Apparatus, method, and program for generating crosslinked polymer models

Abstract

This invention provides a device, method, and program for generating a crosslinked polymer model that takes into account the effects of ZnO and ZnS. [Solution] This crosslinked polymer model generation apparatus comprises: a space formation unit that arranges polymer particle models, crosslinked particles, and zinc compounds in a virtual space; a setting unit that sets the proportion of bindable particles and the binding probability between the bindable particles and the crosslinked particles; and a crosslinking reaction processing unit that performs molecular dynamics calculations and, when the distance between the bindable particles and the crosslinked particles falls below a predetermined value, performs a crosslinking reaction process to bind the bindable particles and the crosslinked particles with the binding probability set for the bindable particles. The setting unit sets the proportion of bindable particles within a predetermined range from the zinc compound to be higher than the proportion of bindable particles outside the predetermined range from the zinc compound, and sets the binding probability within a predetermined range from the zinc compound to be higher than the binding probability outside the predetermined range from the zinc compound.

Description

Technical Field

[0001] The present invention relates to an apparatus, method, and program for generating a crosslinked polymer model, and more particularly, to an apparatus, method, and program for generating a crosslinked polymer model having a spatially non-uniform crosslinking distribution.

Background Art

[0002] In order to calculate characteristics such as the viscoelasticity of tire rubber, it is necessary to analyze the crosslinking distribution in tire rubber. In recent years, it has been studied to generate a crosslinked polymer model having a spatially non-uniform crosslinking distribution by applying predetermined conditions to a polymer particle model in which a plurality of particles are connected by computer simulation.

[0003] Patent Document 1 discloses a method of forming a crosslinked polymer model having a non-uniform crosslinked structure by setting a part of the particles constituting the polymer particle model to crosslink with crosslinking agent particles with a higher probability than the surrounding particles.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] Recent studies have revealed that crosslinking points are concentrated around ZnO added as a vulcanization accelerator and ZnS generated from ZnO during the vulcanization reaction. In the conventional models disclosed in prior art documents and the like, the effects of ZnO and ZnS are not considered, and it is insufficient to generate a more realistic crosslinked polymer model.

[0006] The object of the present invention is to provide a device, method, and program for generating a crosslinked polymer model that takes into account the effects of ZnO and ZnS. [Means for solving the problem]

[0007] The apparatus for generating a crosslinked polymer model according to the present invention comprises: a space forming unit that arranges a polymer particle model in which a plurality of coarse-grained particles are linked, crosslinked particles that can bind to bindable particles among the coarse-grained particles, and a zinc compound in a virtual space; a setting unit that sets the proportion of bindable particles among the coarse-grained particles and the binding probability between the bindable particles and the crosslinked particles; and a crosslinking reaction processing unit that performs molecular dynamics calculations on the virtual space and, when the distance between the bindable particles and the crosslinked particles falls below a predetermined value, performs a crosslinking reaction process to bind the bindable particles and the crosslinked particles with the binding probability set for the bindable particles. The setting unit is characterized in that it sets the proportion of bindable particles within a predetermined range from the zinc compound to be higher than the proportion of bindable particles outside a predetermined range from the zinc compound, and sets the binding probability within a predetermined range from the zinc compound to be higher than the binding probability outside a predetermined range from the zinc compound.

[0008] In the above generating apparatus, the proportion of bindable particles within a predetermined range from the zinc compound may be in the range of 10% to 30%, and the proportion of bindable particles outside the predetermined range from the zinc compound may be in the range of 1% to 10%. Furthermore, the distance from the zinc compound to the outer edge of the predetermined range may be 40% or less of the distance between zinc compounds. In addition, the zinc compound may be at least one of ZnO and ZnS.

[0009] The method for generating a crosslinked polymer model according to the present invention includes the steps of: arranging a polymer particle model in which a plurality of coarse-grained particles are linked, crosslinked particles that can bind to bindable particles among the coarse-grained particles, and a zinc compound in a virtual space; setting the proportion of bindable particles among the coarse-grained particles and the binding probability between the bindable particles and the crosslinked particles; and performing molecular dynamics calculations on the virtual space, and when the distance between the bindable particles and the crosslinked particles falls below a predetermined value, performing a crosslinking reaction process to bind the bindable particles and the crosslinked particles with the binding probability set for the bindable particles, characterized in that the proportion of bindable particles within a predetermined range from the zinc compound is set higher than the proportion of bindable particles outside a predetermined range from the zinc compound, and the binding probability within a predetermined range from the zinc compound is set higher than the binding probability outside a predetermined range from the zinc compound.

