JP2021092903A - Method, system and program for determining parameters of coarse-grained polymer model - Google Patents

Abstract

To provide a method, a system, and a program for determining parameters of a coarse-grained polymer model without using whole-particle simulation.SOLUTION: The method includes the steps of: obtaining a first coarse-grained polymer model M1 having a plurality of linearly bonded first coarse-grained particles 20 and a second coarse-grained polymer model M2 having a plurality of linearly bonded second coarse-grained particles 30 (ST1); setting bond angle bending constants Kangle of the first coarse-grained particles 20 and the second coarse-grained particles 30 and a constant ε regarding intensity of potential (ST2, ST6); performing molecular dynamics calculations to calculate a p ratio of each of the models and a physical quantity representing viscoelasticity of each of the models (ST3, ST4, ST7, ST8); and repeatedly setting the constant ε and the coupling angle bending constant Kangle and calculating the property ratios and physical quantities, until the property ratios and physical quantities meet allowable conditions based on respective experimental values.SELECTED DRAWING: Figure 2

Description

The present disclosure relates to methods, systems and programs for determining parameters of coarse-grained polymer models.

SBR (Styrene-butadiene rubber) has two types of monomers, styrene and butadiene. Simulation using an all-particle model that expresses a polymer model such as SBR with all particles is accurate because the chemical formula structure is reproduced as it is, but on the other hand, it is very large because the number of particles is huge. There is a problem that the calculation cost is high.

In order to reduce the calculation cost, a coarse-grained model in which the structural units (for example, monomers) constituting the polymer model are replaced with one bead is known. In order to use the coarse-grained model, it is necessary to express the characteristics of the chemical formula structure with potential. When the SBR is represented by a coarse-grained model, a coarse-grained polymer model having a first coarse-grained particle showing styrene and a second coarse-grained particle showing butadiene is generated. It is necessary to set different parameters for the first coarse-grained particles and the second coarse-grained particles. It is conceivable that the parameters of each coarse-grained particle are determined so as to match the parameters calculated by the simulation using the whole particle model. However, this method requires simulation using a whole particle model, and enormous calculation cost becomes a problem. It seems that Non-Patent Document 1 proposes a method for determining some parameters. Although not related to the parameter determination method, Patent Document 1 discloses a method for calculating a physical quantity by molecular simulation.

Polymer simulation utilizing the strengths of coarse-grained MD-for application possibilities and correspondence with real systems-, Hiroshi Morita, Taku Ozawa, Journal of Molecular Simulation Study Group "Ensemble", Vol.17, No.3 , July 2015 (Volume 71) P.155-161

The present disclosure provides methods, systems and programs for determining the parameters of a coarse-grained polymer model without the use of whole grain simulation.

The method of determining the parameters of the coarse-grained polymer model of the present disclosure is a method performed by one or more processors, (a1) a first coarse-grained particle having a plurality of linearly bonded first coarse-grained particles. Obtaining a 1 coarse-grained polymer model and a 2nd coarse-grained polymer model having a plurality of linearly bonded second coarse-grained particles, and (b1) the first coarse-grained particles and _{Setting the bond angle bending constant K angle} of the second coarse-grained particle and the constant ε related to the intensity of the potential, and (c1) performing the molecular dynamics calculation, the characteristic ratio of each model and the characteristic ratio of each model are determined. Calculation of the physical quantity representing the viscoelasticity of each model, and (d1) the constant ε and the coupling in the above (b1) until the characteristic ratio and the physical quantity meet the permissible conditions based on the respective experimental values. It includes repeatedly executing the setting of the angle bending constant K _angle and the calculation of the characteristic ratio and the physical quantity in the above (c1).

Block diagram showing a system for determining the parameters of the coarse-grained polymer model of the present disclosure. Flowchart showing the processing performed by the system The figure which shows the 1st coarse-grained polymer model which has a 1st coarse-grained particle, and 2nd coarse-grained polymer model which has a 2nd coarse-grained particle. The figure which shows the experimental value of the storage elastic modulus of polystyrene and polybutadiene The figure which shows the storage elastic modulus G'(ω) of the 1st coarse-grained polymer model (polystyrene) and the 2nd coarse-grained polymer model (polybutadiene) based on a simulation. The figure which shows the 1st SBR model and the 2nd SBR model The figure which shows the simulation result which shows the shape change of tan δ by the dispersibility of styrene using the model shown in FIG.

