Polymer model generation method, system, and program

Abstract

To provide a polymer model generation method, a system and a program with which processing is simplified and a model generation speed is improved.SOLUTION: A polymer model generation method includes: setting a virtual space for arranging multiple types of models including a first type model composed of a chain of a plurality of polymer particles and a second type model having at least one particle, to a second cubic volume that is larger than a first cubic volume corresponding to target density; dividing the virtual space into a plurality of virtual rooms which have the same size and arranged in lattice for;, arranging all of the multiple types of models in any of the virtual rooms so that only one model is arranged in one virtual room; repeatedly executing processing of gradually deforming to contract the cubic volume of the virtual space and molecular dynamics calculation processing in which a prescribed temperature and the cubic volume after the contraction are designated until the cubic volume of the virtual space decreases from the second cubic volume to the first cubic volume; and after the cubic volume of the virtual space decreases to the first cubic volume, achieving equilibration through molecular dynamics calculation in which the prescribed temperature and a prescribed pressure are designated.SELECTED DRAWING: Figure 6

Description

[Technical field]

[0001] The present disclosure relates to a method, system, and program for generating a polymer model. [Background technology]

[0002] The polymer model has a plurality of types of models. An example of the 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 that a plurality of polymer models and a plurality of filler models are arranged in a virtual space, and then the volume of the virtual space is compressed to generate a polymer model. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2020-3921 A Summary of the Invention [Problem to be solved by the invention]

[0004] In the method described in Patent Document 1, the polymer model and the filler model are arranged in the virtual space by first placing the model to be newly arranged at random coordinates in the virtual space, and then judging whether the models overlap based on the coordinates of the newly arranged model and the models already arranged. However, since particles have diameters and the extent to which each particle spreads is different, judging whether the models overlap based on the center coordinates of the particles is a complicated process.

[0005] Furthermore, if the overlap determination process determines that a model to be newly placed overlaps with another model that has already been placed, re-placement will be necessary. Depending on the size of the virtual space, the size of the model, and the number of models to be placed, overlap determinations may occur frequently, causing the model placement process to stall and slowing down the model generation speed.

[0006] The present disclosure provides a method, system, and program for generating a polymer model that simplifies processing and improves the speed of generating the model. [Means for solving the problem]

[0007] The polymer model generation method of the present disclosure is a polymer model generation method executed by one or more processors, the method including: 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; and 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 a largest model among the plurality of types of models, the method further including: arranging all of the plurality of types of models in any one of the virtual rooms such that only one model is arranged in one 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 in which a predetermined temperature and a volume after shrinkage are specified; and after the volume of the virtual space becomes the first volume, equilibrating by molecular dynamics calculation in a state in which the predetermined temperature and a predetermined pressure are specified. [Brief description of the drawings]

[0008] [Figure 1] FIG. 1 is a block diagram showing a system according to an embodiment of the present invention. [Diagram 2] 4 is a flowchart showing a process executed by the system. [Diagram 3] FIG. 13 shows a plurality of polymers, a plurality of fillers and a crosslinked particle arranged in a virtual space set in a second volume. [Figure 4] 11A to 11C are diagrams showing the process of shrinking and deforming a virtual space from a second volume to a first volume. [Diagram 5] FIG. 1 is a diagram showing virtual rooms into which a virtual space is divided and various models placed in each room. [Figure 6] A diagram showing how various models are arranged in a virtual room. [Figure 7] FIG. 11 is a diagram showing the process of shrinking and deforming the virtual space in which the models of the second embodiment are arranged from the second volume to the first volume. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] Hereinafter, an embodiment of the present disclosure will be described with reference to the drawings.

[0010] [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 chain. 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 crosslinked particle model having crosslinked particles such as sulfur, or a filler model filled in rubber.

[0011] In Example 1 of this embodiment, as shown in Fig. 3 and Fig. 5, the first type model is a polymer model 2 in which a plurality of polymer particles 20 are bonded in a linear chain. The second type model is a filler model 3 in which a plurality of filler particles 30 are aggregated. The third type model is a bridged particle model 4 having a plurality of bridged particles 40 that are not bonded to each other.

[0012] 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.

[0013] As shown in FIG. 1, the system 1 has a volume setting unit 10, a space division unit 11, a model arrangement unit 12, and a molecular dynamics calculation execution unit 13. The system 1 may have a maximum size specification unit 14, a number of arrangement 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 a processing routine shown in FIG. 2 that 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 units may be distributed using a network, and multiple processors may execute the processing of each unit. That is, one or multiple processors execute the processing. The memory 1b stores multiple types of model data that constitute a polymer model and analysis conditions (predetermined temperature, predetermined pressure, etc.) for executing molecular dynamics calculation.

