JP7630367B2 - Polymer model generation method, system, and program - Google Patents

Description

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

The polymer model includes multiple types of models. One example of a polymer model is a filler-filled rubber model. The filler-filled rubber model includes at least a filler model and a polymer model. Patent Document 1 describes placing multiple polymer models and multiple filler models in a virtual space, and then compressing the volume of the virtual space to generate a polymer model.

JP 2020-3921 A

In the method described in Patent Document 1, the polymer model and filler model are placed in virtual space by first placing the new model at random coordinates in the virtual space, and then judging whether the models overlap based on the coordinates of the newly placed model and the models already placed. However, because particles have diameters and the extent to which each particle spreads varies, judging whether the models overlap based on the center coordinates of the particles is a complicated process.

In addition, if the overlap detection process determines that a model to be newly placed overlaps with another model that has already been placed, it will need to be re-placed. Depending on the size of the virtual space, the size of the model, and the number of models to be placed, overlap detection may occur frequently, causing the model placement process to stall and slowing down the model generation speed.

This disclosure provides a method, system, and program for generating polymer models that simplifies processing and improves the speed of model generation.

The polymer model generation method of the present disclosure is a polymer model generation method executed by one or more processors, and includes: setting a virtual space for arranging a plurality of types of models, including a first type model in which a plurality of polymer particles are connected in a linear or branched manner and a second type model having at least one particle, to a second volume larger than a first volume corresponding to a target density; dividing the virtual space into a plurality of virtual rooms of the same size and arranged in a lattice pattern, each of the plurality of virtual rooms being equal to or larger than the size of the largest model among the plurality of types of models; and arranging all of the plurality of types of models in one of the virtual rooms so that only one model is arranged in each of the virtual rooms; repeatedly executing a process of gradually shrinking and deforming the volume of the virtual space from the second volume to the first volume; and a molecular dynamics calculation process specifying a predetermined temperature and a volume after shrinkage; and, after the volume of the virtual space becomes the first volume, equilibrating the volume of the virtual space by molecular dynamics calculation under the specified temperature and pressure.

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. 13 shows a plurality of polymers, a plurality of fillers, and a crosslinking particle arranged in a virtual space set in a second volume. 11A to 11C are diagrams showing the steps of a process for shrinking and deforming a virtual space from a second volume to a first volume. FIG. 1 is a diagram showing virtual rooms into which a virtual space is divided and various models placed in each room. A diagram showing how various models are arranged in a virtual room. 13A to 13C are diagrams showing the process of shrinking and deforming the virtual space in which the models are arranged in the second embodiment from the second volume to the first volume.

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. The polymer model includes at least two types of models including a first type model and a second type model. The first type model is a polymer model in which a plurality of polymer particles are connected in a linear or branched manner. The second type model may be a polymer or may not be a polymer as long as it has at least one particle. The second type model may be, for example, a bridged particle model having bridged particles such as sulfur, or a filler model filled in rubber.

In Example 1 of this embodiment, as shown in Figures 3 and 5, the first type model is a polymer model 2 in which multiple polymer particles 20 are bonded in a linear chain. The second type model is a filler model 3 in which multiple filler particles 30 are aggregated. The third type model is a bridged particle model 4 having multiple bridged particles 40 that are not bonded.

In Example 1, an example will be described in which five first type models (polymer models 2), four second type models (filler models 3), and four third type models (bridged particle models 4) are arranged. One polymer model 2 contains two polymers with a chain length (number of particles) of 100. One filler model 3 contains one filler. One bridged particle model 4 contains five bridged particles 40.

As shown in FIG. 1, the system 1 has a volume setting unit 10, a space division unit 11, a model placement unit 12, and a molecular dynamics calculation execution unit 13. The system 1 may also have a maximum size specification unit 14, a placement number specification unit 15, a number of rooms determination unit 16, and a second volume specification unit 17. Each of these units 10 to 17 is realized by software and hardware working together as the processor 1a executes the processing routine shown in FIG. 2, which is pre-stored 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 units may be distributed using a network, and multiple processors may be configured to execute the processing of each unit. In other words, one or multiple processors execute the processing. The memory 1b stores multiple types of model data that constitute the polymer model and analysis conditions (predetermined temperature, predetermined pressure, etc.) for executing molecular dynamics calculations.