Hereinafter, an embodiment of the present disclosure will be described with reference to the drawings.

[System for determining parameters of coarse-grained polymer model]
The system 1 of the present embodiment determines the parameters of the coarse-grained polymer model, which is two types of polymers constituting the coarse-grained polymer model such as SBR.

As shown in FIG. 1, the system 1 includes a model acquisition unit 10, a first setting unit 11, a molecular dynamics calculation execution unit 12, a characteristic ratio calculation unit 13, a first determination unit 14, and a second setting. It has a unit 15, a physical quantity calculation unit 16, and a second determination unit 17. Each of these parts 10 to 17 is realized in collaboration with software and hardware by the processor 1a executing the processing routine shown in FIG. 2 stored in advance in a computer provided with the processor 1a, the memory 1b, various interfaces, and the like. Will be done. In the present embodiment, the processor 1a in one device realizes each part, but the present invention is not limited to this. For example, it may be distributed using a network, and a plurality of processors may be configured to execute the processing of each part. That is, one or more processors execute the process.

The model acquisition unit 10 shown in FIG. 1 acquires the first coarse-grained polymer model M1 and the second coarse-grained polymer model M2. As shown in FIG. 3, the first coarse-grained polymer model M1 has a polymer 2 having a plurality of linearly bonded first coarse-grained particles 20. The second coarse-grained polymer model M2 has a polymer 3 having a plurality of linearly bonded second coarse-grained particles 30. In this embodiment, the first coarse-grained polymer model M1 is polystyrene and the first coarse-grained particles 20 represent styrene. The second coarse-grained polymer model M2 is polybutadiene and the second coarse-grained particles 30 represent butadiene. The model acquisition unit 10 may acquire the first coarse-grained polymer model M1 and the second coarse-grained polymer model M2 from the outside, or the first coarse-grained polymer model M1 and the second coarse-grained polymer model M2. May be generated.

The first setting unit 11 shown in FIG. 1 sets the bond angle bending constant K _angle of the first coarse-grained particles 20 and the second coarse-grained particles 30. As shown in FIG. 3, the bond angle bending constant K _angle is one of the parameters for determining the bond potential for bonding the coarse-grained particles 20 and 30 to each other, and is between the three particles according to the bond angle θ. It is a constant of the force acting on (between two bonds). When the K _angle is 0, the straight line bends freely without the force corresponding to the angle acting between the three particles, and the straight line becomes easy to move and becomes soft. On the other hand, when the K _angle becomes large, the bond angle θ tends to be 180 degrees, and the straight line becomes hard. _{The angle potential U angle,} which is one of the coupling potentials, is expressed by the following equation (1).
U _angle = K _angle (1 + cosθ)… (1)

The second setting unit 15 shown in FIG. 1 sets a constant ε regarding the intensity of the potential in each of the models M1 and M2. Bonding potential and non-binding potential are set in the first coarse-grained polymer model M1 and the second coarse-grained polymer model M2, respectively, based on the parameters set by the first setting unit 11 and the second setting unit 15. ..

In each of the models M1 and M2, a constant σ (parameter) related to the distance on which the potential acts is set. For example, FENE-LJ can be adopted as the bonding potential between coarse-grained particles, and for example, LJ (Lennard-Jones) or WCA (LJ potential with only repulsive force) can be adopted as the non-binding potential. Of course, these potentials are examples, and other settings are possible.

The molecular dynamics calculation execution unit 12 shown in FIG. 1 executes the molecular dynamics calculation under analysis conditions including a predetermined pressure and a predetermined temperature. In this embodiment, LAMMPS (Large-scale Atomic / Molecular Massively Parallel Simulator) is used as the molecular dynamics calculation execution unit 12, but the present embodiment is not limited to this. The molecular dynamics calculation execution unit 12 can execute the equilibration process. The equilibrium treatment involves the first coarse-grained polymer model M1 and the second coarse-grained polymer model M1 and the second coarse-grained polymer model M2 until the energies of the first coarse-grained polymer model M1 and the second coarse-grained polymer model M2 are minimized at a predetermined pressure and temperature. It is a process of repeatedly executing the molecular dynamics calculation of each polymer model M2. To minimize means to calculate the behavior of the particles 20 and 30 until the energies of the first coarse-grained polymer model M1 and the second coarse-grained polymer model M2 become almost constant (energy fluctuation becomes equal to or less than the threshold value). .. This is because it cannot always be said that the first coarse-grained polymer model M1 and the second coarse-grained polymer model M2 are in a stable state in the molecular dynamics calculation immediately after being arranged in the calculation region Ar1.