[0010] In the above production method, the proportion of bindable particles within a predetermined range from the zinc compound is in the range of 10% to 30%, and the proportion of bindable particles outside the predetermined range from the zinc compound may be 1% to 10%. Furthermore, the distance from the zinc compound to the outer edge of the predetermined range may be 40% or less of the distance between the zinc compounds. In addition, the zinc compound may be at least one of ZnO and ZnS.

[0011] The program according to the present invention is characterized by causing a computer to execute the above generation method. [Effects of the Invention]

[0012] According to the crosslinked polymer model generation apparatus, generation method, and program of the present invention, it is possible to generate a crosslinked polymer model that is closer to reality. [Brief explanation of the drawing]

[0013] [Figure 1] This is a schematic diagram illustrating a crosslinked polymer model according to one example of an embodiment. [Figure 2] This is a block diagram of a crosslinked polymer model generation apparatus according to one embodiment. [Figure 3] This figure shows the arrangement of zinc compounds in a virtual space in one example of an embodiment. [Figure 4] This flowchart shows a method for generating a crosslinked polymer model according to one embodiment. [Figure 5] This is a plan view of the crosslinked polymer model produced in Example 1, seen from one direction. [Figure 6] This is a plan view of the crosslinked polymer model produced in Example 2, seen from one direction. [Figure 7] This figure shows the radial distribution function of crosslinked particles in the crosslinked polymer models produced in the examples and comparative examples. [Figure 8] This figure shows the slopes for the embodiment and comparative example in Figure 7 at r=4 to 8. [Modes for carrying out the invention]

[0014] Hereinafter, with reference to the drawings, an example of a crosslinked polymer model generation apparatus, generation method, and program according to the present invention will be described in detail. The embodiments described below are merely examples, and the present invention is not limited to these embodiments. Furthermore, configurations obtained by selectively combining the various components of the multiple embodiments and modifications described below are included in the present invention.

[0015] First, the crosslinked polymer model will be explained with reference to Figure 1. Figure 1 is a schematic diagram illustrating a crosslinked polymer model according to an example of an embodiment. Virtual space 1 is a space where components such as polymer particle models 10 and crosslinked particles 15 are arranged, and a crosslinked polymer model is formed by molecular dynamics calculations in which polymer particle models 10 are bonded to each other via crosslinked particles 15.

[0016] The polymer particle model 10 is composed of a plurality of coarsened particles 12 connected to each other, and the coarsened particles 12 include connectable particles 12a that can be bonded to the crosslinked particles 15. The coarsened particles 12 represent, for example, monomer units. Note that the polymer particle model 10 may have a linear shape in which the coarsened particles 12 are connected linearly, or may have a branched shape in which a part of the connection of the coarsened particles 12 is branched.

[0017] As described above, the crosslinked particles 15 have bonds that can be bonded to the connectable particles 12a. After the molecular dynamics calculation, the bonds of the crosslinked particles 15 that satisfy the predetermined conditions are bonded to the connectable particles 12a.

[0018] <First Embodiment> Hereinafter, a generation device, a generation method, and a program of a crosslinked polymer model, which are examples of embodiments, will be described with reference to FIGS. 2 to 4. <00...​​​​​​​​​​The space formation unit 24 places the polymer particle model 10, crosslinked particles 15, and zinc compound 30 in the virtual space 1. More specifically, the space formation unit 24 receives input from the user via a user interface such as a keyboard or mouse, and places each component, such as the polymer particle model 10, in the virtual space 1.

[0022] The zinc compound 30 is arranged, for example, as shown in Figure 3. Figure 3 is a diagram showing the arrangement of the zinc compound 30 in virtual space 1 in an example of an embodiment. In the example shown in Figure 3, virtual space 1 is a cube with side length LC (lattice constant). Virtual space 1 is divided into eight unit spaces 40 of the same size, and a zinc compound 30 is placed at the center of each unit space 40. That is, in the virtual space 1 shown in Figure 3, eight zinc compounds 30 are arranged, and the distance between the zinc compounds 30 is LC / 2. In this specification, the distance between the zinc compounds 30 refers to the distance between the two closest zinc compounds 30. Note that the arrangement of the zinc compound 30 in virtual space 1 is not limited to the example shown in Figure 3, and the number of unit spaces in virtual space 1 can be changed.

