JP7630364B2 - Polymer model generation method, system, and program - Google Patents

Description

This disclosure relates to a method, system, and program for generating polymer models.

Hydrogenated SBR (styrene butadiene rubber) is known to have better abrasion resistance than non-hydrogenated SBR. In order to understand the factors that make it superior, etc., it is necessary to create a molecular dynamics simulation model that reproduces hydrogenated SBR.

Simulation of SS curves using entanglement density control model, Hiroki Yamamura, Tetsuo Tominaga, Takumi Adachi, Hirofumi Senga, JSR TECHNICAL REVIEW No.126/2019

Non-Patent Document 1 discloses a method of using the Kremer-Grest model to model styrene and butadiene together without distinguishing between them. Specifically, an angle potential is added to the Kremer-Grest model, which is a styrene-butadiene model, and the angle potential is determined so as to match the experimental value of viscoelasticity (equilibrium elastic modulus, Young's modulus). After that, the number of crosslinking points in the styrene-butadiene model is determined so that the hydrogenation rate matches the experimental value of the SS curve (stress-strain curve) of the known hydrogenated SBR.

However, this method uses experimental data with known hydrogenation rates and cannot generate models with unknown hydrogenation rates.
There is also a need for a method for generating a polymer model that is not limited to hydrogenated SBR, but in which the number of crosslinks with crosslinked particles can be changed depending on the proportion of monomers.

This disclosure provides a method, system, and program for generating a polymer model that can be used to accurately evaluate the proportion of monomers even when experimental data is unavailable.

The polymer model generation method of the present disclosure is a polymer model generation method executed by one or more processors, the polymer model includes a plurality of polymer models having a plurality of coarse-grained particles connected in a linear or branched manner, and a bridge particle model, the plurality of coarse-grained particles represent any of a plurality of types of monomer models including a first type monomer model and a second type monomer model, the first type monomer model and the second type monomer model have a plurality of particles connected in a linear or branched manner and have an angular potential representing an interaction between three particles, the first type monomer model can be set to be able to be bound to the bridge particle model, and the second type monomer model can be set to be able to be bound to the bridge particle model, The method includes: calculating the angular potential of each of the first type monomer model and the second type monomer model based on experimental values; assigning one of the multiple types of monomer models to each of the multiple coarse-grained particles constituting the polymer model such that the ratio of the second type monomer model to the first type monomer model is a specified ratio; setting a potential corresponding to the assigned monomer model for each of the multiple coarse-grained particles; and executing a cross-linking process to link the first type monomer model and the cross-linked particle model in the polymer model.

FIG. 1 is a block diagram showing a system according to an embodiment of the present invention. 4 is a flowchart showing a process executed by the system. FIG. 2 is a schematic diagram showing a polymer model (SBR model) generated in this embodiment. 4A and 4B are explanatory diagrams relating to angular potential (angular parameter) and characteristic ratio. 11A and 11B are diagrams showing the relationship between the characteristic ratio and the angle parameter, and between the angular potential and the angle parameter. FIG. 11 is an explanatory diagram relating to a process of assigning a monomer model to each particle of a polymer model. FIG. 2 is an explanatory diagram of four polymer models created in this embodiment. FIG. 4 is a diagram showing SS curves of four polymer models created in this embodiment.

An embodiment of the present disclosure will be described below with reference to the drawings.

[Model Generation System]
The system 1 (apparatus) of this embodiment generates a polymer model. In this embodiment, the polymer model is hydrogenated SBR. SBR is a copolymer of butadiene and styrene, and the butadiene portion is crosslinked with a crosslinking agent such as sulfur. When SBR is hydrogenated, hydrogen is added to the double bond of the butadiene portion, resulting in an ethylene structure. This structural change is modeled.

