JP2018151212A - Simulation method of high polymer material - Google Patents

Abstract

PROBLEM TO BE SOLVED: To specify an interface layer formed around a filler in the system where the filler and the high polymer material coexist.SOLUTION: A method analyzes a reaction between a high polymer material and filler using a computer 1. This method includes: a step S3 of arranging a coarse graining model 2 and a filler model 6 inside a predetermined space 8 so as to set a high polymer material model 10; a step S4 of calculating a structural relaxation of the high polymer material model 10 based on predetermined conditions; a calculation step S6 of obtaining an orientation parameter indicating an arrangement state of each bond 4 by deforming the high polymer material 10 by the predetermined distortion after the calculation of the structural relaxation; and an interface specifying step S8 for specifying an interface layer of the high polymer material formed around the filler based on an orientation parameter. A repulsive potential P2 to become a finite value is defined in coarse graining particles 3, 3 between adjacent coarse graining models 2, 2 even if a distance between the coarse graining particles 3, 3 converges to 0.SELECTED DRAWING: Figure 3

Description

  The present invention relates to a simulation method for a polymer material that can identify an interface layer formed around a filler in a system in which a filler and a polymer material coexist.

  In recent years, various simulation methods for polymer materials using computers have been proposed for the design and development of polymer materials such as rubber (see, for example, Patent Document 1 below). In this type of simulation method, various conditions such as the structure of the polymer material and the blending ratio of the filler can be incorporated into the calculation. Therefore, in this simulation method, the physical property value can be calculated without actually making a prototype of the polymer material.

JP 2012-238168 A

  Incidentally, it has been found that in a system in which a filler and a polymer material coexist, an interface layer is formed around the filler. This interface layer is known to exhibit mechanical properties different from the original part of the polymer material (hereinafter referred to as “bulk part”), and is sometimes referred to as “glass layer”.

  Even in the conventional simulation method, the interface layer is defined prior to calculating the physical property value of the polymer material. However, the conventional simulation method has a problem that much time and cost are required because the interface layer is defined based on, for example, the experimental results using a polymer material and a filler. Therefore, there has been a strong demand for a simulation method of a polymer material that can quantitatively specify the interface layer.

  The present invention has been devised in view of the actual situation as described above, and in a system in which a filler and a polymer material coexist, a simulation of a polymer material that can identify an interface layer formed around the filler The main purpose is to provide a method.

  The present invention is a method for analyzing a reaction between a polymer material and a filler using a computer, wherein the polymer chain of the polymer material includes a plurality of coarse-grained particles, A step of setting a coarse-grained model modeled using a bond that bonds between coarse-grained particles, a step of setting a filler model in which the filler is modeled with filler particles in the computer, and the computer A step of arranging a coarse-grained model and the filler model in a predetermined space to set a polymer material model, wherein the computer performs structural relaxation of the polymer material model based on a predetermined condition; After calculating the structural relaxation, the computer deforms the polymer material model with a predetermined strain to represent the arrangement state of the bonds. A calculation step for determining an orientation parameter; based on the orientation parameter, the computer identifies an interfacial layer of the polymeric material formed around the filler and exhibiting mechanical properties different from the bulk portion of the polymeric material A repulsive potential that is defined as a finite value even when the distance between the coarse-grained particles converges to 0 is defined between the coarse-grained particles of adjacent coarse-grained models. It is characterized by.

  In the simulation method of the polymer material according to the present invention, the calculating step includes a step of dividing the space in which the coarse-grained model is arranged into a plurality of regions at a boundary surface along an outer surface of the filler model. Preferably, the method includes a step of deforming the polymer material model with the strain and a step of calculating the orientation parameter for each region.

  In the simulation method of the polymer material according to the present invention, the interface specifying step responds to the step of obtaining an average of the orientation parameters for each region, and the average of the orientation parameters in phase with respect to the strain. Preferably, the method includes decomposing into a storage component and a dissipative component that responds to the strain at a different phase, and determining a region where the storage component is larger than the dissipative component as the interface layer.

ここで、各定数及び変数は次のとおりである。
ｉ：各ボンドのインデックス
ｍ：各領域のインデックス
ｔ：時刻
θ_i：ボンドベクトルｕ_i（ｍ，ｔ）と重心ベクトルｎ_i（ｍ，ｔ）とがなす角度 In the simulation method of the polymer material according to the present invention, the orientation parameter χ _i (m, t) includes a bond vector u _i (m, t) along the bond, a center of gravity of the bond, and a filler model. It is desirable to be defined by the following equation (1) based on the centroid vector n _i (m, t) connecting the centroid.