[0023] The zinc compound 30 is, for example, at least one of ZnO and ZnS.

[0024] In the virtual space 1, for example, 50 to 400 polymer particle models 10, each consisting of 50 to 400 coarse-grained particles 12 linked together, are arranged. Also in the virtual space 1, for example, 200 to 600 cross-linked particles 15 are arranged. The same number of polymer particle models 10 and cross-linked particles 15 may be arranged in each unit space 40.

[0025] The setting unit 26 shown in Figure 2 sets the proportion of bindable particles 12a in the coarse-grained particles 12, and the binding probability between the bindable particles 12a and the crosslinking particles 15. More specifically, the setting unit 26 accepts user input via a user interface such as a keyboard or mouse, and sets the proportion of bindable particles and the binding probability.

[0026] The setting unit 26 sets the proportion of bindable particles R1 within a predetermined range from the zinc compound 30 to be higher than the proportion of bindable particles R2 outside the predetermined range from the zinc compound 30, and sets the binding probability P1 within a predetermined range from the zinc compound 30 to be higher than the binding probability P2 outside the predetermined range from the zinc compound 30. As a result, in the molecular dynamics calculation described later, crosslinking reactions are more likely to occur near the zinc compound 30, and a crosslinked polymer model with a uniform crosslinked structure that is closer to reality can be generated.

[0027] The distance from the zinc compound 30 to the outer edge of the predetermined range is, for example, 40% or less of the distance between two zinc compounds 30. In the example shown in Figure 3, the distance from the zinc compound 30 to the outer edge of the predetermined range is 0.2 LC or less. That is, the crosslinking reaction is set to occur easily within a sphere with a radius of 0.2 LC centered on the zinc compound 30.

[0028] R1 is, for example, in the range of 10% to 30%, and R2 is, for example, in the range of 1% to 10%. The value R1 / R2, obtained by dividing R1 by R2, is, for example, in the range of 1.1 to 10.

[0029] P1 is, for example, in the range of 5% to 20%, and P2 is, for example, in the range of 0.5% to 5%. The value P1 / P2, obtained by dividing P1 by P2, is, for example, in the range of 1.1 to 10.

[0030] The crosslinking reaction processing unit 28 performs molecular dynamics calculations on the virtual space 1, and when the distance between the bindable particle 12a and the crosslinking particle 15 falls below a predetermined value, it performs a crosslinking reaction process to bind the bindable particle 12a and the crosslinking particle 15 with the binding probability set for the bindable particle 12a. Note that the zinc compound 30 is set not to move during the molecular dynamics calculations. For example, when the distance between the bindable particle 12a and the crosslinking particle 15 becomes less than or equal to the sum of the radius of the bindable particle 12a and the radius of the crosslinking particle 15, the crosslinking reaction process is performed with a predetermined binding probability.

[0031] Next, a method for generating a crosslinked polymer model will be described with reference to Figure 4. Figure 4 is a flowchart showing a method for generating a crosslinked polymer model according to an example of an embodiment.

[0032] First, a polymer particle model 10 in which multiple coarse-grained particles 12 are linked together, cross-linked particles 15 that can bind to the bindable particles 12a among the coarse-grained particles 12, and a zinc compound 17 are placed in the virtual space 1 (S11).

[0033] Next, the proportion of bindable particles 12a in the coarse-grained particles 12, and the binding probability between the bindable particles 12a and the crosslinked particles 15 are set (S12). At this time, the proportion of bindable particles R1 within a predetermined range from the zinc compound 30 is set higher than the proportion of bindable particles R2 outside the predetermined range from the zinc compound 30, and the binding probability P1 within a predetermined range from the zinc compound 30 is set higher than the binding probability P2 outside the predetermined range from the zinc compound 30.

[0034] Next, molecular dynamics calculations are started (S13), and when the distance between the bindable particle 12a and the crosslinking particle 15 falls below a predetermined value, a crosslinking reaction process is executed to bind the bindable particle 12a and the crosslinking particle 15 with the binding probability set for the bindable particle 12a (S14). After that, it is confirmed that the virtual space 1 has reached equilibrium, and the molecular dynamics calculations are terminated (S15), ending this flow.

[0035] <Second Embodiment> Next, we will describe an apparatus, method, and program for generating a crosslinked polymer model, which is another example of the embodiment. In the following embodiments, the same reference numerals as in the first embodiment are used for the same configurations, and their descriptions are omitted. Also, in the following embodiments, we will omit descriptions of the same effects and modifications as in the first embodiment.