[0014] In Example 1 of this embodiment, as shown in FIG. 3, the polymer model is a model representing a 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 described in the present disclosure, a filler-filled crosslinked rubber model can be obtained. The crosslinking process is a process in which a molecular dynamics calculation is performed 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 is bound with a predetermined probability, and if it is determined that the particles are bound, the two are bound by a binding potential, and all the crosslinked particles are bound.

[0015] As shown in Fig. 3, the polymer model 2 represents a polymer in which a plurality of polymer particles 20 are linked in a linear or branched manner by a bonding potential (sometimes referred to as a bonding interaction). A non-bonding potential (sometimes referred to as a non-bonding interaction) with other particles is set for each polymer particle 20. 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.

[0016] The filler model 3 shows a model in which a plurality of filler particles 30 are bonded by a bonding potential. A non-bonding potential with other particles is set for each filler particle 30. The filler model 3 is data in which the coordinates of each filler particle 30, the bonding potential between the filler particles 30 in a bonding relationship with each other, and the non-bonding potential with other particles are set. In the embodiment shown in FIG. 3, a plurality of filler particles 30 are bonded in a spherical shape, but this is not limited thereto, and various shapes can be adopted.

[0017] The bridging particle model 4 has at least one particle 40. In this embodiment, one bridging particle model 4 includes a plurality of bridging particles 40, but the number of bridging particles 40 can be changed arbitrarily as long as it is one or more. No bonding potential is set to the bridging particle 40, and a non-bonding potential is set.

[0018] In this embodiment, the bonding potential acting between particles is set to FENE-LJ (Lenard Jones). Specifically, the bonding potential is used for bonding 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.

[0019] In this embodiment, the non-bonding potential acting between particles is set to WCA (LJ potential with only repulsive force). Specifically, the non-bonding potential is set between the filler particle 30 and other particles, between the filler particle 30 and 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 can be changed in various ways.

[0020] 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. Thereafter, as shown in FIG. 4, the volume setting unit 10 gradually shrinks and deforms the virtual space 6 from the second volume V2 to the first volume V1. 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 becomes 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. The rate of change [%] = {volume before the change - volume after the change} / volume before the 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 Fig. 7 shows the process of shrinkage deformation with a ratio = 0.01 / 0.82 = about 0.012 by molecular dynamics calculation of 100,000 steps.

[0021] The second volume V2 may be a preset fixed value if it is sufficiently larger than the first volume V1. In order to accurately determine a sufficient second volume V2, a maximum size specifying unit 14, a number of layout specifying unit 15, a number of rooms determining unit 16, and a second volume specifying unit 17 may be provided as shown in FIG.

[0022] 1 specifies the total number of arrangements of a plurality of types of models. As shown in FIG 5, in the first embodiment, the numbers of the first to third types of models are 5, 4, and 4, respectively, and the total number is 13.

[0023] The space dividing unit 11 shown in FIG. 1 divides the cubic virtual space 6 into a plurality of (N 3 The virtual space 6 is divided into N virtual rooms 60 (number of virtual rooms 60 in total). The virtual rooms 60 are similar to the number 6, and N rooms are arranged on the X axis, N rooms on the Y axis, and N rooms on the Z axis. N is a natural number equal to or greater than 1. 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 determines the number of virtual rooms per side in the virtual space 6 to be N, and 3 Identify N that satisfies the relationship of ≧total value. In the first embodiment, the total number of models is 13, and if N=3, the condition is satisfied.

[0024] The maximum size identifying unit 14 identifies the size of the largest model among a plurality of types of models. Specifically, the maximum size determination unit 14 obtains the size (length of one side) of the filler model 3 from its diameter. The maximum size determination 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 = 0.85. One polymer model 2 in Example 1 has a chain length of 100 x 2 chains = 200 particles, so the volume is 200 / 0.85 = 235.29. The length of one side of a rectangular parallelepiped is 235 1 / 3 =6.17. If the length of one side of 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 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.

[0025] 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 It becomes.

[0026] 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 that are candidates for placement 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 as to be 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.

[0027] The molecular dynamics calculation execution unit 13 shown in FIG. 1 executes a molecular dynamics calculation for particles arranged in the virtual space 6 based on the specified conditions (predetermined temperature, volume, and pressure). In the molecular dynamics calculation, 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 calculation is executed so that the volume setting unit 10 sets the volume and the specified temperature, and the pressure becomes variable. For example, the pressure becomes 0.1 in the second volume V2, and the pressure becomes 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.

[0028] On the other hand, after the volume of the virtual space 6 becomes the first volume V1, molecular dynamics calculations are executed so that the specified temperature and pressure are reached, 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 becomes equal to or less than a threshold). 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) is the volume of the filler-filled uncrosslinked polymer model. This completes the polymer model.

[0029] [How to generate polymer models] 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.