_{The characteristic ratio calculation unit 13 shown in FIG. 1 calculates the characteristic ratio C ∞} of each of the models M1 and M2 based on the calculation result of the equilibrium processing by the molecular dynamics calculation execution unit 12. The calculation result of the equilibration process includes the position of each particle. The characteristic ratio C _∞ is a measure of the rigidity of the molecular chain itself. Characteristic ratio calculator 13, as shown in FIG. 3, to calculate the end-to-end distance R _ee of each linear constituting each model M1, M2. The characteristic ratio calculation unit 13 calculates the characteristic ratio C _∞ using the following equation (2).
C _∞ = <R ² _ee > / Nb ² ... (2)
N indicates the number of bonds contained in one polymer chain, and b indicates the length of one bond. <> Means the average value. If the three particles are linearly connected, the number of bonds is two.

_{The first determination unit 14 shown in FIG. 1 determines whether or not the characteristic ratio C ∞ of} each of the models M1 and M2 calculated by the characteristic ratio calculation unit 13 satisfies the first permissible condition based on the experimental value. The first permissible condition is set in advance. In this embodiment, since the first coarse-grained polymer model M1 is polystyrene, the experimental value of the characteristic ratio is 10.5. The second coarse-grained polymer model M2 was polybutadiene, and the experimental value of the characteristic ratio was 4.9. The first permissible condition is set on the condition that the calculation result of the characteristic ratio calculation unit 13 matches the experimental value or the value is close to the experimental value within a certain range. The first permissible condition can be appropriately set according to the object to be coarse-grained.

_{Setting (adjustment) of the bond angle bending constant K angle} by the first setting unit 11, equilibration processing by the molecular dynamics calculation execution unit 12, and characteristic ratio calculation until the first determination unit 14 determines that the first allowable condition is satisfied. The calculation of the characteristic ratio C _∞ by the unit 13 is repeatedly executed. In the simulation result (calculation result of the characteristic ratio calculation unit 13), the _{characteristic ratio C ∞ is 1.78 when the K angle} is 0, and the characteristic ratio C _∞ is 5. when the K _{angle is 3.0.} If the K _angle is 5.1, the characteristic ratio C _∞ is 10.17. Therefore, since a correlation can be confirmed between _{the K angle} and the characteristic ratio C _{∞ , the K angle} is reset so as to approach the experimental value.

The physical quantity calculation unit 16 shown in FIG. 1 calculates a physical quantity representing the viscoelasticity of each of the models M1 and M2 based on the calculation result of the equilibrium processing by the molecular dynamics calculation execution unit 12. Examples of the physical quantity include a storage elastic modulus G ″ (ω), a loss elastic modulus G ″ (ω), and tan δ. In the present embodiment, the storage elastic modulus G'(ω) is calculated as a physical quantity, but the present invention is not limited to this and can be changed as appropriate.

The calculation result of the equilibration process includes the position of each particle and the stress data at each analysis time point (time step). The physical quantity calculation unit 16 calculates the relaxation elastic modulus G (t) at the time of each analysis based on the stress data, calculates the relaxation spectrum H (τ) based on the relaxation elastic modulus G (t), and calculates the relaxation spectrum H (τ). ), The physical quantity of at least one of the storage elastic modulus G'(ω), the loss elastic modulus G'' (ω), and the loss tangent tan δ is calculated.