[0036] The crosslinked polymer model generation apparatus according to this embodiment differs from the crosslinked polymer model generation apparatus according to the first embodiment in the execution of the space formation unit 24 and the setting unit 26. When the space formation unit 24 according to this embodiment places the polymer particle model 10, crosslinked particles 15, and zinc compound 30 in the virtual space 1, it places all the crosslinked particles 15 in the vicinity of the zinc compound 30 in the virtual space 1. Here, the vicinity of the zinc compound 30 is, for example, within 30% of the distance between zinc compounds 30. Furthermore, the setting unit 26 according to this embodiment forms bindable particles 12a on all polymer particle models 10 with the same bindable particle ratio, regardless of whether they are within or outside a predetermined range from the zinc compound 30, and sets the same binding probability for all bindable particles 12a. The bindable particle ratio is, for example, in the range of 10% to 30%. The binding probability is, for example, in the range of 0.5% to 5%.

[0037] The method for generating the crosslinked polymer model according to this embodiment differs from the method for generating the crosslinked polymer model according to the first embodiment in the contents of S11 and S12. In S11, all crosslinked particles 15 are placed near the zinc compound 30 in the virtual space 1. In S12, regardless of whether they are within or outside a predetermined range from the zinc compound 30, bindable particles 12a are formed in all polymer particle models 10 with the same proportion of bindable particles, and the same binding probability is set for all bindable particles 12a. The program for the crosslinked polymer model according to this embodiment is a control program that causes an information processing device to execute the above generation method. [Examples]

[0038] The present invention will be further described below with reference to examples, but the present invention is not limited to these examples.

[0039] <Example 1> A virtual space with a lattice constant LC of 34.563072 was prepared. As shown in Figure 3, the virtual space was divided into eight unit spaces, and ZnS was placed in the center of each unit space. In each unit space, 25 polymer particle models, each consisting of 200 coarse-grained particles linked together, were placed, and 50 cross-linked particles were placed. The proportion of bindable particles R1 within a predetermined range from the zinc compound was set to 20%, and the proportion of bindable particles R2 outside the predetermined range from the zinc compound was set to 5%. Furthermore, the binding probability P1 within a predetermined range from the zinc compound was set to 10%, and the binding probability P2 outside the predetermined range from the zinc compound was set to 1%. The predetermined range from the zinc compound was set to a range of 5 from the zinc compound. Example 1 is based on the first embodiment.

[0040] Molecular dynamics calculations were performed under the following conditions. Non-bonding potential: U LJ (r) (Attraction present)

number

number

[0041] Under the above conditions, a cross-linked polymer model was generated according to the flowchart shown in Figure 4.

[0042] <Example 2> In each unit space, all crosslinked particles were placed in the range of 1.02 to 5.0 relative to the zinc compound, the proportion of bindable particles in all polymer particle models was set to 20%, and the binding probability of all bindable particles was set to 1%. Except for these differences, the crosslinked polymer model was generated in the same manner as in Example 1. Example 2 is based on the second embodiment.

[0043] <Comparative Example 1> The crosslinked polymer model was generated in the same manner as in Example 1, except that crosslinked particles were randomly arranged in each unit space, the proportion of bindable particles in all polymer particle models was set to 20%, and the binding probability of all bindable particles was set to 1%.

[0044] <Comparative Example 2> The crosslinked polymer model was generated in the same manner as in Example 1, except that crosslinked particles were randomly arranged in each unit space, the proportion of bindable particles in all polymer particle models was set to 10%, and the binding probability of all bindable particles was set to 1%.

[0045] <Comparative Example 3> In each unit space, crosslinked particles were randomly arranged, the proportion of bindable particles in all polymer particle models was set to 5%, and the binding probability of all bindable particles was set to 1%, except that the crosslinked polymer models were generated in the same manner as in Example 1.

[0046] Figure 5 is a plan view of the crosslinked polymer model produced in Example 1, viewed from one direction, and Figure 6 is a plan view of the crosslinked polymer model produced in Example 2, viewed from one direction. Note that the polymer particle model is not shown in Figures 5 and 6; only the crosslinked particles (filled particles) and ZnS (white particles) are shown. From Figures 5 and 6, it can be seen that in both Example 1 and Example 2, crosslinked polymer models with a spatially heterogeneous crosslinking distribution were produced.