Here, each constant and variable are as follows.
i: Index of each bond m: Index of each region t: Time θ _i : Angle formed by bond vector u _i (m, t) and centroid vector n _i (m, t)

ここで、各定数及び変数は次のとおりである。
ｉ：各ボンドのインデックス
ｍ：各領域のインデックス
ｔ：時刻
Ｎ：各領域に配置されるボンドの総数
γ₀：歪振幅
ω：角速度 In the simulation method of the polymer material according to the present invention, the average Χ (m, t) of the orientation parameters is defined by the following formula (2), the strain γ is defined by the following formula (3), The orientation parameter average Χ (m, t) is preferably decomposed into the storage component Χ ′ and the dissipative component Χ ″ based on the following equation (4).

Here, each constant and variable are as follows.
i: Index of each bond m: Index of each region t: Time N: Total number of bonds arranged in each region γ ₀ : Strain amplitude ω: Angular velocity

  In the simulation method for the polymer material according to the present invention, it is preferable that 100 or more bonds are arranged in each region.

ここで、各定数及び変数は、次のとおりである。
ａ_ij：粗視化粒子間に作用する斥力の強度に対応する定数
ｒ_ij：粗視化粒子間の距離
ｒ_c：カットオフ距離 In the simulation method of the polymer material according to the present invention, it is preferable that the repulsive potential is defined by the following formula (5).

Here, each constant and variable are as follows.
a _ij : Constant corresponding to the strength of repulsive force acting between coarse-grained particles r _ij : Distance between coarse-grained particles r _c : Cut-off distance

  In the polymer material simulation method of the present invention, the computer deforms the polymer material model with a predetermined strain to obtain an orientation parameter representing the alignment state of each bond, and based on the orientation parameter, An interface specifying step for specifying the interface layer of the polymer material is included.

  In general, in an interface layer of a polymer material, since a polymer chain is constrained by a filler, there is a tendency that the polymer chain is not easily deformed compared to a bulk portion in which the polymer chain is not constrained by a filler. In the present invention, paying attention to such a tendency, bond orientation parameters correlated with deformation of the polymer material model are used. In the present invention, the interface layer of the polymer material is specified based on the orientation parameter. Therefore, in the present invention, the interface layer of the polymer material can be specified without performing an experiment using the polymer material.

  Furthermore, in the present invention, a repulsive potential that is a finite value is defined between the coarse-grained particles of the adjacent coarse-grained models even when the distance between the coarse-grained particles converges to zero. Such repulsive potential can prevent the repulsive force from becoming infinitely large due to entanglement between adjacent coarse-grained models, so that the structural relaxation and deformation of the polymer material model can be calculated stably in a short time. can do. Therefore, in the simulation method of the present invention, the interface layer of the polymer material can be specified reliably.

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 flowchart which shows an example of the process sequence of the calculation method of this embodiment. It is a conceptual diagram of a coarse-grained model. It is a conceptual diagram explaining the potential of a coarse-grained model and a filler model. It is a conceptual diagram of a polymer material model. It is a flowchart which shows an example of the process sequence of the calculation process of this embodiment. It is a conceptual diagram of the area | region where the space was divided. It is an enlarged view of FIG. FIG. 5 is a diagram of a polymeric material including an interface layer and a bulk portion. It is a flowchart which shows an example of the process sequence of the interface specific process of this embodiment. It is a graph which shows the relationship of the distance from the outer surface of a filler model to the boundary surface of each area | region, and the storage component Χ 'and the dissipation component Χ "of an area | region. It is a conceptual diagram of an interface layer, a bulk part, and those boundaries.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
The simulation method of the polymer material of the present embodiment (hereinafter, simply referred to as “simulation method”) is a method for analyzing the reaction between the polymer material and the filler using a computer.

  As shown in FIG. 1, 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, 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, and elastomer. In the present embodiment, as shown in FIG. 2, cis-1,4 polyisoprene (hereinafter sometimes simply referred to as “polyisoprene”) is exemplified as the polymer material. Polymer chain constituting the polyisoprene is methine group (-CH =,> C =) , methylene group _(-CH 2 -), and a monomer isoprene constituted by a methyl group (-CH ₃₎ ( Isoprene molecules) 5 are connected with a polymerization degree n. As the polymer material, a polymer material other than polyisoprene may be used. Moreover, as a filler, carbon black, a silica, or an alumina is contained, for example.

  FIG. 3 shows a specific processing procedure of the simulation method of the present embodiment. In the simulation method of the present embodiment, first, a coarse-grained model that models a polymer chain of a polymer material is set in the computer 1 (step S1). As shown in FIG. 4, the coarse-grained model 2 includes a plurality of coarse-grained particles 3 and a bond 4 that couples the coarse-grained particles 3 and 3.

  As shown in FIG. 2 and FIG. 4, when the polymer chain of the polymer material is polyisoprene, for example, 12 monomers are defined as the structural unit 5, and the structural unit 5 is coarse-grained by one. The particles 3 are replaced. Thereby, a plurality of (for example, 10 to 5000) coarse-grained particles 3 are set in each coarse-grained model 2. In such a simulation using the coarse-grained model 2, for example, the calculation time can be greatly shortened and a large-scale and long-time phenomenon can be handled as compared with a simulation using an all-atom model.