As shown in FIG. 1, the system 1 has an angular potential calculation unit 10, a monomer allocation unit 11, a potential setting unit 12, and a crosslinking process execution unit 13. The system 1 may have an extension process execution unit 14 that stretches the generated polymer model. Each of these units 10 to 14 is realized by software and hardware working together as the processor 1a executes the processing routine shown in FIG. 2, which is stored in advance in a computer equipped with a processor 1a, a memory 1b, various interfaces, etc. In this embodiment, the processor 1a in one device realizes each unit, but this is not limited to this. For example, the system may be configured to be distributed using a network, with multiple processors executing the processing of each unit. In other words, one or multiple processors execute the processing. The memory 1b stores the generated polymer model 2, multiple types of monomer models (5, 6, 7), and analysis conditions (predetermined temperature, predetermined pressure, etc.) for executing molecular dynamics calculations.

As shown in FIG. 3, the polymer model 2 has a plurality of polymer models 3 and a crosslinked particle model 4. The polymer model 3 has a plurality of coarse-grained particles 30 that are linearly or branched. The crosslinked particle model 4 bonds (crosslinks) with the particles 30 of the polymer model 3 that are set to be crosslinkable. The coarse-grained particles 30 represent any of a plurality of types of monomer models including a first type monomer model 5 and a second type monomer model 6. In FIG. 3, each of the coarse-grained particles that constitute the chain of the polymer 3 is described as including a monomer having a plurality of particles, but this is described for ease of understanding. The coarse-grained particles 30 do not have particles that represent monomers therein, but various potentials (described later) for representing the characteristics of the monomers are set, and the number of particles is reduced to reduce calculation costs.
In this embodiment, the multiple types of monomer models further include a third type monomer model 7, the first type monomer model 5 represents butadiene, the second type monomer model 6 represents ethylene, and the third type monomer model 7 represents styrene. The first type monomer model 5 represents butadiene, and can be set to be bondable with the crosslinked particle model 4. This does not mean that all of the first type monomer models 5 need to be set to be bondable with the crosslinked particle model 4, but a part of the first type monomer model 5 may be set to be bondable with the crosslinked particle model 4, and the remaining part may be set to be unable to be bonded with the crosslinked particle model 4. The second type monomer model 6 represents ethylene, and is set to be unable to be bonded with the crosslinked particle model 4. In addition, the third type monomer model 7 represents styrene, and is set to be unable to be bonded with the crosslinked particle model 4.

In each of the multiple types of monomer models, multiple particles are connected in a linear or branched manner. In each of the multiple types of monomer models, a bonding potential and a non-bonding potential are set for each particle. In this embodiment, in the first type monomer model 5, multiple particles 50 are connected in a linear or branched manner by a bonding potential, and a non-bonding potential is set for each particle 50. In the second type monomer model 6, multiple particles 60 are connected in a linear or branched manner by a bonding potential, and a non-bonding potential is set for each particle 60. In the third type monomer model 7, multiple particles 70 are connected in a linear or branched manner by a bonding potential, and a non-bonding potential is set for each particle 70. The bonding potential is a potential that acts between the binding partner. The non-bonding potential is a potential that acts between other particles.

The multiple types of monomer models 5 to 7 of this embodiment use the Kremer-Grest model and have a non-bonded potential (U _non-bond ) of the Kremer-Grest model and a bonded potential (U _bond ) of the Kremer-Grest model. In the Kremer-Grest model, the characteristic ratio representing the spread and entanglement of the polymer chain is uniquely determined, so an angle potential (U _angle ) representing the interaction between three particles is further added to the potential of the multiple types of monomer models. The characteristic ratio can be changed by the angle potential that changes depending on the angle with the bonded partner. The non-bonded potential can be expressed by formula (1), and the bonded potential can be expressed by formula (2). The angle potential is expressed by formula (3). This formula is only an example.