The second determination unit 17 shown in FIG. 1 determines whether or not the physical quantities of the models M1 and M2 calculated by the physical quantity calculation unit 16 meet the second permissible condition based on the experimental values. The second permissible condition is set in advance. In the present embodiment, the storage elastic modulus G'of the first coarse-grained polymer model M1 (polystyrene) and the storage elastic modulus G'of the second coarse-grained polymer model M2 (polybutadiene) intersect on the graph. There is. FIG. 4 shows experimental values of storage elastic modulus of polystyrene and polybutadiene. FIG. 5 shows the storage elastic moduli G'(ω) of the first coarse-grained polymer model M1 (polystyrene) and the second coarse-grained polymer model M2 (polybutadiene) based on simulations. The unit system of experimental values shown in FIG. 4 and the simulated LJ unit system shown in FIG. 5 are different from each other, and numerical comparison cannot be performed. The experimental results shown in FIG. 4 are characterized in that the storage elastic moduli G'of polystyrene and polybutadiene intersect on the graph, and this fact was set as the second permissible condition. In the simulation, the storage elastic modulus G'(ω) of polystyrene and polybutadiene deviates due to the constant σ, and if the constant σ deviates even a little, the storage elastic modulus G'(ω) of both deviates. We believe that a high degree of agreement with the experimental values can be ensured even if the fact that the test is performed is used as a judgment condition.

Until the second determination unit 17 determines that the second permissible condition is met, the second setting unit 15 sets (adjusts) the constant ε, the molecular dynamics calculation execution unit 12 balances the process, and the physical quantity calculation unit 16 determines the physical quantity. The calculation of (storage elastic modulus G'(ω)) is repeatedly executed.

If the second determination unit 17 determines that the second allowable condition is met, the process may be terminated, but the characteristic ratio C is calculated again and the K _{angle is reached until the first allowable condition is met.} It is preferable to repeat the setting (adjustment) of. This is because the characteristic ratio C may change by changing the constant ε.

[How to determine the parameters of the coarse-grained polymer model]
A method of determining the parameters of the coarse-grained polymer model performed by one or more processors in the system 1 shown in FIG. 1 will be described with reference to FIG.

First, in step ST1, the model acquisition unit 10 acquires the first coarse-grained polymer model M1 and the second coarse-grained polymer model M2.

In the next step ST2, the first setting unit 11 sets the Kangles of the first coarse-grained particles 20 and the second coarse-grained particles 30, respectively. As a result, the potential based on the set parameters is set.

In the next step ST3, the molecular dynamics calculation execution unit 12 executes the equilibrium processing by the molecular dynamics calculation on the first coarse-grained polymer model M1 and the second coarse-grained polymer model M2. In the next step ST4, the characteristic ratio calculation unit 13 calculates the characteristic ratio C _∞ of each of the models M1 and M2.

In the next step ST5, the first determination unit 14 _{determines whether or not the characteristic ratio C ∞ of} each of the models M1 and M2 meets the first permissible condition based on the experimental value. _{In step ST5, the setting (adjustment) of the bond angle bending constant K angle} in step ST2 and the calculation of the characteristic ratio in steps ST3 and 4 are repeatedly executed until it is determined that each characteristic ratio meets the first permissible condition (step ST2). ST5: NO).

When the first determination unit 14 determines in step ST5 that each characteristic ratio meets the first permissible condition (ST4: YES), in the next step ST6, the second setting unit 15 determines the strength of the potential. The constant ε with respect to is set in each model M1 and M2.

In the next step ST7, the molecular dynamics calculation execution unit 12 executes the equilibrium processing by the molecular dynamics calculation on the first coarse-grained polymer model M1 and the second coarse-grained polymer model M2. In the next step ST8, the physical quantity calculation unit 16 calculates the physical quantities (storage elastic modulus G'(ω)) of each of the models M1 and M2.

Next, in step ST9, the second determination unit 17 determines whether or not the physical quantities of the respective models M1 and M2 meet the second permissible condition (whether they intersect). In step ST9, the setting (adjustment) of the constant ε in step ST6 and the calculation of the physical quantity in steps ST7 and 8 are repeatedly executed until it is determined that each physical quantity meets the second permissible condition (ST9: NO).

If the second determination unit 17 determines in step ST9 that each physical quantity meets the second permissible condition (ST9: YES), the molecular dynamics calculation using _{K angle and ε in the next step ST10.} The balancing process is executed by the execution unit 12, and the characteristic ratio C _∞ is calculated by the characteristic ratio calculation unit 13.

