1) is connected via the bond model 7. Thereby, the separated particle model unit 21 having a stable structure can be set in the quantum mechanical calculation.

Next, in the quantum mechanical calculation step S36 of the present embodiment, the theory and basis functions used for the quantum mechanical calculation are defined in the particle model 6 of the separated particle model unit 21 (step S362). In step S362, the binding potential Pn (shown in FIG. 4) set between the first particle models 23A and 23A of the separated particle model unit 21 is invalidated, and the theory and basis functions used for the quantum mechanical calculation are defined. It The theory and basis functions used for the quantum mechanical calculation are as described above.

Next, in the quantum mechanical calculation step S36 of the present embodiment, the quantum mechanical calculation is performed on the first region 22 (shown in FIG. 15) (step S363). As described above, in the quantum mechanical calculation, the electronic state and the movement of the particle model 6 are traced for each unit time step of the simulation, assuming that the interaction is based on the nucleus and the electron. Therefore, in step S363, the extension of the separated particle model unit 21 (that is, between the pair of first particle models 23A and 23A) can be calculated with higher accuracy than in the molecular dynamics calculation. In step S363, the quantum mechanical calculation is performed only on the first region 22 extracted from the polymer material model 16. Therefore, the calculation time can be significantly shortened as compared with the case where the quantum mechanical calculation is performed on the entire region of the polymer material model 16 shown in FIG. 7.

In step S363, a physical quantity including the energy Ec of the first region 22 and the force Fc acting on the first region 22 is calculated. The physical quantity including the energy Ec and the force Fc is stored in the computer 1.

Next, in the cutting calculation step S3 of the present embodiment, molecular mechanics calculation is performed on the first region 22 (second molecular mechanics calculation step S37). As shown in FIG. 15, the first region 22 is a non-whole region in which only the dissociated particle model portion 21 is extracted from the molecular chain model 5 of the polymer material model 16 deformed in the extension step S33. Therefore, in the second molecular mechanics calculation step S37, a physical quantity including the energy Eb of the first region 22 and the force Fb acting on the first region 22 is calculated. The physical quantity including the energy Eb and the force Fb is used to obtain the energy Et of the polymer material model 16 and the force Ft acting on the polymer material model 16 according to the ONIOM method described later. A physical quantity including energy Eb and force Fb is stored in the computer 1. In the second molecular dynamics calculation step S37, the bond potential Pn is set between the particle models 6 and 6 of the separated particle model unit 21.

Next, in the cutting calculation step S3 of the present embodiment, the energy Et of the polymer material model 16 is calculated (step S38). The energy Et of this embodiment is calculated based on the following equation (7) according to the ONIOM (Owner N-layered Integrated molecular Orbital and molecular Mechanics) method.
Et=Ea-Eb+Ec (7)
here,
Ea: Energy of the polymer material model obtained in the first molecular mechanics calculation step Eb: Energy of the first region obtained in the second molecular mechanics calculation step Ec: Energy of the first region obtained in the quantum mechanics calculation step

In the above formula (7), the energy Ea obtained in the first molecular dynamics calculation step S34 is the energy of the entire region of the polymer material model 16. Further, the energy Eb obtained in the second molecular mechanics calculation step S37 is the energy in the first region 22. Since these energies Ea and Eb are obtained by molecular mechanics calculation, the calculation accuracy is lower than that of quantum mechanics calculation. The energy Ec obtained in the quantum mechanical calculation step S36 is the energy of the first region 22. Since this energy Ec is obtained by quantum mechanical calculation, the calculation accuracy is higher than that of molecular mechanical calculation.

The ONIOM method is a method of obtaining an optimum solution by combining hierarchical structures having different calculation accuracy. In the present embodiment, of the energy Ea of the polymer material model whose calculation accuracy is relatively low, the energy Eb of the first region is replaced with the energy Ec of the first region whose calculation accuracy is relatively high, so that the polymer material model The energy Et of 16 is sought. Since such an energy Et can take into account the influence of the cleavage of the molecular chain model 5 in detail, the calculation accuracy can be improved. Further, in the present embodiment, for example, the energy Et of the polymer material model 16 can be obtained without obtaining the energy of the entire region of the polymer material model 16 based on the quantum mechanical calculation, so that the calculation time is shortened. be able to. The energy Et is stored in the computer 1.