In Example 1 of this embodiment, as shown in FIG. 3, the polymer model is a model representing filler-filled uncrosslinked rubber. It has at least one polymer model 2 as a first type model, a filler model 3 as a second type model, and a crosslinked particle model 4 as a third type model. If a crosslinking process is performed on the filler-filled uncrosslinked rubber model completed by the method disclosed in this disclosure, a filler-filled crosslinked rubber model can be obtained. The crosslinking process is a process in which a molecular dynamics calculation is advanced by a predetermined step, and when a crosslinked particle approaches a crosslinkable point set in the polymer model within a predetermined distance, it is determined whether the crosslinked particle will bond with a predetermined probability, and if it is determined that the particles are bonded, the two are bonded with a bond potential to bond all the crosslinked particles.

As shown in FIG. 3, the polymer model 2 represents a polymer in which multiple polymer particles 20 are connected in a linear or branched fashion by a bonding potential (sometimes referred to as a bonding interaction). Each polymer particle 20 is set with a non-bonding potential (sometimes referred to as a non-bonding interaction) with other particles. The polymer model 2 is data in which the coordinates of each polymer particle 20, the bonding potential between the polymer particles 20 that are in a bonding relationship with each other, and the non-bonding potential with other particles are set.

The filler model 3 shows a model in which multiple filler particles 30 are bonded by a bonding potential. Each filler particle 30 is set with a non-bonding potential with other particles. The filler model 3 is data in which the coordinates of each filler particle 30, the bonding potential between the filler particles 30 that are in a bonding relationship with each other, and the non-bonding potential with other particles are set. In the embodiment shown in FIG. 3, multiple filler particles 30 are bonded in a spherical shape, but this is not limited to this and various shapes can be adopted.

The bridging particle model 4 has at least one particle 40. In this embodiment, one bridging particle model 4 includes multiple bridging particles 40, but the number of bridging particles 40 can be changed as desired as long as it is one or more. No bonding potential is set for the bridging particle 40, and a non-bonding potential is set.

In this embodiment, the bonding potential acting between particles is set to FENE-LJ (Lenard Jones). Specifically, the bonding potential is used to bond between filler particles 30 and between polymer particles 20. The parameter representing the strength of the potential and the parameter representing the particle diameter are set to the same value. These are just examples and can be changed in various ways.

In this embodiment, the non-bonding potential acting between particles is set to WCA (LJ potential with only repulsive forces). Specifically, the non-bonding potential is set between the filler particle 30 and other particles, between the filler particle 30 and the polymer particle, between the polymer particle 20 and other particles, between the bridging particle and other particles, etc. The parameter representing the strength of the potential and the parameter representing the particle diameter are set to the same value. These are just examples, and various changes are possible.

The volume setting unit 10 shown in FIG. 1 sets (or changes) the volume of the virtual space 6 in which the above-mentioned multiple types of models are arranged. As shown in FIG. 4, the volume setting unit 10 sets the volume of the virtual space 6 to a second volume V2 that is larger than the first volume V1 corresponding to the target density (0.85 in this embodiment) when the model is completed. After that, the volume setting unit 10 gradually shrinks and deforms the virtual space 6 from the second volume V2 to the first volume V1, as shown in FIG. 4. It is preferable to suppress the rate of change of the volume in one shrinkage deformation (volume change) to a predetermined value or less. This is because if the volume is changed suddenly, the change in the force acting on each particle due to the volume change may become excessive, which may cause the calculation to fail. It is preferable that the rate of change of the volume in the shrinkage deformation is 0.01% or less of the volume before the change per step of the molecular dynamics calculation involving the shrinkage deformation. Change rate [%] = {volume before change - volume after change} / volume before change x 100. The ratio of the second density at the second volume V2 to the target density is preferably 0.1 or less. Ratio = second density / target density. The example in Figure 7 shows the process of shrinkage deformation with a ratio of 0.01/0.82 = approximately 0.012, using 100,000 steps of molecular dynamics calculations.