  In addition, 12 monomers were used as the structural unit 5 because the paper of Kremer-Grest model (Kurt Kremer & Gary S. Grest, “Dynamics of entangled linear polymer melts: A molecular-dynamics simulation”, J. Chem. Phys. Vol.92, No.8, 15 April 1990) and the coarse-grained unit of dissipative particle dynamics (DPD) is about 7 times that of the Kremer-Grest model paper. Is. Even when the polymer chain is other than polyisoprene, for example, the above paper and paper (L, J. Fetters, DJ Lohse and RHColby, "Chain Dimension and Entanglement Spacings" Physical Properties of Polymers Handbook Second Edition P448) The structural unit can be set from

  The coarse-grained particle 3 is handled 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 coarse-grained particles 3.

For the bond 4, an interaction potential P1 is set. The interaction potential P1 of this embodiment is a binding potential U _Harmonic defined by the following formula (6).

ここで、各定数及び変数は、次のとおりである。
ｋ：粒子間のばね定数
ｒ_ij：粗視化粒子間の距離

Here, each constant and variable are as follows.
k: Spring constant between particles r _ij : Distance between coarse-grained particles

The bond potential U _Harmonic is of the Harmonic type. The Harmonic type is a potential where a so-called linear spring is defined and a restoring force proportional to the distance r _ij works.

Bonding potential U _Harmonic, when the distance r _ij becomes large in the direction the coarse-grained particles 3,3 approaches, bonding potential U _Harmonic (attraction) increases. In this way, the binding potential U _Harmonic is defined as a restoring force for returning the distance r _ij to zero.

About the spring constant k of the said Formula (6), it can set suitably. In the present embodiment, similarly to the interaction potential P1, the following values are set based on the above paper.
Spring constant k: 4

As shown in FIG. 5, a repulsive potential P <b> 2 is defined between the coarse-grained particles 3 and 3 of the adjacent coarse-grained models 2 and 2. The repulsive potential P2 is a soft core potential U _softcore defined by the following equation (5).

ここで、各定数及び変数は、次のとおりである。
ａ_ij：粗視化粒子間に作用する斥力の強度に対応する定数
ｒ_ij：粗視化粒子間の距離
ｒ_c：カットオフ距離
なお、粗視化粒子間の距離ｒ_ij及びカットオフ距離ｒ_cは、各粗視化粒子３、３の中心３ｃ、３ｃ（図４に示す）間の距離として定義される。

Here, each constant and variable are as follows.
a _ij : Constant corresponding to the strength of repulsive force acting between coarse-grained particles r _ij : Distance between coarse-grained particles r _c : Cut-off distance Note that the distance r _ij and the cut-off distance r between coarse-grained particles _c is defined as the distance between the centers 3c, 3c (shown in FIG. 4) of each coarse grained particle 3, 3.

The soft core potential U _softcore is based on dissipative particle dynamics (DPD). The dissipative particle dynamics method is a kind of coarse-grained molecular dynamics method. In the dissipative particle dynamics method, the force applied to the coarse-grained particle is applied to the interaction potential P1 by adding a random force in consideration of the relative position / velocity with the coarse-grained particle 3 and a friction force corresponding to the particle velocity. Calculated. According to such a dissipative particle dynamics method, not only the movement of the polymer can be calculated at high speed, but also the movement of the polymer near the interface can be calculated with high accuracy.

Repulsive potential P2, the distance r _ij becomes 0 when the cutoff distance r _c above. On the other hand, the repulsive potential P2, the distance r _ij becomes large when less than the cutoff distance r _c. Further, the repulsive potential P2 becomes a finite value even when the distance r _ij converges to zero. Therefore, the repulsive potential P2 does not diverge infinitely, unlike a potential (hard core potential) that increases infinitely as the distance between particles decreases, for example.

Each constant and variable value of the repulsive potential P2 can be set as appropriate. In this embodiment, a paper (Rosse D. Groot and Patrick B. Warren, “Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation”, J. Chem Phys. Vol.107, No.11, 15 September 1997) Based on this, the following values are set:
Constant a _ij : 25
Cut-off distance r _c : 1.0

  Such a coarse-grained model 2 is numerical data that can be handled by the computer 1 and is stored in the computer 1.

  Next, the filler model 6 that models the filler is set in the computer 1 (step S2). The filler model 6 is modeled by, for example, one filler particle 7. The filler particles 7 are handled as mass points of the equations of motion in the molecular dynamics calculation, like the coarse-grained particles 3.

An interaction potential P3 is defined between the coarse-grained particles 3 and the filler particles 7 and between the filler particles 7 and 7. The interaction potential P3 is an LJ potential U _LJ (r _ij ) defined by the following formula (7).