In the next step ST10, the first determination unit 14 determines whether or not each characteristic ratio meets the first permissible condition. In step ST10, the process returns to step ST2 until it is determined that each characteristic ratio meets the first permissible condition. That is, when it is determined in step ST10 that the characteristic ratios do not meet the first permissible condition (ST10: NO), the process proceeds to step ST2. When it is determined in step ST10 that each characteristic ratio satisfies the first permissible condition (ST10: YES), it is assumed that the parameters K _angle and ε can be specified, and the process ends. The processes ST10 and ST11 can be omitted.

_{In the present embodiment, the parameter (K angle} ) of the first coarse-grained polymer model M1 (polystyrene model) is 5.1, the parameter (ε) is 0.5, and the second coarse-grained polymer model M1 (polystyrene model) is subjected to the above processing. _{It was identified that the parameter (K angle} ) of the polymer model M2 (polybutadiene model) was 3.0 and the parameter (ε) was 5.0. In each case, σ is 1.0.

Using this simulation result, the first SBR model M3 and the second SBR model M4 shown in FIG. 6 were generated. Each of the SBR models M3 and M4 is an SBR in which the first coarse-grained particles 20 representing styrene and the second coarse-grained particles 30 representing butadiene are linearly linked. In each case, the chain length is 120 particles, and there are 30 first coarse-grained particles 20 representing styrene and 90 second coarse-grained particles 30 representing butadiene. The first SBR model M3 is a model in which the first coarse-grained particles 20 representing styrene are arranged so as to be totally random. On the other hand, the second SBR model M4 is a model in which the first coarse-grained particles 20 representing styrene are arranged so as to be unevenly distributed.

FIG. 7 shows the simulation results showing the shape change of tan δ due to the dispersibility of styrene using the models M3 and M4 shown in FIG. As shown in FIG. 7, the biased model M4 has a lower storage elastic modulus G'(ω) in the low frequency region (left side in the figure) and a loss elastic modulus G''(ω) than the model M3. It's up. As a result, tan δ is increased. This matches the equation of tan δ = G ″ (ω) / G ″ (ω). That is, it can be understood from the simulation results that tan δ increases when the distribution of styrene is biased. This is a result that is consistent with the experiment. Therefore, it can be understood that the above parameters have been appropriately determined.

In this embodiment, styrene and butadiene are given as examples, but the present invention is not limited to this, and can be adopted as a model for coarse-graining any chemical formula structural unit.

As described above, the method for determining the parameters of the coarse-grained polymer model of the present embodiment is
A method executed by one or more processors 1a.
(A1) A first coarse-grained polymer model M1 having a plurality of linearly bonded first coarse-grained particles 20 and a second coarse-grained polymer model M1 having a plurality of linearly bonded second coarse-grained particles 30. 2 Acquiring the coarse-grained polymer model M2 (ST1) and
_{(B1) Setting the bond angle bending constant K angle of} the first coarse-grained particles 20 and the second coarse-grained particles 30 and the constant ε regarding the potential intensity (ST2, ST6), and
(C1) Execute molecular dynamics calculation to calculate the characteristic ratio of each model and the physical quantity representing the viscoelasticity of each model (ST3, ST4, ST7, ST8).
_{(D1) Setting the constant ε and bond angle bending constant K angle} in (b1) and calculating the characteristic ratio and physical quantity in (c1) until the characteristic ratio and physical quantity meet the permissible conditions based on the respective experimental values. , And repeatedly
including.

The system 1 for determining the parameters of the coarse-grained polymer model of the present embodiment
A first coarse-grained polymer model M1 having a plurality of linearly bonded first coarse-grained particles 20 and a second coarse-grained polymer model M1 having a plurality of linearly bonded second coarse-grained particles 30. The model acquisition unit 10 that acquires the chemical polymer model M2,
The first setting unit 11 for setting _{the bond angle bending constant K angle} of the first coarse-grained particles 20 and the second coarse-grained particles 30.
The second setting unit 15 that sets the constant ε related to the strength of the potential,
Molecular dynamics calculation execution unit 12 that executes molecular dynamics calculation,
The characteristic ratio calculation unit 13 for calculating the characteristic ratio of each model M1 and M2, and
A physical quantity calculation unit 16 for calculating a physical quantity representing the viscoelasticity of each model M1 and M2,
With
Until the characteristic ratio and physical quantity meet the permissible conditions based on the respective experimental values, the first setting unit 11 sets the constant ε, the second setting unit 15 sets the coupling angle bending constant K _angle , and the characteristic ratio calculation unit. The calculation of the characteristic ratio by 13 and the calculation of the physical quantity by the physical quantity calculation unit 16 are repeatedly executed.