The characteristic ratio can be calculated by the average of all particle chains (square of the distance between the ends)/(number of particles x square of the distance between particles) = <(r ₁ -r _N ) ² >/(NL ² ). N indicates the number of particles constituting one particle chain. As exemplified by the first type monomer model 5 in FIG. 4, the distance between the position r ₁ of the particle 50 at the first end of the particle chain connected (bonded) in a linear or branched manner and the position r _N of the particle 50 at the second end opposite to the first end is represented by |r ₁ -r _N |. If the particle identification number is i, the position is represented by r _i , the position of the particle with identification number 1 is represented by r ₁ , the position of the particle with identification number 2 is represented by r ₂ , and the position of the particle with identification number N is represented by r _N. The distance between two adjacent particles 50 in a bonded state is represented by L. The characteristic ratio is a value obtained from light scattering in an experiment. In addition, when the particle chain is branched, the one with the longest distance between the ends is adopted.

The angular potential calculation unit 10 calculates the angular potential U _angle (angle parameter (K _angle )) of each of the first type monomer model 5, the second type monomer model 6, and the third type monomer model 7 based on experimental values. In this embodiment, various parameters for determining the potential are unified to K = 30.0, R ₀ = 1.5, ε = 1.0, and σ = 1.0 for all models. In this embodiment, the first type monomer model 5 is butadiene, and the characteristic ratio described in the literature (Polymer, Vol. 48, September issue, p. 737 (1999), Society of Polymer Science) is 5.4. The second type monomer model 6 is ethylene, and the characteristic ratio described in the above literature is 6.8. The third type monomer model 7 is styrene, and the characteristic ratio described in the above literature is 10.8. Each monomer model in this embodiment is a model in which 200 particles are connected in a linear chain using the Kremer-Grest model, and the inter-particle distance L is 0.97. If the angle parameter (K _angle ) that determines the angle potential is provisionally determined, the relationship between the angle potential U(θ) and the angle θ can be calculated as shown in the lower diagram of Fig. 5. By setting a number of different angle parameters (K _angle = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 in Fig. 5) in the first type monomer model 5 and continuing the molecular dynamics calculation until an equilibrium state is reached, the end-to-end distance |r ₁ -r _N | can be calculated for each angle parameter, and the relationship between the angle parameter (K _angle ) and the characteristic ratio can be calculated as shown in the upper diagram of Fig. 5. In the upper part of Fig. 5, data for angle parameters (K _angle ) = 2 to 7 are fitted to the approximation formula [characteristic ratio = α × K _angle + β] using the least squares method, and the coefficients α and β of the approximation formula are calculated. α = 1.7288, β = -0.0513, and the sum of squares of the residuals (coefficient of determination) R ² = 0.9987. The angular potential calculation unit 10 calculates the angular parameters (K _angle ) corresponding to the experimental values and determines the angular potential. Using the above approximation formula, the angular parameter (K _angle ) of the first type monomer model is calculated to be 3.1, the angular parameter (K _angle ) of the second type monomer model is calculated to be 4.0, and the angular parameter (K _angle ) of the third type monomer model is calculated to be 6.3.
From the above, the angular potential (parameters that determine the angular potential) of each monomer model 5 can be calculated so as to match the characteristic ratio of each monomer.

As shown in FIG. 6, the monomer allocation unit 11 assigns one of the multiple types of monomer models 5 to 7 to each of the multiple coarse-grained particles 30 that make up the polymer model 3 (hydrogenated SBR). In FIG. 6, the particle 30 to which the first type monomer model 5 (butadiene) is assigned is represented as B, the particle 30 to which the second type monomer model 6 (ethylene) is assigned is represented as E, and the particle 30 to which the third type monomer model (styrene) is assigned is represented as S. At this time, the ratio of the second type monomer model 6 (ethylene) to the first type monomer model 5 (butadiene) is set to a specified ratio. The specified ratio is a ratio specified by the user and can be freely set. For example, SBR is 23.5% styrene and the remaining 76.5% is butadiene. When hydrogen is added, hydrogen is added to the double bond of butadiene to form an ethylene structure, so the ratio of butadiene decreases and the ratio of ethylene increases instead. If the hydrogenation rate is Y [%], the percentage [%] of butadiene is 76.5 × (100-Y), and the percentage [%] of ethylene is 76.5 × Y. The monomer allocation unit 11 determines the number of coarse-grained particles 30 to be allocated to the first type monomer model 5 and the number of coarse-grained particles 30 to be allocated to the second type monomer model 6 so as to achieve the specified percentage. In this embodiment, one polymer model 3 has 200 coarse-grained particles, and the three types of monomer models 5 to 7 are randomly allocated so as to match the number allocated to each monomer model. The number of particles allocated to the third type monomer model 7 (styrene) is 47. If the hydrogenation rate is 0%, the number of particles allocated to the first type monomer model 5 (butadiene) is 153. If the hydrogenation rate is 10%, the number of particles allocated to the first type monomer model 5 (butadiene) is about 137, and the number of particles allocated to the second type monomer model 6 (ethylene) is about 16.