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：粒子間の距離
ｒ_c：カットオフ距離
ε：粒子間に定義されるＬＪポテンシャルの強度
σ：粒子の直径に相当
なお、距離ｒ_ij及びカットオフ距離ｒ_cは、各粗視化粒子３、３の中心３ｃ、３ｃ（図４に示す）間の距離、又は、粗視化粒子３の中心３ｃとフィラー粒子７の中心（図示省略）との間の距離として定義される。
として定義される。

Here, each constant and variable are parameters of Lennard-Jones potential, and are as follows.
r _ij: distance between the particles r _c: cutoff distance epsilon: the intensity of the LJ potential which is defined between the particles sigma: corresponds to the diameter of the particles should be noted that the distance r _ij and cutoff distance r _c is the coarse-grained particles 3, the distance between the centers 3c and 3c (shown in FIG. 4), or the distance between the center 3c of the coarse-grained particle 3 and the center of the filler particle 7 (not shown).
Is defined as

In the interaction potential P3, the repulsive force acting between the particles increases as the distance r _ij between the particles becomes smaller than 2 ^1/6 σ. The interaction potential P3 is minimized when the inter-particle distance r _ij is 2 ^1/6 σ, and when the inter-particle distance r _ij is longer than 2 ^1/6 σ, an attractive force acts between the particles. . Furthermore, the interaction potential P3 has a smaller attractive force acting between the particles as the distance r _ij between the particles becomes larger than (26/7) ^1/6 σ. As described above, the interaction potential P3 can define repulsive force and attractive force according to the distance r _ij between the particles.

The values of the constants and variables of the interaction potential P3 can be set as appropriate, but it is desirable to set the following values based on the above paper. The filler model 6 is numerical data that can be handled by the computer 1 and is stored in the computer 1.
Constant ε: 1.0
Constant σ: 1.0

  Next, the coarse-grained model 2 and the filler model 6 are arranged in a predetermined space, and the polymer material model 10 is set (step S3). As shown in FIG. 6, the space 8 of the present embodiment is defined as a cube having three pairs of planes 11 and 11 facing each other. A periodic boundary condition is defined for each plane 11. Thereby, the space 8 is handled as one plane 11 connected to the opposite plane 11.

The length L1 of one side of the space 8 can be set as appropriate, but is preferably set to be twice or more the inertia radius Rg of the coarse-grained model 2. The inertia radius Rg is a parameter indicating the spread of the coarse-grained model 2 in the molecular dynamics calculation. In such a space 8, the motion of the coarse-grained model 2 can be calculated smoothly in the molecular dynamics calculation. Further, the size of the space 8 is desirably set to a particle number density of about 3 / σ ³ based on the above-mentioned paper, for example.

  A plurality of coarse-grained models 2 and filler models 6 are arranged in the space 8. In this embodiment, about 100 to 10000 coarse-grained models 2 and about 4 to 32 filler models 6 are arranged. Thus, the space 8 in which the coarse-grained model 2 and the filler model 6 are arranged is configured as a polymer material model 10 that is a microstructure portion of the polymer material to be analyzed. Such a polymer material model 10 is also numerical data and is stored in the computer 1.

  Next, the computer 1 calculates the structural relaxation of the polymer material model 10 based on a predetermined condition (step S4). In the molecular dynamics calculation of the present embodiment, for example, Newton's equation of motion is applied assuming that the coarse-grained model 2 and the filler model 6 follow classical mechanics for a predetermined time with respect to the space 8. The movements of the coarse-grained particles 3 and the filler particles 7 at each time are tracked every unit time. Such calculation of structural relaxation can be processed using, for example, COGNAC included in the soft material general simulator (OCTA).

  In the space relaxation calculation, the pressure and temperature are constant or the volume and temperature are kept constant in the space 8. Thereby, in step S4, the initial arrangement of the coarse-grained model 2 and the filler particles 7 can be relaxed with high accuracy by approximating the molecular motion of the actual polymer material.

In the present embodiment, a repulsive potential that becomes a finite value even when the distance r _ij between the coarse-grained particles 3 and 3 converges to 0 between the coarse-grained particles 3 and 3 of the adjacent coarse-grained models 2 and 2. P2 (shown in FIG. 4) is defined. For this reason, in step S4, it is possible to prevent the repulsive force from becoming infinitely large between the coarse-grained particles 3 and 3 of the adjacent coarse-grained models 2 and 2, for example. Therefore, in step S4, the adjacent coarse-grained models 2 and 2 can be smoothly crossed (passed through), and the initial arrangement of the coarse-grained model 2 and the filler particles 7 can be relaxed in a short time. .