_{In this way, the constant ε and the coupling angle bending constant K angle} are set and the molecular dynamics calculation is repeatedly executed until the characteristic ratio and the physical quantity derived by the molecular dynamics calculation meet the allowable conditions based on the experimental values. Therefore, it is possible to determine _{each parameter (ε, K angle} ) based on the experimental value without executing the whole particle simulation.

That is, although it is possible to convert the parameters calculated from the total particle simulation results to the parameters of the coarse-grained polymer model, the calculation cost is a problem, and a method for matching the measured values has not been proposed. According to the present disclosure, the parameters can be determined so as to match the measured values.

As in the method of the present embodiment, (b2) the bond angle bending constant K _angle between the first coarse-vision particles 20 and the second coarse-vision particles 30 is set, respectively (ST2), and (c2) the molecular power. The equilibrium processing by the academic calculation is executed to calculate the characteristic ratio of each model M1 and M2 (ST3, ST4), and (d2) each characteristic ratio calculated in (c2) above is used as an experimental value. The setting of the coupling angle bending constant K _angle in (b2) and the calculation of the characteristic ratio in (c2) are repeated until the first allowable condition is satisfied, and if the first allowable condition is satisfied, the following (e2) is performed. Execution (ST5), (e2) Setting the constant ε related to the intensity of the potential to each model M1 and M2 (ST6), and (f2) the equilibrium process are executed, and the respective models M1 and M2 are executed. Calculation of the physical quantity representing the viscous elasticity of (ST8) and setting of the constant ε in (e2) until each physical quantity calculated in (g2) and (f2) meets the second permissible condition based on the experimental value. And repeating the calculation of the physical quantity in (f2) above,
Is preferably included.

_{Like the system of the present embodiment, the bond angle bending constant K angle} is set by the first setting unit 11 until each characteristic ratio calculated by the characteristic ratio calculation unit 13 meets the first permissible condition based on the experimental value. And the calculation of the characteristic ratio by the characteristic ratio calculation unit 13 is repeated.
When the first permissible condition is satisfied, the constant ε is set by the second setting unit 15, and each physical quantity is calculated by the physical quantity calculation unit 16.
It is preferable that the setting of the constant ε by the second setting unit 15 and the calculation of the physical quantity by the physical quantity calculation unit 16 are repeated until each physical quantity calculated by the physical quantity calculation unit 16 meets the second permissible condition based on the experimental value.

In this way, molecular dynamics is executed until a characteristic ratio that matches the first permissible condition based on the experimental value is obtained and a physical quantity that represents viscoelasticity that matches the second permissible condition is obtained based on the experimental value. By repeating the above, it _{is possible to determine the bond angle bending constant K angle of} the coarse-grained particles and the constant ε regarding the potential intensity. Nevertheless, since the whole particle simulation is not executed, the calculation cost can be reduced.

When each physical quantity meets the second permissible condition in (g2) as in the method of the present embodiment, _{the equilibrium process is executed using the bond angle bending constant K angle} and the constant ε, and each of them is executed. It is preferable to calculate the characteristic ratio of the model and return to (b2) until each of the characteristic ratios calculated in (h2) and (g2) meets the first permissible condition.

When each physical quantity calculated by the physical quantity calculation unit 16 meets the second permissible condition as in the system of the present embodiment, the molecular dynamics calculation execution unit 12 _{uses the coupling angle bending constant K angle and the constant ε.} Executes the equilibrium process, the characteristic ratio calculation unit 13 calculates the characteristic ratio of each model, and the first setting is performed until each characteristic ratio calculated by the characteristic ratio calculation unit 13 meets the first allowable condition. It is preferable to repeat the setting of the coupling angle bending constant K _angle by the unit and the calculation of the characteristic ratio by the characteristic ratio calculation unit 13.