[0047] Figure 7 shows the radial distribution function of crosslinked particles in the crosslinked polymer models produced in the examples and comparative examples, and Figure 8 shows the slopes of the examples and comparative examples in Figure 7 at r=4 to 8. The more non-uniform the degree of dispersion of the crosslinked particles, the larger the angle at r=4 to 8 in Figure 7. Therefore, the larger the value shown in Figure 8, the more spatially non-uniformly the crosslinked particles are distributed. From the results in Figures 7 and 8, it can be seen that the examples were able to produce a crosslinked polymer model with a more spatially non-uniform crosslinking distribution than the comparative examples. [Explanation of Symbols]

[0048] 1 Virtual space, 10 Polymer particle model, 12 Coarse-grained particles, 12a Bondable particles, 15 Crosslinked particles, 20 Generating device, 21 Processor, 22 Memory, 24 Space formation unit, 26 Setting unit, 28 Crosslinking reaction processing unit, 30 Zinc compound, 40 Unit space, LC lattice constant

Claims

1. A space-forming section in which a polymer particle model in which multiple coarse-grained particles are linked, crosslinked particles that can bind to the bindable particles among the coarse-grained particles, and a zinc compound are arranged in a virtual space, A setting unit for setting the proportion of bindable particles in the coarse-grained particles and the binding probability between the bindable particles and the crosslinking particles, The system includes a crosslinking reaction processing unit which performs molecular dynamics calculations on the virtual space and, when the distance between the bindable particles and the crosslinking particles falls below a predetermined value, performs a crosslinking reaction process to bind the bindable particles and the crosslinking particles with the binding probability set for the bindable particles, The setting unit sets the proportion of bindable particles within a predetermined range from the zinc compound to be higher than the proportion of bindable particles outside the predetermined range from the zinc compound, and sets the binding probability within the predetermined range from the zinc compound to be higher than the binding probability outside the predetermined range from the zinc compound, in a device for generating a crosslinked polymer model.

2. The apparatus for producing a crosslinked polymer model according to claim 1, wherein the proportion of bindable particles within the predetermined range from the zinc compound is in the range of 10% to 30%, and the proportion of bindable particles outside the predetermined range from the zinc compound is in the range of 1% to 10%.

3. The apparatus for producing a crosslinked polymer model according to claim 1, wherein the binding probability from the zinc compound within the predetermined range is in the range of 5% to 20%, and the binding probability from the zinc compound outside the predetermined range is in the range of 0.5% to 5%.

4. The apparatus for producing a crosslinked polymer model according to claim 1, wherein the distance from the zinc compound to the outer edge of the predetermined range is 40% or less of the distance between the zinc compounds.

5. The apparatus for producing a crosslinked polymer model according to claim 1, wherein the zinc compound is at least one of ZnO and ZnS.

6. The steps include arranging a polymer particle model in which multiple coarse-grained particles are linked together, crosslinked particles that can bind to the bindable particles among the coarse-grained particles, and a zinc compound in a virtual space, The steps include setting the proportion of bindable particles in the coarse-grained particles and the binding probability between the bindable particles and the crosslinking particles, The process includes the step of performing molecular dynamics calculations on the virtual space, and when the distance between the bindable particles and the crosslinking particles falls below a predetermined value, performing a crosslinking reaction process to bind the bindable particles and the crosslinking particles with the binding probability set for the bindable particles, A method for generating a crosslinked polymer model, wherein the proportion of bindable particles within a predetermined range from the zinc compound is set higher than the proportion of bindable particles outside the predetermined range from the zinc compound, and the binding probability within the predetermined range from the zinc compound is set higher than the binding probability outside the predetermined range from the zinc compound.

7. The method for producing a crosslinked polymer model according to claim 6, wherein the proportion of bindable particles within the predetermined range from the zinc compound is in the range of 10% to 30%, and the proportion of bindable particles outside the predetermined range from the zinc compound is in the range of 1% to 10%.

8. The method for producing a crosslinked polymer model according to claim 6, wherein the binding probability from the zinc compound within the predetermined range is in the range of 5% to 20%, and the binding probability from the zinc compound outside the predetermined range is in the range of 0.5% to 5%.

9. The method for producing a crosslinked polymer model according to claim 6, wherein the distance from the zinc compound to the outer edge of the predetermined range is 40% or less of the distance between the zinc compounds.

10. The method for producing a crosslinked polymer model according to claim 6, wherein the zinc compound is at least one of ZnO and ZnS.

11. A program that causes a computer to execute the generation method described in any one of claims 6 to 10.

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