The potential setting unit 12 sets potentials corresponding to the assigned monomer models 5 to 7 for each of the multiple coarse-grained particles 30. In this embodiment, the potentials of formulas (1) and (2) are the same regardless of the type of monomer model. The potential setting unit 12 sets the angle potentials by setting the angle parameter (K _angle ) of the coarse-grained particle 30 assigned as the first type monomer model 5 (butadiene) to 3.1, the angle parameter (K _angle ) of the coarse-grained particle 30 assigned as the second type monomer model 6 (ethylene) to 4.0, and the angle parameter (K _angle ) of the coarse-grained particle 30 assigned as the third type monomer model 7 (styrene) to 6.3.

The crosslinking process execution unit 13 places a specified number of polymer models 3 and crosslinked particle models 4 in space, performs equilibration processing, and then executes crosslinking processing to bond the first type monomer model 5 and the crosslinked particle model 4 in the polymer model 3 in an equilibrium state. The equilibration processing executes molecular dynamics calculations at a specified pressure and a specified temperature until an equilibrium state is reached. When the first type monomer model 5 and the crosslinked particle model 4 approach each other within a specified distance, the crosslinking process execution unit 13 bonds them with a specified probability. The crosslinking process execution unit 13 repeatedly executes the process until all the crosslinked particle models 4 are bonded. This completes the generation of the hydrogenated SBR model (polymer model 2). An example of an equilibrium state is a state in which the fluctuation in the potential of the entire model over a certain period of time is within a certain range.

Although all the coarse-grained particles 30 of the first type monomer model 5 (butadiene) may be set to be bondable to the crosslinked particle model 4, since the number of the first type monomer models 5 (butadiene) in the polymer model 3 is relatively large compared to other monomer models, it is preferable to set only a part of the coarse-grained particles 30 of the first type monomer model 5 (butadiene) to be bondable to the crosslinked particle model 4. Since it is preferable that the crosslinked particle model 4 be bonded to the first type monomer model 5 of a certain polymer model 3 and to the first type monomer model 5 of another polymer model 3, it is preferable that a predetermined number of coarse-grained particles centered on the coarse-grained particle 30 set to be bondable to the crosslinked particle model 4 are set to be unable to be bonded to the crosslinked particle model 4. This makes it possible to prevent one crosslinked particle model 4 from bonding to multiple first type monomer models 5 (butadiene) of the same polymer model 3, thereby improving the uniformity of the crosslinking. In addition, as the hydrogenation rate increases, the number of first type monomer models 5 (butadiene) decreases, so it is preferable to reduce the number of coarse-grained particles 30 (first type monomer models 5) that can be bonded to the crosslinked particle models 4 in accordance with the reduction in the number of first type monomer models 5 (butadiene). This makes it possible to improve the uniformity of the crosslinking.

[Method of generating polymer model]
A method for generating a polymer model executed by the above system 1 will be described with reference to Fig. 2. Here, an example of generating a hydrogenated SBR model will be given as a polymer model. A predetermined pressure and a predetermined temperature used in the molecular dynamics calculation are set and stored in advance in the memory 1b. Also, the characteristic ratios of styrene, butadiene, and ethylene are set and stored in advance in the memory 1b.