In this way, even if the characteristic ratio changes due to the change to the constant ε, the bond angle bending constant K _angle is calculated again, so that the constant ε and the bond angle bending constant K _angle can be calculated appropriately. Is.

As in the present embodiment, the first coarse-grained particles are styrene, the second coarse-grained particles are butadiene, the physical quantity is the storage elastic modulus, and the second allowable condition is the first. It is preferable that the storage elastic modulus of the coarse-grained polymer model and the storage elastic modulus of the second coarse-grained polymer model intersect on the graph.

In this way, for example, even if the LJ unit system on the simulation and the unit system of the experimental value are different and the numerical values cannot be compared, the storage elastic moduli of each cross to match the experimental value. It can be handled and parameters can be determined based on experimental values.

As in the present embodiment, the physical quantity is preferably at least one of a storage elastic modulus, a loss elastic modulus, and tan δ.

The program according to this embodiment is a program that causes a computer to execute the above method.
By executing these programs, it is possible to obtain the effects of the above method.

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

It is possible to adopt the structure adopted in each of the above embodiments in any other embodiment. The specific configuration of each part is not limited to the above-described embodiment, and various modifications can be made without departing from the gist of the present disclosure.

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

It is possible to adopt the structure adopted in each of the above embodiments in any other embodiment. The specific configuration of each part is not limited to the above-described embodiment, and various modifications can be made without departing from the gist of the present disclosure.

It is possible to adopt the structure adopted in each of the above embodiments in any other embodiment.

For example, the execution order of each process such as operation, procedure, step, and step in the device, system, program, and method shown in the claims, specification, and drawings may be the output of the previous process after the output. Unless used in processing, it can be realized in any order. Even if the claims, the specification, and the flow in the drawings are explained using "first", "next", etc. for convenience, it does not mean that it is essential to execute in this order. ..

Although each part 10 to 17 shown in FIG. 1 is realized by executing a predetermined program by 1 or a processor, each part may be configured by a dedicated memory or a dedicated circuit. In the system 1 of the above embodiment, each part 10 to 17 is mounted on the processor 1a of one computer, but each part 10 to 17 may be distributed and mounted on a plurality of computers or the cloud. That is, the above method may be executed by one or more processors.

System 1 includes processor 1a. For example, the processor 1a can be a central processing unit (CPU), a microprocessor, or any other processing unit capable of executing computer executable instructions. Further, the system 1 includes a memory 1b for storing the data of the system 1. In one example, memory 1b includes a computer storage medium, including RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, DVD or other optical disc storage, magnetic cassette, magnetic tape, magnetic disk storage or other. Includes a magnetic storage device, or any other medium that can be used to store the desired data and that System 1 can access.

1 ... System, 10 ... Model acquisition unit, 11 ... First setting unit, 12 ... Molecular dynamics calculation execution unit, 13 ... Characteristic ratio calculation unit, 15 ... Second setting unit, 16 ... Physical quantity calculation unit, 20 ... First Coarse-grained particles, 30 ... 2nd coarse-grained particles, M1 ... 1st coarse-grained polymer model, M2 ... 2nd coarse-grained polymer model, ε ... constants related to potential strength, K _angle ... bond angle bending constant

Claims (11)