Next, in the cutting calculation step S3 of the present embodiment, the force Ft acting on the polymer material model 16 is calculated (step S39). The force Ft of the present embodiment is calculated based on the following equation (8) according to the ONIOM method, similarly to the energy Et of the polymer material model.
Ft=Fa−Fb+Fc (8)
here,
Fa: Force acting on the polymer material model obtained in the first molecular mechanics calculation step Fb: Force acting on the first region obtained in the second molecular mechanics calculation step Fc: No. determined in the quantum mechanics calculation step Force acting on one area

In the present embodiment, among the forces Fa of the polymer material model 16 having relatively low calculation accuracy, the force Fb of the first region 22 is replaced with the force Fc of the first region having relatively high calculation accuracy, so that the polymer The force Ft of the material model 16 is calculated. Since such force Ft can consider in detail the influence of the breakage of the molecular chain model 5, the calculation accuracy can be improved. Further, in the present embodiment, it is not necessary to calculate the force acting on the entire region of the polymer material model 16 based on the quantum mechanical calculation, so that the calculation time can be shortened. This force Ft is stored in the computer 1.

Next, in the cutting calculation step S3 of the present embodiment, the coordinate value and velocity of each particle model 6 of the molecular chain model 5 are updated at the current unit time step (step S40). In this embodiment, the acceleration is calculated from the energy Et and the force Ft calculated by the ONIOM method. Then, from the acceleration obtained from the energy Et and the force Ft and the coordinate value of each particle model 6 of the molecular chain model 5, a new coordinate value of each particle model 6 (that is, the coordinate value used in the next unit time step). ) Is calculated.

Since the coordinate value of each particle model 6 includes the coordinate value obtained by the quantum mechanical calculation of the first region 22 that is highly likely to be cut, the cutting of the molecular chain model 5 can be accurately analyzed. it can. In addition, for a portion that is unlikely to be cut, a relatively low-precision molecular dynamics calculation is performed, so that the calculation time can be shortened.

In the present embodiment, a bond potential Pn that is close to the bond dissociation potential Pu is defined in the first molecular mechanics calculation step S34 and the second molecular mechanics calculation step S37. Therefore, it is possible to minimize the difference between the force acting on each particle model 6 after the second molecular mechanics calculation step S37 and the force acting on each particle model 6 after the quantum mechanics calculation step S36. it can. Therefore, the calculation accuracy of the coordinate value based on the ONIOM method can be improved. The velocity of each particle model 6 is calculated based on the coordinate value of each particle model 6 of the molecular chain model 5, the energy Et of the polymer material model 16, and the force Ft acting on the polymer material model 16. ..

If it is determined in step S35 described above that the dissociated particle model unit 21 does not exist (“N” in step S35), quantum mechanical calculation (step S36) and molecular mechanics for the first region 22 are performed. Calculation (step S37) has not been performed. In this case, in step S40, the coordinate values of the particle model 6 obtained by the molecular mechanics calculation for the polymer material model 16, the energy Ea obtained in the first molecular mechanics calculation step, and the first molecular mechanics calculation The coordinate value and the velocity are updated from the force Fa obtained in the process.

Next, in the cutting calculation step S3 of the present embodiment, after the quantum mechanical calculation step S36, and in the present embodiment, the first region 22 after the quantum mechanical calculation step S36 and the second molecular mechanical calculation step S37, the first particle model 23A , 23A is larger than the predetermined second distance Lb, it is determined whether or not there is a separated particle model unit 21 (step S41). In step S41, based on the coordinate values of each particle model 6 of the molecular chain model 5 updated in step S40, the first particle model 23A, for all the separated particle model portions 21 arranged in the first region 22, The distance r between 23A is calculated.

The second distance Lb in the present embodiment is defined based on the distance Ln between the particle models 6 and 6 at the inflection point 13 of the bond dissociation potential Pu shown in FIG. The second distance Lb of the present embodiment is set larger than the first distance La. Further, the second distance Lb is set to be not less than the distance Ln between the particle models at the inflection point 13.