Next, the computer 1 determines whether or not the initial arrangement of the coarse-grained model 2 and the filler model 6 has been sufficiently relaxed (step S5). In this step S5, when it is determined that the initial arrangement of the coarse-grained model 2 and the filler model 6 has been sufficiently relaxed, the next calculation step S6 is performed. On the other hand, when it is determined that the initial arrangement of the coarse-grained model 2 and the filler model 6 has not been sufficiently relaxed, the unit time is advanced (step S7), and the step S4 is performed again. Thereby, in process S4, the equilibrium state (state in which the structure was relaxed) of coarse-grained model 2 and filler particle 7 can be calculated reliably. Note that the computation time of the structural relaxation, under the above conditions, if the relaxation time of the end-to-end vector was tau _n, at least tau _n, more preferably at least 10Tau _n is desired.

  Next, after the calculation of the structure relaxation, the computer 1 deforms the polymer material model 10 with a predetermined strain to obtain the orientation parameter of each bond 4 (calculation step S6). FIG. 7 shows an example of the processing procedure of the calculation step S6 of the present embodiment.

  In the calculation step S6 of the present embodiment, first, as shown in FIG. 8, in the polymer material model 10, the space 8 in which the coarse-grained model 2 is arranged is divided into a plurality of regions T (step S61). ). Each region T is divided by a plurality of boundary surfaces Ts along the outer surface 6s of the filler model 6. Each boundary surface Ts is concentrically arranged with a constant thickness dw with the center of gravity 6g of the filler model 6 as the center.

  The number of regions T in the present embodiment is set for N from the first first region T1 closest to the filler model 6 to the Nth Nth region TN. These areas T are numerical data such as coordinate values and are stored in the computer 1.

  Next, the polymer material model 10 (shown in FIG. 6) is deformed with a predetermined strain (step S62). In step S62 of the present embodiment, the polymer material model 10 is subjected to tensile deformation from the initial state shown in FIG. 6, and then subjected to compressive deformation with the same strain in the opposite direction to the tensile deformation, to the initial state. Tensile / compressive deformation with a period of returning to 1 is simulated. The strain γ of this embodiment is defined by the following formula (3).

ここで、各定数及び変数は次のとおりである。
γ₀：歪振幅
ω：角速度
ｔ：時刻

Here, each constant and variable are as follows.
γ ₀ : Strain amplitude ω: Angular velocity t: Time

  The strain γ is a sinusoidal vibration strain. Such vibration strain approximates, for example, strain applied to a polymer material to be analyzed in dynamic viscoelasticity measurement.

  In the space 8, in the region T (for example, the first region T1 to the fifth region T5) in the vicinity of the filler model 6, the attractive force of the interaction potential P3 that acts between the coarse-grained particles 3 and the filler particles 7 is increased. . For this reason, in the region T in the vicinity of the filler model 6, the coarse-grained particles 3 are constrained, and even when the strain γ is defined, the deformation of the region T is reduced.

  In a region T (for example, a sixth region T6 to an Mth region TM) that is greatly separated from the filler model 6, the attractive force of the interaction potential P3 that acts between the coarse-grained particles 3 and the filler particles 7 is small. For this reason, in the region T that is far away from the filler model 6, the movement of the coarse-grained particles 3 is increased, and the deformation in the region T is increased.

  Thus, in step S62, the deformation of the polymer material in which the filler is blended can be accurately reproduced using the polymer material model 10. In the present embodiment, since the repulsive potential (DPD potential) P2 as described above is defined between the coarse-grained particles 3 and 3 of the adjacent coarse-grained models 2 and 2, the adjacent coarse-grained particles are defined. The models 2 and 2 can be smoothly crossed (passed through). For this reason, in this embodiment, for example, the calculation time required for relaxation is shortened as compared with the case where the hard core potential is defined, and it is possible to reliably prevent the calculation from being ended in error.

  In step S62, while the deformation calculation is performed, the coordinate values of the coarse-grained particles 3, the bonds 4, and the filler particles 7 of the polymer material model 10 are calculated every time t. These coordinate values are numerical data and are stored in the computer 1. Such deformation calculation of the polymer material model 10 can also be processed using, for example, COGNAC included in the soft material general simulator (OCTA).

About each constant and variable of the said Formula (3), although it can set suitably, it is desirable to set the following value, for example. Further, deformation calculation of the polymeric material model 10, for example, if the relaxation time of the point entanglement was tau _e, it is desirable is calculated by defining one period with either 1～10000Tau _e, also, It is desirable to output 20 to 100 coordinate data in one deformation calculation.
Strain amplitude γ ₀ : 5% to 20%
Angular velocity ω: 2π / (10000τ _e ) to 2π / (1τ _e )

Next, the orientation parameter of each bond 4 is calculated for each region T (step S63). As shown in an enlarged view in FIG. 9, in step S63, orientation parameters are calculated based on the coordinate values of the coarse-grained particles 3, the bonds 4, and the filler particles 7 calculated in step S62. The orientation parameter χ _i (m, t) is defined by the following formula (1).