If the second volume V2 is sufficiently larger than the first volume V1, a preset fixed value may be used. In order to accurately determine a sufficient second volume V2, a maximum size determination unit 14, a number of layout determination unit 15, a number of rooms determination unit 16, and a second volume determination unit 17 may be provided as shown in FIG. 1.

The placement number determination unit 15 shown in FIG. 1 determines the total number of placements of multiple types of models. As shown in FIG. 5, in Example 1, the numbers of the first to third types of models are 5, 4, and 4, respectively, for a total of 13.

As shown in FIG. 5, the space division unit 11 shown in FIG. 1 divides a cubic virtual space 6 into a plurality of (N ³ ) virtual rooms 60 that are the same size and arranged in a lattice pattern. The virtual rooms 60 are similar to 6, and N are arranged on the X axis, N on the Y axis, and N on the Z axis. N is a natural number of 1 or more. The number of virtual rooms 60 on one side (X axis, Y axis, Z axis) in the virtual space 6 is N. The room number determination unit 16 shown in FIG. 1 specifies N that satisfies the relationship N ³ ≧total value, assuming that the number of virtual rooms per side in the virtual space 6 is N. In the first embodiment, the total number of models is 13, and if N=3, the condition is met.

The maximum size specification unit 14 specifies the size of the largest model among a plurality of types of models.
Specifically, the maximum size specification unit 14 obtains the size (length of one side) of the filler model 3 from its diameter. The maximum size specification unit 14 obtains the size (length of one side) of the polymer model 2 from the number of particles and density. It is preferable to determine the volume of the polymer model so that the number of particles/volume is 0.85. Since one polymer model 2 in Example 1 has a chain length of 100 x 2 = 200 particles, the volume is 200/0.85 = 235.29. The length of one side of the rectangular parallelepiped is 235 ^1/3 = 6.17. If the length of one side of the filler model 3 is 4.85, the polymer model 2 is larger, so the maximum size is 6.17. On the other hand, if the length of one side of the filler model 3 is 9.7, the filler model 3 is larger, so the maximum size is 9.7. The volume of the smaller model is enlarged to match the volume of the larger model. Only the volume is enlarged, and the size of the model is not changed.

1 determines the length of one side of the virtual space 6 and the second volume V2 based on the size of one side of the largest model and the number N of virtual rooms per side in the virtual space 6. In the first embodiment, if the maximum size is 6.17, the length of one side of the virtual space 6 is 6.17×3=18.51, and the second volume V2=18.51/ ³ . In the first embodiment, if the maximum size is 9.7, the length of one side of the virtual space 6 is 9.7×3=29.1, and the second volume V2=29.1/ ³ .

The model placement unit 12 shown in FIG. 1 places all of the multiple types of models in one of the virtual rooms 60 so that only one model is placed in each virtual room 60. FIG. 6 is a schematic diagram of the virtual space 6 (virtual room 60) viewed from a line of sight parallel to the Z axis perpendicular to the X axis and the Y axis. As shown in FIG. 6, first, all of the first type models (polymer models 2) are placed, then, as shown in the same figure, all of the third type models (bridged particle models 4) are placed, and then, as shown in the same figure, all of the second type models (filler models 3) are placed. Selection of models as placement candidates and determination of the virtual room 60 in which the selected models are placed are performed randomly. Here, the virtual room 60 in which a model has been selected and placed once is managed in memory so that it is removed from the placement target. This makes it possible to place multiple types of models in the virtual space 6 without overlapping, and can be realized with simple logic.

The molecular dynamics calculation execution unit 13 shown in FIG. 1 executes molecular dynamics calculations on particles arranged in the virtual space 6 based on the specified conditions (predetermined temperature, volume, and pressure). In the molecular dynamics calculations, the behavior (including the position) of the particles is calculated for each time step (each time point). As shown in FIG. 4, until the volume of the virtual space 6 changes from the second volume V2 to the first volume V1, the molecular dynamics calculations are executed so that the volume setting unit 10 sets the volume and the specified temperature, and the pressure becomes variable. For example, the pressure is 0.1 in the second volume V2, and 1.0 in the first volume V1. That is, until the volume of the virtual space 6 changes from the second volume V2 to the first volume V1, the process of gradually shrinking and deforming the volume of the virtual space 6 by the volume setting unit 10 and the molecular dynamics calculation process by the molecular dynamics calculation execution unit 13 specifying the specified temperature and the volume after shrinkage are repeatedly executed.