As described above, the inflection point 13 can be considered as a boundary point between coupling and dissociation between the particle models 6, 6. Therefore, when the distance r between the first particle models 23A and 23A is larger than the second distance Lb, it can be determined that the first particle models 23A and 23A are cut. Therefore, in step S41, it is determined whether or not the distance r between the first particle models 23A and 23A is larger than the second distance Lb, and thus the separated particle model cut between the first particle models 23A and 23A. The presence or absence of the part 21 can be determined. In order to accurately determine the separated particle model unit 21 that is cut between the first particle models 23A and 23A, the second distance Lb is larger than the distance Ln between the particle models 6 and 6 at the inflection point 13. A large value (that is, greater than 100% of the distance Ln at the inflection point 13) is desirable.

When the second distance Lb is small, the difference between the energy of the first region obtained by the quantum mechanical calculation and the energy of the first region obtained by the molecular mechanical calculation between the cut first particle models 23A, 23A. Becomes larger and the calculation is more likely to end abnormally. Therefore, the second distance Lb is preferably set to a value obtained by adding 1.0 to 2.5Å to the distance Ln between the particle models 6 at the inflection point 13.

In step S41, when it is determined that the separated particle model portion 21 in which the distance r between the first particle models 23A and 23A is the second distance Lb or more exists (“Y” in step S41), the next cutting step S42 is performed. Be implemented. On the other hand, when it is determined that the distance between the first particle models 23A and 23A is less than the second distance Lb in all the separated particle model units 21 (“N” in step S41), the polymer material model 16 is A step S43, which will be described later, is executed to determine whether or not the extension has reached the predetermined condition.

Next, in the cutting calculation step S3 of the present embodiment, the particle models 6, 6 are cut (cutting step S42). In the cutting step S42, molecules corresponding to the first particle models 23A and 23A of the separated particle model unit 21 to be cut (that is, the first particle models 23A and 23A determined to have the distance r equal to or greater than the second distance Lb). Regarding the particle models 6 and 6 of the chain model 5 (shown in FIG. 4), the definition of the bond model 7 between the particle models 6 and 6 is invalidated. Further, the bond potential Pn defined between the cut particle models 6 and 6 is invalidated, and the second potential P2 defined between the particle models 6 and 6 adjacent to each other without the bond model 7 is defined. It This defines a break between the particle models 6 and 6 of the molecular chain model 5.

As described above, in the simulation method according to the present embodiment, the particle models 6 and 6 are generated for the first region 22 including the dissociated particle model unit 21 based on the result of the quantum mechanical calculation with higher calculation accuracy than the molecular mechanical calculation. The gap is cut off. Therefore, in the present embodiment, the cleavage of the molecular chain model 5 can be approximated to the actual cleavage of the molecular chain, which is useful for analyzing the polymer material with high accuracy.

Further, the presence/absence of the dissociated particle model unit 21 in which the quantum mechanical calculation is performed is determined in step S35 based on the result of the molecular mechanics calculation that requires a shorter calculation time than the quantum mechanics calculation. Therefore, it is not necessary to perform the quantum mechanical calculation for the entire area of the polymer material model 16. Therefore, the simulation method of the present embodiment can reduce the calculation time.

In the cut particle models 6 and 6, for example, from the valence of atoms modeled by the particle model 6 (for example, in the case of sulfur atom: 2), the number of bonds of the particle model 6 (for example, 1) The number of hydrogen particle models 6H (for example, one) reduced by is connected via the bond model 7. Thereby, the molecular chain model 5 can maintain a stable structure.

Next, in the cutting calculation step S3 of the present embodiment, it is determined whether or not the polymer material model 16 has expanded to a predetermined condition (step S43). In step S43, when it is determined that the polymer material model 16 has expanded to the upper limit value (“Y” in step S43), the next step S4 is performed. On the other hand, when it is determined that the polymer material model 16 has not expanded to the upper limit value (“N” in step S43), the unit time step is advanced by one (step S44), and steps S33 to S43. Will be carried out again. Thereby, in the cutting calculation step S3, the polymer material model can be extended to the upper limit value and the cutting of the molecular chain model 5 can be analyzed.