First, in step ST1, the angular potential calculation unit 10 calculates the angular potentials (angle parameters) of the first to third monomer models (butadiene, ethylene, styrene) based on experimental values. In this embodiment, the angular parameter (K angle ) of the first monomer model 5 (butadiene) is calculated to be 3.1, the angular parameter (K _angle ) of the second monomer model 6 (ethylene) is calculated to be 4.0, and the angular parameter (K _angle ) of the third monomer model 7 ( _styrene ) is calculated to be 6.3.

In the next step ST2, as shown in FIG. 6, the monomer allocation unit 11 allocates one of the first to third monomer models to each of the multiple coarse-grained particles 30 that make up the polymer model 3. The ratio of each is set to a specified ratio.

In step ST2, when the assignment of the first to third types of monomer models to all of the coarse-grained particles 30 is completed, in the next step ST3, the potential setting unit 12 sets a potential corresponding to the assigned monomer model for each of the multiple coarse-grained particles 30. In this embodiment, since the bond potentials other than the angular potential are common, only the angular potential is set to the potential corresponding to the assigned monomer model.

In the next step ST4, the system 1 sets the coarse-grained particles 30 assigned to the second type monomer model (ethylene) and the third type monomer model 7 (styrene) as not capable of bonding with the cross-linked particle model 4. In addition, some of the coarse-grained particles 30 of the first type monomer model (butadiene) are set as capable of bonding with the cross-linked particle model 4. The remaining coarse-grained particles 30 of the first type monomer model (butadiene) are set as not capable of bonding with the cross-linked particle model 4. In this embodiment, approximately 13% of the number of coarse-grained particles 30 assigned to the first type monomer model (butadiene) are set as capable of bonding with the cross-linked particle model 4, but the percentage is not limited to this.

In the next step ST5, the crosslinking process execution unit 13 executes a crosslinking process to bond the first type monomer model (butadiene) set to be bondable in the polymer model 3 with the crosslinked particle model 4. This completes the generation of the model. Before the crosslinking process, it is recommended to execute an equilibration process to stabilize the uncrosslinked polymer model. Once the crosslinking process is completed (when all the crosslinked particle models have been bonded), it is recommended to execute an equilibration process.

[Tensile test simulation]
A tensile test simulation was performed to confirm whether the created polymer model exhibited qualitative behavior. A known method described in JP 2017-96871 A is used, so detailed description is omitted. The extension processing execution unit 14 shown in FIG. 1 places a polymer model in a virtual space, gradually extends the virtual space in the z-axis direction under constant volume and temperature conditions, and calculates the extension ratio and stress. Since it is not possible to extend the model to the desired extension ratio all at once, a process of slightly extending the model and a relaxation process (equilibrium process) are repeatedly performed. For example, the model is extended to about 1.0139 times, then a relaxation process is performed, and a process of extending the model to 1.0139 times again is repeatedly performed. If the process of extending the model to about 1.0139 times in the z-axis direction is repeated 100 times, the extension ratio can be obtained from 1 to 7, and the stress at each time point can be obtained, and the strain can also be obtained.

Example As shown in FIG. 7, four polymer models (hydrogenated SBR) with hydrogenation rates of 0%, 30%, 50%, and 70% were generated. In each model, the chain length of one polymer model 3 is 200 (200 coarse-grained particles 30), the number of polymer models 3 is 200, and 200 crosslinked particle models 4 are arranged as single particles. As shown in FIG. 7, with an increase in the hydrogenation rate, the number of first-type monomer models 5 (butadiene) that are set to be able to bond with the crosslinked particle models 4 (number of possible bonding points) is reduced. This is to improve the uniformity of the crosslinking. FIG. 7 shows four polymer models, their total particle numbers, butadiene particle numbers, the ratio set to possible bonding points, the number of possible bonding points, and the ratio of the number of possible bonding points to the total particles.
Figure 8 shows the SS curves of the four hydrogenated SBR models (polymer models) shown in Figure 7. These were obtained by the tensile simulation described above. In all of the models, the stress increases as the hydrogenation rate increases, and it can be seen that the hydrogenated SBR can be qualitatively reproduced. The stress in Figure 8 increases upward. Each grid on the vertical axis shows the same amount.