A method executed by one or more processors.
(A1) A first coarse-grained polymer model having a plurality of linearly bonded first coarse-grained particles and a second coarse-grained polymer having a plurality of linearly bonded second coarse-grained particles. To obtain a polymer model and
_{(B1) Setting the bond angle bending constant K angle of} the first coarse-grained particles and the second coarse-grained particles and the constant ε regarding the potential intensity, and
(C1) Execute molecular dynamics calculation to calculate the characteristic ratio of each model and the physical quantity representing the viscoelasticity of each model.
_{(D1) The setting of the constant ε and the bond angle bending constant K angle} in (b1) and the characteristic in (c1) until the characteristic ratio and the physical quantity meet the permissible conditions based on the respective experimental values. Repeatedly executing the calculation of the ratio and the physical quantity, and
A method of determining the parameters of a coarse-grained polymer model, including. _{(B2) Setting the bond angle bending constant K angle} between the first coarse-grained particles and the second coarse-grained particles, respectively,
(C2) To calculate the characteristic ratio of each model by executing the equilibrium process by molecular dynamics calculation.
_{(D2) Setting of the bond angle bending constant K angle} in (b2) and the characteristic ratio in (c2) until each characteristic ratio calculated in (c2) meets the first permissible condition based on the experimental value. If the first permissible condition is satisfied, the following (e2) is executed.
(E2) Setting a constant ε related to the intensity of the potential in each model and
(F2) Performing the equilibrium process to calculate the physical quantity representing the viscoelasticity of each model,
(G2) The setting of the constant ε in (e2) and the calculation of the physical quantity in (f2) are repeated until each physical quantity calculated in (f2) meets the second permissible condition based on the experimental value. ,
The method according to claim 1, wherein the method comprises. When each of the physical quantities in (g2) meets the second permissible condition, the _{equilibration process is executed using the bond angle bending constant K angle} and the constant ε, and the characteristics of each model are obtained. Calculate the ratio,
(H2) The method according to claim 2, wherein the process returns to (b2) until the respective characteristic ratios calculated in (g2) meet the first permissible condition. The first coarse-grained particles are styrene and the second coarse-grained particles are butadiene.
The physical quantity is the storage elastic modulus.
The second permissible condition is that the storage elastic modulus of the first coarse-grained polymer model and the storage elastic modulus of the second coarse-grained polymer model intersect on the graph, according to claim 2 or 3. The method described. The method according to any one of claims 1 to 4, wherein the physical quantity is at least one of a storage elastic modulus, a loss elastic modulus, and tan δ. A first coarse-grained polymer model with a plurality of linearly bonded first coarse-grained particles and a second coarse-grained polymer model with a plurality of linearly bonded second coarse-grained particles. And the model acquisition department to acquire
A first setting unit for setting _{the bond angle bending constant K angle} of the first coarse-grained particles and the second coarse-grained particles, and
The second setting part that sets the constant ε related to the strength of the potential,
Molecular dynamics calculation execution department that executes molecular dynamics calculation,
A characteristic ratio calculation unit that calculates the characteristic ratio of each model,
A physical quantity calculation unit that calculates a physical quantity that represents the viscoelasticity of each model,
With
Until the characteristic ratio and the physical quantity meet the permissible conditions based on the respective experimental values, the setting of the constant ε by the first setting unit, the setting of the coupling angle bending constant K _angle by the second setting unit, and the setting of the coupling angle bending constant K angle. A system for determining parameters of a roughened polymer model, which is configured to repeatedly execute the calculation of the characteristic ratio by the characteristic ratio calculation unit and the calculation of the physical quantity by the physical quantity calculation unit. _{The bond angle bending constant K angle} is set by the first setting unit and the characteristics by the characteristic ratio calculation unit until each characteristic ratio calculated by the characteristic ratio calculation unit meets the first permissible condition based on the experimental value. Repeat the calculation of the ratio,
When the first permissible condition is satisfied, the constant ε is set by the second setting unit, and each physical quantity is calculated by the physical quantity calculation unit.
Claim that the setting of the constant ε by the second setting unit and the calculation of the physical quantity by the physical quantity calculation unit are repeated until each physical quantity calculated by the physical quantity calculation unit meets the second permissible condition based on the experimental value. 6. The system according to 6. When each of the physical quantities calculated by the physical quantity calculation unit meets the second permissible condition, the _{molecular dynamics calculation execution unit uses the bond angle bending constant K angle} and the constant ε to perform the equilibrium processing. Is executed, the characteristic ratio calculation unit calculates the characteristic ratio of each model, and
_{The coupling angle bending constant K angle} is set by the first setting unit and the characteristic ratio is calculated by the characteristic ratio calculation unit until each of the characteristic ratios calculated by the characteristic ratio calculation unit meets the first permissible condition. 7. The system according to claim 7. The first coarse-grained particles are styrene and the second coarse-grained particles are butadiene.
The physical quantity is the storage elastic modulus.
The second permissible condition is that the storage elastic modulus of the first coarse-grained polymer model and the storage elastic modulus of the second coarse-grained polymer model intersect on the graph, according to claim 7 or 8. Described system. The system according to any one of claims 6 to 9, wherein the physical quantity is at least one of a storage elastic modulus, a loss elastic modulus, and tan δ. A program that causes one or more processors to execute the method according to any one of claims 1 to 5.

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