Next, in the simulation method of this embodiment, it is determined whether the physical quantity of the polymer material model 16 is within the allowable range (step S4). In this step S4, when it is determined that the physical quantity of the polymer material model 16 is within the allowable range (“Y” in step S4), the polymer material is manufactured based on the polymer material model 16 ( Step S5). On the other hand, when the physical quantity of the polymer material model 16 is determined to be outside the allowable range (“N” in step S4), the conditions of the molecular chain model 5 are changed (step S6), and steps S1 to S1 S4 is performed again. As described above, in the present embodiment, various conditions of the molecular chain model 5 are changed until the physical quantity of the polymer material model 16 falls within an allowable range, so that a polymer material having desired performance can be efficiently designed. can do.

As shown in FIG. 15, the first region 22 of the above-described embodiments includes the pair of first particle models 23A and 23A that are adjacent to each other through the bond model 7 among the particle models 6 that form the molecular chain model 5. Although the embodiment including the separated particle model unit 21 configured by is illustrated, the invention is not limited to such an embodiment. FIG. 16A is a conceptual diagram showing a part of the molecular chain model 5. FIG. 16B is a partial view of the first region 22 according to still another embodiment of the present invention. In addition, in this embodiment, the same components as those in the previous embodiment are denoted by the same reference numerals, and description thereof may be omitted.

The first region 22 includes at least one second particle model 23B adjacent to the first particle model 23A via the bond model 7. Further, the first region 22 further includes at least one third particle model 23C adjacent to the second particle model 23B via the bond model 7.

When the molecular chain 2A shown in FIG. 2 has a double bond in the vicinity of the atom to be cleaved (radical generated by the cleavage), it is known that the bond dissociation energy is reduced by resonance stabilization with the double bond. Has been. In order to consider such a resonance stable structure of radicals, as shown in FIG. 16A, the bond model 7 between the first particle model 23A and the second particle model 23B is a single bond bond model 10A. And the bond model 7 between the second particle model 23B and the third particle model 23C is preferably defined as the double bond bond model 10B.

In the quantum mechanical calculation (step S363) for the first region 22 as described above, not only the first particle model 23A of the molecular chain model 5 but also the first particle The influence of the second particle model 23B and the third particle model 23C adjacent to the model 23A can be considered.

The decrease in bond dissociation energy as described above is likely to occur when the bond between the carbon atom and the sulfur atom is broken or when the bond between the carbon atoms of unsaturated hydrocarbon such as rubber is broken. Therefore, when the pair of first particle models 23A and 23A is composed of the sulfur particle model 6S and the carbon particle model 6C, or when it is composed of the pair of carbon particle models 6C and 6C, the second particle model The bond model 7 between 23B and the third particle model 23C preferably includes a double bond bond model 10B. Thereby, the extension of the separated particle model unit 21 (that is, between the pair of first particle models 23A and 23A) can be calculated with higher accuracy.

In the present embodiment, all the third particle models 23C (in the present embodiment, the carbon particle model 6C and the hydrogen particle model 6H are included), as shown in a region 26 surrounded by a two-dot chain line in FIG. 16A. Is preferably included in the first region 22. This makes it possible to consider the effect that the radicals generated at the time of disengagement delocalize among the first particle model 23A, the second particle model 23B, and the third particle model 23C. Can be calculated with high accuracy. In addition, in the third particle model 23C, the number of hydrogen particle models 6H obtained by subtracting the number of bonds of the third particle model 23C from the valence of the atoms modeled in the third particle model 23C, via the bond model 7. It is desirable that they are connected together. Thereby, a stable structure can be maintained in the quantum mechanical calculation.

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

[Example A]
According to the procedure shown in FIGS. 3 and 5, a molecular chain model and a polymer model were defined, and a cutting step of cutting the molecular chain model was performed (Example 1, Comparative Example).

In the cutting step of Example 1, the step of performing molecular mechanics calculation based on the polymer material model according to the processing procedure shown in FIGS. 8, 10 and 14, the distance between the particle models is larger than the first distance La. A step of performing quantum mechanics calculation and a step of performing molecular mechanics calculation for the first area are performed on the first region including the dissociated particle model unit, and based on the above equations (7) and (8). , The energy Et of the polymer material model and the force Ft acting on the polymer material model were calculated.

In the step of performing the molecular mechanics calculation, a bond potential approximate to the bond dissociation potential was defined between the particle models of the molecular chain model. Further, in the cutting step of Example 1, the step of cutting between the particle models was performed when the distance between the particle models was larger than the second distance Lb.