As described above, the method for generating a polymer model according to the present embodiment is executed by one or more processors, and the polymer model 2 includes a plurality of polymer models 3 having a plurality of coarse-grained particles 30 connected in a linear or branched manner, and a cross-linked particle model 4, and the plurality of coarse-grained particles 30 represent any one of a plurality of types of monomer models 5 to 7 including a first type monomer model 5 and a second type monomer model 6, and the first type monomer model 5 and the second type monomer model 6 have a plurality of particles (50, 60) connected in a linear or branched manner and have an angular potential representing the interaction between the three particles, and the first type monomer model 5 can be set to be bonded to the cross-linked particle model 4, and the second type monomer model 5 can be set to be bonded to the cross-linked particle model 4. The polymer model 6 is set so as not to be bonded to the crosslinked particle model 4, and the method may include: calculating the angular potential of each of the first type monomer model 5 and the second type monomer model 6 based on experimental values; assigning one of the multiple types of monomer models 5 to 7 to each of the multiple coarse-grained particles 30 constituting the polymer model 3 so that the ratio of the second type monomer model 6 to the first type monomer model 5 is a specified ratio; setting a potential corresponding to the assigned monomer model for each of the multiple coarse-grained particles 30; and performing a crosslinking process to bond the first type monomer model 5 and the crosslinked particle model 4 in the polymer model 3.

In this way, instead of determining the angular parameters of a model in which the first monomer (butadiene) and the second monomer (ethylene) are mixed without distinction, the first monomer model 5 and the second monomer model 6 are distinguished and the angular potentials of each of the monomer models 5 to 7 are determined. Each of the monomer models 5 to 7 is assigned to a coarse-grained particle that constitutes the polymer model. Thus, the ratio of the first monomer and the second monomer can be freely controlled, and the degree of entanglement can be controlled by controlling this. Since the characteristic ratio can be reproduced by the degree of entanglement, it is possible to generate a model that can be used for accurate evaluation even for models with unknown ratios.

As in this embodiment, the multiple types of monomer models 5 to 7 may include a third type of monomer model 7 that cannot be bonded to the crosslinked particle model 4. This makes it possible to increase the number of types of polymers that can be reproduced.

As in this embodiment, the first monomer model 5 may be a butadiene model, the second monomer model 6 may be an ethylene model, the third monomer model 7 may be a styrene model, and the polymer model 2 may be a hydrogenated SBR model.
This makes it possible to generate a model of hydrogenated SBR, with the ratio being the hydrogenation rate.

As in the present embodiment, the method includes generating a first polymer model (hydrogenation rate 0%) and a second polymer model (hydrogenation rate 30%) as the polymer model 2, the ratio of the second type monomer model 6 to the first type monomer model 5 in the second polymer model (hydrogenation rate 30%) is higher than the ratio of the second type monomer model 6 to the first type monomer model 5 in the first polymer model (hydrogenation rate 0%), and the number of first type monomer models set to be crosslinkable in the second polymer model (hydrogenation rate 30%) is set to be less than the number of first type monomer models set to be crosslinkable in the first polymer model.
According to this configuration, when the ratio of the second type monomer model to the first type monomer model becomes high, the number of first type monomer models that can be set as crosslinkable decreases, and by reducing the number of first type monomer models that are set as crosslinkable accordingly, unintended crosslinking can be prevented and crosslinking uniformity can be improved.

The program according to this embodiment is a program for causing one or more computers to execute the above-described method.
By executing these programs, it is possible to obtain the effects of the above-mentioned methods.