On the other hand, after the volume of the virtual space 6 becomes the first volume V1, molecular dynamics calculations are performed to obtain the specified temperature and pressure, the volume becomes variable, and an equilibration process is performed. In the equilibration process, the behavior of each molecule is calculated until the volume of the virtual space 6, i.e., the model, becomes almost constant (the volume change is below a threshold value). The volume is calculated by arranging the particles so as to include all the particles based on the coordinates of each particle arranged in the virtual space 6, and the volume of the smallest cubic or rectangular parallelepiped calculation region (cell) becomes the volume of the filler-filled uncrosslinked polymer model. This completes the polymer model.

[Method of generating polymer model]
A method for generating a polymer model executed by the above-mentioned system 1 will be described with reference to Fig. 2. Here, a first volume, a predetermined pressure, and a predetermined temperature used in the molecular dynamics calculation are set and stored in advance in the memory 1b.

First, in step ST1, the arrangement number specifying unit 15 specifies the total number of arrangements of the multiple types of models constituting the polymer model. In the first embodiment, it is specified as 13. In the next step ST2, the room number specifying unit 16 specifies the number N of the virtual rooms 60 so that the cube (N ³ ) of the number N of virtual rooms per side in the virtual space 6 is equal to or greater than the total number of arrangements of the models. In the first embodiment, since the total number of models is 13, it is specified as N=3. In the next step ST3, the maximum size specifying unit 14 specifies the size of the largest model among the multiple types of models. In the next step ST4, the second volume specifying unit 17 specifies the length of one side of the virtual space 6 and the second volume based on the size of one side of the largest model and the number N of virtual rooms per side in the virtual space 6. Steps ST1 to ST4 can be omitted when the second volume V2 is determined in advance.

In the next step ST5, the volume setting unit 10 sets the virtual space 6 to the second volume V2. Next, in step ST6, the space dividing unit 11 divides the virtual space 6 into a plurality of virtual rooms 60. In the next step ST7, the model placing unit 12 places all of the plurality of types of models in one of the virtual rooms 60 so that only one model is placed in each virtual room 60. Next, steps ST8 and ST9 are repeatedly executed until the volume of the virtual space 6 changes from the second volume V2 to the first volume V1. In step ST8, the volume setting unit 10 shrinks and deforms the volume of the virtual space 6. One shrinkage deformation may be performed at a predetermined rate. In step ST9, the molecular dynamics calculation executing unit 13 executes a molecular dynamics calculation with a specified temperature and a volume after shrinkage specified, and attempts equilibration.
After the volume of the virtual space 6 becomes the first volume V1, the molecular dynamics calculation execution unit 13 performs equilibration by performing molecular dynamics calculations in a state where a predetermined temperature and a predetermined pressure are specified. When the equilibration is completed, the generation of the polymer model is completed.

Example 2
In Example 2, the polymer model is composed of first to fourth type models. The first type model is a first type polymer model and has one polymer with a chain length of 100. The second type model is a second type polymer model and has one polymer with a chain length of 100. The third type model is a bridged particle model 4 having ten bridged particles 40. The fourth type model is one filler model 3. The first type models are arranged in ten virtual rooms 60, the second type models are arranged in five virtual rooms 60, the third type models are arranged in eight virtual rooms 60, and the third type models are arranged in four virtual rooms 60. The total number of models arranged is 10 + 5 + 8 + 4 = 27.

FIG. 7 shows a state in which, after each model of the second embodiment is arranged in the virtual space 6 of the second volume V2, a volume contraction process and an equilibration process are repeated until the volume becomes the first volume V1.