ここで、各定数及び変数は次のとおりである。
ｉ：各ボンドのインデックス
ｍ：各領域のインデックス
ｔ：時刻
θ_i：ボンドベクトルｕ_i（ｍ，ｔ）と重心ベクトルｎ_i（ｍ，ｔ）とがなす角度（狭角）

Here, each constant and variable are as follows.
i: Index of each bond m: Index of each region t: Time θ _i : Angle (narrow angle) formed by bond vector u _i (m, t) and centroid vector n _i (m, t)

The orientation parameter χ _i (m, t) includes the bond vector u _i (m, t) along the bond 4 arranged in the m-th region Tm, and the centroid 4g of the bond 4 and the centroid of the filler model 6. It is defined based on the center of gravity vector n _i (m, t) connecting 6g. Such an orientation parameter χ _i (m, t) can define the arrangement state of the bonds 4 of the coarse-grained model 2 with respect to the filler model 6.

In step S63, the orientation parameter χ _i (m, t) is calculated for every bond 4 arranged in the space 8 at every time t. These orientation parameters χ _i (m, t) are numerical data and are stored in the computer 1. In the case where each bond 4 is disposed across adjacent regions T, the orientation parameter χ _i (m, t) is calculated in the region T where the center of gravity 4g of the bond 4 is disposed.

Next, the computer 1 specifies the interface layer of the polymer material based on the average Χ (m, t) of the orientation parameters χ _i (m, t) (interface specifying step S8).

  As shown in FIG. 10, it is known that the interface layer 14 a is formed around the filler 13 in a system in which the filler 13 and the polymer material 14 coexist. Further, the interface layer 14 a exhibits different mechanical characteristics from the bulk portion 14 b that is the original portion of the polymer material 14. Therefore, when calculating the physical property value of the polymer material using the polymer material model 10 shown in FIG. 8, it is important to define the thickness W2 of the interface layer 14a in advance.

  In general, in the interface layer 14 a of the polymer material 14, since the polymer chain is constrained by the filler 13, the polymer chain tends to be less likely to be deformed than the bulk portion 14 b in which the polymer chain is not constrained by the filler 13.

In the present embodiment, the interface layer 14a of the polymer material 14 is specified using the average value (m, t) of the orientation parameters χ _i (m, t) of the bond 4 that correlates with the deformation of the polymer material model 10. doing. FIG. 11 shows a specific processing procedure of the interface identification step S8 of the present embodiment.

In the interface identification step S8 of the present embodiment, first, the average of the orientation parameters χ _i (m, t) is obtained for each region T (step S81). The average Χ (m, t) of the orientation parameters is defined by the following formula (2).

ここで、各定数及び変数は次のとおりである。
ｉ：各ボンドのインデックス
ｍ：各領域のインデックス
ｔ：時刻
Ｎ：各領域に配置されるボンドの総数

Here, each constant and variable are as follows.
i: Index of each bond m: Index of each area t: Time N: Total number of bonds arranged in each area

In the above equation (2), the average of the orientation parameters χ _i (m, t) of the bond 4 in the m-th region T is calculated every time t. In the present embodiment, the average Χ (m, t) of the orientation parameters is calculated in all the regions T from the first region T1 to the Nth region TN. The average Χ (m, t) of these orientation parameters is numerical data and is stored in the computer 1.

As described above, in the region T in the vicinity of the filler model 6, the attractive force of the interaction potential P3 that acts between the coarse-grained particles 3 and the filler particles 7 increases. For this reason, the angle θ _i formed by the bond vector u _i (m, t) defined by the bond 4 between the coarse-grained particles 3 and 3 and the centroid vector n _i (m, t) becomes large, and the orientation parameter χ The average Χ (m, t) of _i (m, t) approaches 1.

On the other hand, in the region T that is far away from the filler model 6, the attractive force of the interaction potential P <b> 3 that acts between the coarse-grained particles 3 and the filler particles 7 is small. For this reason, the angle θ _i formed by the bond vector u _i (m, t) defined by the bond 4 between the coarse-grained particles 3 and 3 and the centroid vector n _i (m, t) becomes messy (ie, Since the binding force is weak, the angle θ _i is directed in a random direction), and since the orientation parameter χ _i (m, t) takes various values in the range of −1 to +1, the orientation parameter average Χ (m, t ) Approaches 0.

In this manner, in the region T in the vicinity of the filler model 6, the bonds 4 are aligned concentrically with the filler model 6 in the region T. Therefore, the average Χ (m, t) of the alignment parameters χ _i (m, t) is 1. Get closer to. On the other hand, in the region T that is largely separated from the filler model 6, the deformation in the region T and the orientation parameter χ _i (m, t) become more messy compared to the region T in the vicinity of the filler model 6 (ie, The orientation parameter χ _i (m, t) varies in the range of −1 to +1), and the average パ ラ メ ー タ (m, t) of the orientation parameter approaches 0. Therefore, the orientation parameter χ _i (m, t) is correlated with the deformation of the polymer material model 10.