Although the embodiments of the present disclosure have been described above with reference to the drawings, the specific configuration should not be considered to be limited to these embodiments. The scope of the present disclosure is indicated not only by the description of the above embodiments but also by the claims, and further includes all modifications within the meaning and scope equivalent to the claims.

(1) The polymer model 2 in the above embodiment has a third monomer model 7 as styrene, but the third monomer model 7 can be omitted.

(2) In the above embodiment, the polymer model is SBR, but is not limited to this. As long as it has two types of monomers whose ratios are in a competitive relationship (negative correlation), it can be used to reproduce various polymers.

The structures employed in each of the above embodiments can be employed in any other embodiment. The specific configurations of each part are not limited to the above-mentioned embodiments, and various modifications are possible without departing from the spirit of this disclosure.

For example, the order of execution of each process, such as operations, procedures, steps, and stages, in the devices, systems, programs, and methods shown in the claims, specifications, and drawings, can be realized in any order, so long as the output of a previous process is not used in a subsequent process. Even if the flow in the claims, specifications, and drawings is explained using "first," "next," etc. for convenience, this does not mean that it is necessary to execute the processes in this order.

Each unit shown in FIG. 1 is realized by executing a specific program on one or more processors, but each unit may also be configured with a dedicated memory or dedicated circuit. In the above embodiment of system 1, each unit is implemented in processor 1a of a single computer, but each unit may be distributed and implemented on multiple computers or in the cloud. In other words, the above method may be executed on one or more processors.

System 1 includes a processor 1a. For example, processor 1a can be a central processing unit (CPU), a microprocessor, or other processing unit capable of executing computer-executable instructions. System 1 also includes memory 1b for storing data for system 1. In one example, memory 1b includes computer storage media, including RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, DVD or other optical disk storage, magnetic cassettes, magnetic tapes, magnetic disk storage or other magnetic storage devices, or any other media that can be used to store desired data and that can be accessed by system 1.

3...polymer model, 4...crosslinked particle model, 5...first type monomer model, 6...second type monomer model, 7...third type monomer model, 30...coarse-grained particle, 50, 60, 70...particle.

Claims (6)

1. A method for generating a polymer model, executed by one or more processors, comprising:
The polymer model includes a plurality of polymer models having a plurality of coarse-grained particles connected in a linear or branched manner, and a bridged particle model;
the plurality of coarse-grained particles represent any one of a plurality of types of monomer models including a first type monomer model and a second type monomer model;
The first type monomer model and the second type monomer model each have a plurality of particles connected in a linear or branched chain form and an angular potential representing an interaction between three particles,
The first type monomer model can be set to be capable of being bound to the bridge particle model,
The second type monomer model is set to be incapable of bonding with the bridge particle model,
The method comprises:
Calculating the angular potentials of the first type monomer model and the second type monomer model based on experimental values;
Allocating any one of the plurality of types of monomer models to each of the plurality of coarse-grained particles constituting the polymer model such that a ratio of the second type monomer model to the first type monomer model is a designated ratio;
Setting a potential corresponding to the assigned monomer model for each of the plurality of coarse-grained particles;
and performing a cross-linking process to bond the first type monomer model and the cross-linked particle model in the polymer model. The method of claim 1, wherein the multiple types of monomer models include a third type of monomer model that cannot bind to the bridge particle model. The method of claim 2, wherein the first monomer model is a butadiene model, the second monomer model is an ethylene model, the third monomer model is a styrene model, and the polymer model is a hydrogenated SBR model. The method includes generating a first polymer model and a second polymer model as the polymer model;
a ratio of the second type monomer model to the first type monomer model in the second polymer model is higher than a ratio of the second type monomer model to the first type monomer model in the first polymer model;
The method according to any one of claims 1 to 3, wherein the number of the first type monomer models set to be crosslinkable in the second polymer model is set to be less than the number of the first type monomer models set to be crosslinkable in the first polymer model. A system comprising one or more processors for executing the method according to any one of claims 1 to 4. A program for causing one or more processors to execute the method according to any one of claims 1 to 4.