As described above, the method for generating a polymer model according to the present embodiment is executed by one or more processors, and includes the steps of: setting a virtual space 6 for arranging a plurality of types of models, including a first type model (polymer model 2) in which a plurality of polymer particles 20 are connected in a linear or branched manner, and a second type model (filler model 3) having at least one particle 30, to a second volume V2 larger than a first volume V1 corresponding to a target density (ST5); and dividing the virtual space 6 into a plurality of virtual rooms 60 of the same size and arranged in a lattice pattern (ST6), each of the plurality of virtual rooms 60 being a plurality of types of The size of the model is equal to or larger than the largest model among the models, and the method may further include repeatedly executing the steps of arranging all of the multiple types of models in one of the virtual rooms 60 so that only one model is arranged in each virtual room 60 (ST7), gradually shrinking and deforming the volume of the virtual space 6 from the second volume V2 to the first volume V1 (ST8), and performing a molecular dynamics calculation process (ST9) specifying a predetermined temperature and a volume after shrinkage, and equilibrating the virtual space 6 by molecular dynamics calculation at a specified temperature and pressure after the volume of the virtual space 6 becomes the first volume V1 (ST10).

In this way, the virtual space 6 for arranging multiple types of models is divided into multiple virtual rooms 60, and each virtual room 60 is larger than the largest model, and all of the multiple types of models are arranged in one of the virtual rooms 60 so that only one model is arranged in each virtual room 60. According to this process, if one only manages the virtual rooms 60 in which models have already been arranged, all of the models will not overlap, so it is possible to arrange the models so that they do not overlap without implementing complex overlap determination processing. Also, since there is no need to redo the arrangement, the model arrangement processing speed can be improved.

As in this embodiment, the steps may include determining the total number of the multiple types of models arranged (ST1), specifying the number of virtual rooms 60 per side in the virtual space 6 as N (N is a natural number) and determining N that satisfies the relationship ^N3 ≧ total number (ST2), determining the size of the largest model among the multiple types of models (ST3), and determining the length of one side of the virtual space 6 and the second volume V2 based on the size of one side of the largest model and N (ST4).
According to this configuration, the number of virtual spaces 6 and the second volume V2 can be specified so that multiple types of models can be arranged without excess or deficiency without making the second volume V2 unnecessarily large, which improves reliability and shortens the time required to generate models, which would be otherwise caused by making the second volume V2 larger than necessary.

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) In the above embodiment, the virtual space is a cube and the virtual room is also a cube, but this is not limiting. As long as the virtual space and the virtual room are similar in shape, they may be rectangular parallelepipeds.
Furthermore, the number of points per side of the virtual room is the same for all three axes (three sides), but may be different.

(2) In the above embodiment, steps ST1 to ST4 are executed. However, if the second volume V2 is determined to be larger than the first value, steps ST1 to ST4 can be omitted. Accordingly, each of the units 14 to 17 shown in FIG. 1 can also be omitted.

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.

2...Polymer model (first type model), 3...Filler model (second type model), 6...Virtual space, 60...Virtual room.

Claims (4)

1. A method for generating a polymer model, executed by one or more processors, comprising:
setting a virtual space for arranging a plurality of types of models including a first type model in which a plurality of polymer particles are connected in a linear or branched manner and a second type model having at least one particle to a second volume larger than a first volume corresponding to a target density;
Dividing the virtual space into a plurality of virtual rooms of equal size and arranged in a grid pattern;
Including,
each of the plurality of virtual rooms is equal to or larger than the size of the largest model among the plurality of types of models;
The method comprises:
placing all of the plurality of types of models in any one of the virtual rooms such that only one model is placed in one of the virtual rooms;
Repeating a process of gradually shrinking and deforming the volume of the virtual space from the second volume to the first volume, and a molecular dynamics calculation process in which a predetermined temperature and a volume after shrinkage are specified;
The method for generating a polymer model further includes, after the volume of the virtual space becomes the first volume, equilibrating the virtual space by performing a molecular dynamics calculation under conditions in which the specified temperature and the specified pressure are designated. Identifying a total number of arrangements of the plurality of types of models;
Specifying the number of virtual rooms per side in the virtual space as N (N is a natural number), and specifying N such that N ³ ≧the total number;
Identifying a size of a largest model among the plurality of types of models;
and determining the length of a side of the virtual space and the second volume based on the size of a side of the largest model and N. A system comprising one or more processors for executing the method according to claim 1 or 2. A program for causing one or more processors to execute the method according to claim 1 or 2.