  Next, the average Χ (m, t) of the orientation parameters is decomposed into a storage component that responds to the strain in the same phase and a dissipative component that responds to the strain in a different phase (step S82). In this step S82, first, the distortion response in each region T is calculated by the following equation (8).

ここで、各定数及び変数は、次に示すものを除き、上記式（２）及び（３）と同一である。
Χ₀：配向パラメータχの振幅
δ：位相差

Here, the constants and variables are the same as those in the equations (2) and (3) except for the following.
Χ ₀ : Orientation parameter χ amplitude δ: Phase difference

  The above equation (8) is calculated based on the average Χ (m, t) of the orientation parameters of each region T defined by the above equation (2) and the strain defined by the above equation (3). The distortion response is defined.

  Next, the response of the polymer material model 10 defined by the above equation (8) is decomposed as the following equation (4).

ここで、各定数及び変数は、上記式（２）、上記式（３）及び上記式（８）と同一である。

Here, each constant and variable are the same as the above formula (2), the above formula (3), and the above formula (8).

  The above formula (4) is obtained by decomposing the above formula (8) based on the addition theorem. According to the above equation (4), the response of the polymer material model 10 (average orientation parameter (Χ, m, t)) is a storage component 貯 蔵 ′ that responds to the strain in the same phase, and the strain. In contrast, the storage component 散 ′ and the dissipation component Χ ″ can be separated from the time t in the above equation (4). The component Χ ′ and the dissipative component Χ ”can be uniquely determined. FIG. 12 shows the storage component Χ ′ and the dissipative component Χ” of each region T and the boundary surface of each region T from the outer surface 6s of the filler model 6. A graph showing the relationship of the distance to Ts is shown.

  Next, the interface layer is determined based on the storage component Χ ′ and the dissipative component Χ ”(step S83). As described above, in the interface layer 14a of the polymer material 14 shown in FIG. Therefore, in the interface layer of the polymer material model 10 shown in Fig. 8, the storage component Χ 'that responds to the strain in the same phase has a phase different from that of the strain. It can be assumed that it is larger than the responding dissipative component Χ ”. Accordingly, in step S83, a region T in which the storage component Χ 'is larger than the dissipative component Χ "is determined as the interface layer 17 (shown in FIG. 13).

  Further, in the bulk portion of the polymer material model 10, it can be assumed that the storage component Χ 'is smaller than the dissipative component Χ ". Accordingly, in step S83, the region T in which the storage component Χ' is smaller than the dissipative component Χ" Determined as bulk portion 18 (shown in FIG. 13).

  Furthermore, it can be assumed that the boundary between the interface layer and the bulk portion is the same as the storage component Χ ′ and the dissipative component Χ ″. The position of the boundary 20 (shown in FIG. 13) between the interface layer 17 and the bulk portion 18 is determined.

  In addition, when the boundary 20 is arrange | positioned between the adjacent boundary surfaces Ts and Ts (shown in FIG. 8), it is desirable to specify the interface layer 17 and the bulk part 18 on the basis of the boundary 20. FIG. In step S83, the thickness W3 (shown in FIG. 13) of the interface layer 17 is obtained by calculating the distance of the intersection 19 from the outer surface 6s of the filler model 6.

  As described above, in the simulation method of the present invention, the interface layer 17 is specified and the thickness W3 thereof is ensured without performing the experiment using the polymer material and the filler as in the conventional simulation method. Can be calculated. Therefore, in the simulation method of the present invention, the interface layer 17 can be accurately specified without requiring much time and expense.

  Moreover, in the simulation method of the present invention, since the interface layer 17 can be specified in the simulation using the coarse-grained model 2, the interface layer 17 of a polymer chain that does not actually exist can be specified. Useful for material development.

  Furthermore, in the simulation method of the present invention, since the repulsive potential P2 (shown in FIG. 5) is defined between the coarse-grained particles 3 and 3 of the adjacent coarse-grained models 2 and 2, the interface is defined as follows. The deformation of the polymer material model 10 that is included can be calculated stably and accurately in a short time. Therefore, in the simulation method of the present embodiment, the interface layer 17 can be specified reliably.

In order to specify the interface layer 17 with high accuracy, it is desirable that 100 or more bonds 4 are arranged, and the thickness dw of each region T is determined within a unit length of 1σ or less. If the number of bonds 4 arranged in each region T is less than 100, the orientation parameter χ _i (m, t) of each region T may not be sufficiently equalized. Further, when the thickness dw exceeds the unit length 1σ, the resolution may be lowered.

  Next, the computer 1 calculates the physical property value of the polymer material model 10 (step S9). In this step S9, predetermined parameters such as the thickness W3 of the interface layer 17 are set in the space 8, and the physical property value (for example, complex elastic modulus) of the polymer material is calculated.