[0030] First, in step ST1, the arrangement number specification unit 15 specifies the total number of arrangements of the multiple types of models that make up the polymer model. In the first embodiment, it is specified as 13. In the next step ST2, the room number specification unit 16 calculates the number of virtual rooms per side in the virtual space 6, which is the cube of N (N 3The number N of virtual rooms 60 is specified so that (N=3) is equal to or greater than the total number of models arranged. In the first embodiment, since the total number of models is 13, N is specified as 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 if the second volume V2 is determined in advance.

[0031] 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 placement 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 execution unit 13 executes 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 molecular dynamics calculation 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.

[0032] Example 2 In Example 2, the polymer model is composed of first to fourth types of models. The first type of model is a first type of polymer model, and has one polymer with a chain length of 100. The second type of model is a second type of polymer model, and has one polymer with a chain length of 100. The third type of model is a bridged particle model 4 having ten bridged particles 40. The fourth type of model is one filler model 3. The first type of models are arranged in ten virtual rooms 60, the second type of models are arranged in five virtual rooms 60, the third type of models are arranged in eight virtual rooms 60, and the third type of models are arranged in four virtual rooms 60. The total number of arranged models is 10+5+8+4=27. FIG. 7 shows a state in which, after each model of the second embodiment is placed 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.

[0033] As described above, the method for generating a polymer model according to the present embodiment is a method for generating a polymer model 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), The size of the model is equal to or larger than the size of the largest model among the models, and the method may further include repeatedly executing a process (ST7) of placing 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, a process (ST8) of gradually shrinking and deforming the volume of the virtual space 6 from the second volume V2 to the first volume V1, and a molecular dynamics calculation process (ST9) specifying a predetermined temperature and a volume after the shrinkage, and after the volume of the virtual space 6 becomes the first volume V1, equilibrating it by molecular dynamics calculation at a specified state of a predetermined temperature and a specified pressure (ST10).

[0034] In this way, the virtual space 6 for arranging a plurality of types of models is divided into a plurality of virtual rooms 60, and each virtual room 60 is equal to or larger than the largest model, and all of the plurality of types of models are arranged in one of the virtual rooms 60 such that only one model is arranged in each virtual room 60. According to this process, if only the management of the virtual rooms 60 in which models have already been arranged is performed, all the models do not overlap, and therefore it is possible to arrange the models without overlapping without implementing a complex overlap determination process. Also, since there is no need to redo the arrangement, it is possible to improve the speed of the model arrangement process.

[0035] As in this embodiment, the total number of arrangements of a plurality of types of models is specified (ST1), the number of virtual rooms 60 per side in the virtual space 6 is set to N (N is a natural number), and N 3 It may also include identifying N that satisfies the relationship >= total number (ST2), identifying the size of the largest model among the multiple types of models (ST3), and identifying 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 making the second volume V2 unnecessarily large, thereby improving reliability and shortening the time required to generate models that would otherwise be required if the second volume V2 were made larger than necessary.

[0036] The program according to this embodiment is a program for causing one or more computers to execute the above method. By executing these programs, it is possible to obtain the effects of the above-mentioned methods.

[0037] Although the embodiments of the present disclosure have been described above based on the drawings, the specific configurations 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-mentioned embodiments but also by the claims, and further includes all modifications within the meaning and scope equivalent to the claims.

[0038] (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. Also, the number of points per side of the virtual room is the same for all three axes (three sides), but may be different.

[0039] (2) In the above embodiment, steps ST1 to ST4 are executed, but if the second volume V2 is determined to be relatively large in advance, steps ST1 to ST4 can be omitted. Accordingly, the units 14 to 17 shown in FIG. 1 can also be omitted.

[0040] The structures employed in the above-described embodiments may be employed in any other embodiment. The specific configurations of the components are not limited to the above-described embodiments, and may be modified in various ways without departing from the spirit of the present disclosure.

[0041] 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 arbitrary, as 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 described using "first," "next," and the like for convenience, this does not mean that it is essential to execute the processes in this order.

[0042] Each unit shown in Fig. 1 is realized by executing a predetermined program on one or more processors, but each unit may be configured with a dedicated memory or a dedicated circuit. In the system 1 of the above embodiment, each unit is implemented in the processor 1a of one 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.

[0043] The system 1 includes a processor 1a. For example, the processor 1a can be a central processing unit (CPU), a microprocessor, or other processing unit capable of executing computer-executable instructions. The system 1 also includes a memory 1b for storing data for the system 1. In one example, the memory 1b includes a computer storage medium, including RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, DVD or other optical disk storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage device, or any other medium that can be used to store desired data and that can be accessed by the system 1. [Explanation of symbols]

[0044] 2...polymer model (first type model), 3...filler model (second type model), 6...virtual space, 60...virtual room.

Claims

1. 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.

2. Identifying a total number of arrangements of the plurality of types of models; The number of virtual rooms per side in the virtual space is N (N is a natural number), ３ Identifying N that satisfies the relationship of ≧ 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.

3. A system comprising one or more processors for carrying out the method of claim 1 or 2.

4. A program causing one or more processors to execute the method according to claim 1 or 2.

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