In the cutting step of the comparative example, quantum mechanical calculation was performed for the entire region of the polymer material model, and the cutting of the molecular chain model was calculated according to the distance between the particle models. The potential set between the particle models is as described in the specification. The common specifications are as follows.
Computer: SGI workstation
Number of CPU cores: 12 cores
On-board memory: 64GB
Polymer model:
One side length L1: 2.3 nm
Number of molecular chain models: 1 Molecular chain model:
Crosslink sulfur (1 atom) to polyisoprene (isoprene molecule: 100 polymerization)
Number of particle models (atoms): 1301 Distance at inflection point Ln: 3.09Å
First distance La: 2.69Å
Second distance Lb: 3.35Å
Elongation simulation:
Extension direction: Uniaxial direction (Z-axis direction)
Extension speed Va: 250 m/sec
First region: disjointed particle model section (a pair of first particle models)

FIG. 17 is a graph showing the relationship between the number of cuts between the particle models of Example 1 and the elongation rate of the polymer material model. As shown in FIG. 17, in Example 1, it was possible to show a state in which the number of cuts between the particle models increased as the polymer material model extended. In Example 1, the cleavage rate of the C—S bond was calculated at an extension rate of about 300%, and the cleavage rate of the C—C bond was calculated at an extension rate of about 560%. As described above, in Example 1, the elongation rate at which the cutting starts could be calculated for each particle model.

FIG. 18 is a graph showing the relationship between the stress of the polymer material of Example 1 and the elongation rate of the polymer material model. As shown in FIG. 18, the stress sharply increases from the elongation rate of about 500%, but the stress sharply decreases from the elongation rate of about 600%. This is because the breakage of the C—C bond reduced the stress.

As described above, in Example 1, since the breakage of the molecular chain model could be calculated accurately by the extension simulation using the polymer material model, the polymer material could be analyzed accurately. In Example 1, the quantum mechanical calculation was performed only for the first region including the dissociated particle model portion that is likely to be cut between particle models, so that the calculation time could be shortened.

On the other hand, in the comparative example, the quantum mechanical calculation is performed for the entire region of the polymer material model, so that it is practically impossible to perform the deformation simulation similar to that in Example 1 with the processing capacity of the computer. It is believed that there is. Therefore, in the comparative example, the cleavage of the molecular chain model could not be calculated.

[Example B]
In the same procedure as in Example 1 of Example A, a molecular chain model and a polymer model were defined, and a cutting step of cutting the molecular chain model was performed (Examples 2 to 4).

The first region of the second embodiment includes only the separated particle model unit (a pair of first particle models). The first region of Example 3 includes a pair of first particle model and second particle model. The first region of Example 4 includes a pair of first particle model, second particle model, and third particle model.

Then, for the molecular chain models of Examples 2 to 4, bond dissociation energy when the bond between the carbon particle model and the sulfur particle model was broken was obtained. The common specifications are the same as in Example A, and the results are shown in Table 1.

According to the literature (Shigeru Ootsu, “Organic Sulfur Chemistry (Reaction Mechanism Edition)”, Kagaku Dojin, September 1982, p.3), the bond dissociation energy of C—S in CH ₃ ═CH═CH ₂ —SH. Is stated to be 52 kcal/mol. Therefore, in Example 3 including the first particle model and the second particle model, and Example 4 further including the third particle model, the C of the above document is more than that in Example 2 including the first particle model in the first region. It is close to the bond dissociation energy of -S. Therefore, the larger the number of particle models included in the first region, the closer the bond energy to the actual bond dissociation energy, and the more accurate the analysis of the polymer material.

[Example C]
In the same procedure as in Example 1 of Example A, a molecular chain model and a polymer model were defined, and a cutting step of cutting the molecular chain model was carried out (Examples 5 and 6).

The first region of Example 5 includes a second particle model and a third particle model that form a structure (C=C double bond, sulfur atom, etc.) in which radicals generated by molecular chain scission can be resonance-stabilized. ing.
The first region of Example 6 further includes not only the first particle model to the third particle model of Example 5, but also the fourth particle model.