  Next, the computer 1 determines whether the physical property value of the polymer material model 10 is within an allowable range (step S10). In this step S10, when it is determined that the physical property value is within the allowable range, a polymer material is manufactured based on the condition of the space 8 including the coarse-grained model 2 (step S11). On the other hand, when it is determined that the physical property value is not within the allowable range, various conditions of the space 8 including the coarse-grained model 2 are changed (step S12), and steps S4 to S11 are performed again. As described above, in the simulation method of the present embodiment, the various conditions of the space 8 including the coarse-grained model 2 are changed until the physical property value of the polymer material model 10 falls within the allowable range. It is possible to efficiently design a polymer material having the same.

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

  According to the procedure shown in FIG. 3, FIG. 7, and FIG. 11, the bond orientation parameter of the polymer material model was determined, and the interface layer of the polymer material was specified (Example).

In the examples and comparative examples, the time required to determine the thickness of the interface layer was measured. In addition, each parameter of potential, strain, and the like are as described in the specification, and common specifications are as follows.
Coarse-grained model:
Number of coarse-grained particles: 143 particles / inertia radius: 4.86σ
Filler model radius: 4.0σ
Each area:
Thickness dw: 0.5σ
Number: 10 Number of bonds arranged in each region: 340-1443 Space:
Length of one side L1: 21.0σ
Number of coarse-grained models: 189 Number of filler models: 1

  As a result of the test, the thickness of the interface layer calculated in the example was 4.8σ. Therefore, in the example, the thickness of the interface layer could be uniquely specified without performing an experiment using a polymer material. In the embodiment, since the repulsive potential (DPD potential) is defined, the adjacent coarse-grained models can be smoothly crossed (passed through), and the calculation can be prevented from being ended in error. It was.

2 Coarse-grained model 4 Bond 6 Filler model 10 Polymer material model

Claims (7)

A method for analyzing a reaction between a polymer material and a filler using a computer,
Setting a coarse-grained model obtained by modeling the polymer chain of the polymer material in the computer using a plurality of coarse-grained particles and a bond that bonds the coarse-grained particles;
Setting a filler model in which the filler is modeled with filler particles in the computer;
Setting the polymer material model by arranging the coarse-grained model and the filler model in a predetermined space in the computer;
The computer calculating a structural relaxation of the polymer material model based on a predetermined condition;
After the calculation of the structural relaxation, the computer deforms the polymer material model with a predetermined strain to obtain an orientation parameter representing the alignment state of each bond,
Based on the orientation parameter, the computer includes an interface identifying step that identifies an interface layer of the polymeric material formed around the filler and exhibiting mechanical properties different from the bulk portion of the polymeric material;
A polymer material characterized in that a repulsive potential that is finite even if the distance between the coarse-grained particles converges to 0 is defined between the coarse-grained particles of the adjacent coarse-grained models. Simulation method. The calculation step includes a step of dividing the space in which the coarse-grained model is arranged into a plurality of regions at a boundary surface along an outer surface of the filler model;
Deforming the polymer material model with the strain;
The method of claim 1, further comprising: calculating the orientation parameter for each region. The interface specifying step is a step of obtaining an average of the orientation parameters for each region;
Decomposing an average of the orientation parameters into a storage component that responds in phase to the strain and a dissipative component that responds to the strain in a different phase;
The simulation method of the polymeric material of Claim 2 including the process of determining the area | region where the said storage component is larger than the said dissipative component as the said interface layer. The orientation parameter χ _i (m, t) is a centroid vector n _i (m, t) that connects the bond vector u _i (m, t) along the bond and the centroid of the bond and the centroid of the filler model. The simulation method of the polymeric material in any one of Claims 1 thru | or 3 defined by following formula (1) based on these.

Here, each constant and variable are as follows.
i: Index of each bond m: Index of each region t: Time θ _i : Angle formed by bond vector u _i (m, t) and centroid vector n _i (m, t) The average Χ (m, t) of the orientation parameters is defined by the following formula (2):
The strain γ is defined by the following formula (3):
The method for simulating a polymer material according to claim 4, wherein the average Χ (m, t) of the orientation parameters is decomposed into the storage component Χ 'and the dissipative component Χ "based on the following formula (4): .

Here, each constant and variable are as follows.
i: Index of each bond m: Index of each region t: Time N: Total number of bonds arranged in each region γ ₀ : Strain amplitude ω: Angular velocity   The method for simulating a polymer material according to any one of claims 2 to 5, wherein 100 or more of the bonds are arranged in each region. The said repulsive potential is the simulation method of the polymeric material in any one of Claims 1 thru | or 6 defined by following formula (5).

Here, each constant and variable are as follows.
a _ij : Constant corresponding to the strength of repulsive force acting between coarse-grained particles r _ij : Distance between coarse-grained particles r _c : Cut-off distance

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