Then, for the molecular chain models of Examples 5 and 6, bond dissociation energy when the bond between the pair of carbon particle models was broken was obtained. The common specifications are the same as in Example A, and the results are shown in Table 1 above.

The generally known bond dissociation energy of C—C is 70 kcal/mol. Therefore, Example 5 and Example 6 approximated the bond dissociation energy of C—C in the above document. Further, since the first region of Example 5 is limited to the first particle model to the third particle model, the calculation accuracy is maintained as compared with Example 6 including the first particle model to the fourth particle model. , The calculation time could be shortened significantly.

2 Polymer Material 2A Molecular Chain 5 Molecular Chain Model 6 Particle Model 7 Bond Model 16 Polymer Material Model 17 Space 21 Separated Particle Model Section

Claims (12)

A simulation method for analyzing the breakage of a molecular chain of a polymer material by using a computer,
A plurality of particle models based on the molecular chains, and a molecular chain model including a bond model that bonds between the particle models is defined in the computer,
In a space defined on the computer, a step of defining a polymer material model in which at least one of the molecular chain models is arranged, and the computer cuts the molecular chain model based on a predetermined condition. Including a cutting calculation step to calculate,
The cutting calculation step, a first molecular dynamics calculation step of performing a molecular dynamics calculation based on the polymer material model;
In the molecular chain model after the first molecular dynamics calculation step, whether or not there is a dissociated particle model part in which the distance between the particle models adjacent to each other via the bond model is larger than a predetermined first distance. And a step of determining
When it is determined that the dissociated particle model unit exists, a quantum mechanical calculation step of performing quantum mechanical calculation for a first region that is a non-whole region including the dissociated particle model unit,
The first region after the quantum mechanical calculation step, when the distance between the particle models is larger than a predetermined second distance, a step of cutting between them is included. Simulation method for molecular materials. The method for simulating a polymer material according to claim 1, wherein a potential close to a bond dissociation potential is defined as a bond potential between the particle models in the molecular dynamics calculation. The bond potential in the molecular mechanics calculation is defined by a function approximating to the bond dissociation potential in a range from the lower limit value of the energy of the bond dissociation potential to 50% to 80% of the upper limit value of the energy. The method for simulating a polymer material according to claim 2. The method for simulating a polymer material according to claim 2, wherein the bond dissociation potential is obtained by quantum mechanical calculation. The polymer material simulation method according to claim 1, wherein the first distance is smaller than the second distance. The polymer material simulation according to any one of claims 1 to 5, wherein the second distance is defined based on a distance between particle models at an inflection point at which an energy increment becomes small for a bond dissociation potential. Method. The polymer material simulation method according to claim 1, wherein the cutting calculation step further includes a second molecular dynamics calculation step of performing a molecular dynamics calculation on the first region. The cutting calculation step includes a step of calculating a physical quantity including the energy Et of the polymer material model,
The method for simulating a polymer material according to claim 7, wherein the energy Et is calculated based on the following equation.
Et=Ea-Eb+Ec
here,
Ea: Energy of the polymer material model obtained in the first molecular mechanics calculation step Eb: Energy of the first region obtained in the second molecular mechanics calculation step Ec: Energy of the first region obtained in the quantum mechanics calculation step The cutting calculation step includes a step of calculating a physical quantity including a force Ft acting on the polymer material model,
The method for simulating a polymer material according to claim 8, wherein the force Ft is calculated based on the following formula.
Ft=Fa−Fb+Fc
here,
Fa: Force acting on the polymer material model obtained in the first molecular mechanics calculation step Fb: Force acting on the first region obtained in the second molecular mechanics calculation step Fc: No. determined in the quantum mechanics calculation step Force acting on one area The separated particle model unit includes a pair of first particle models adjacent to each other via the bond model,
The method for simulating a polymer material according to claim 1, wherein the first region further includes at least one second particle model adjacent to the first particle model via the bond model. The method for simulating a polymer material according to claim 10, wherein the first region further includes at least one third particle model adjacent to the second particle model via the bond model. The bond model between the first particle model and the second particle model includes a single bond bond model that defines a single bond between a pair of atoms constituting the molecular chain,
The bond model between the second particle model and the third particle model includes a double bond bond model that defines a double bond between a pair of atoms forming the molecular chain. Simulation method for polymer materials.

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