JP2006064658A - Evaluation method for rubber material - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an evaluation method for a rubber material containing a rubber and carbon black. <P>SOLUTION: The evaluation method for the rubber material, containing at least the rubber and carbon black, includes a process S1 for specifying at least two compounds constituting the rubber from the rubber, a compound model setting process S2 for determining compound models for simulation, based on respective molecular structures with respective to the respective compounds, a carbon model setting process S3 for determining a carbon model, wherein a graphite structure containing carbon atoms arranged on a plane into a hexagonal shape is modeled and an adsorption energy calculating process S4 for calculating the adsorption energy related to a combination of the carbon model and all the compound models that use first-principle calculation. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a method for evaluating a rubber material containing rubber and carbon black.

  Carbon rubber is added to rubber materials used in industrial products such as tires for the purpose of increasing hardness, tensile strength, elasticity, tear resistance, abrasion resistance, and the like. The degree of dispersion of carbon black in the rubber greatly affects the mechanical properties of the rubber. For example, it is known that the wear resistance of a rubber material is improved by increasing the dispersibility of carbon black.

  Carbon black is mixed in the rubber before vulcanization and is kneaded to disperse in the rubber. At this time, if the adsorbability between carbon black and rubber molecules or compounds constituting the same (hereinafter referred to as rubber molecules) is high, the carbon black is adsorbed by various rubber molecules during kneading and is totally absorbed. Spread and good dispersibility can be obtained. On the contrary, when the adsorptivity between carbon black and rubber molecules is low, the dispersibility of carbon black is lowered. Therefore, examining the adsorption energy between rubber and carbon black is effective in evaluating the mechanical properties of rubber. However, it is impossible to experimentally know the atomic level mechanism for the adsorption energy between rubber and carbon black.

  First-principles calculation can be considered as one of the methods for quantitatively grasping the adsorption energy between carbon black and rubber molecules at the atomic level. First-principles calculations do not basically use the results obtained from experiments, but rather calculate the elementary processes of physical and chemical phenomena based on quantum mechanics. However, in consideration of the practical calculation capability, there is a limit to the size of the system that can be calculated in the first-principles calculation. At present, the first principle calculation cannot be applied to the entire system composed of a rubber polymer (or monomer) and the carbon black surface.

  In addition, it is possible to evaluate the energy state of the interface between carbon black and polymer by using empirical interatomic interactions using large-scale molecular dynamics calculations. However, this method has a problem that the calculation accuracy is low because many approximations are included in the calculation. In particular, it is important to ensure sufficient accuracy in the calculation results in order to distinguish a minute energy state difference due to a difference in molecular structure.

  The inventors have conducted various studies on the premise that the first-principles calculation is used. As a result, the rubber is not incorporated into the system as a whole, but at least two compounds constituting the rubber, more preferably the number of carbon atoms. It was found that 10 or less compounds were specified, and a compound model for simulation was set for each compound based on each molecular structure.

  Further, as shown in the cross-sectional view of FIG. 35A, the carbon black CB is obtained by agglomerating graphite laminates c in a spherical shape. FIG. 2B shows a plan view of a single layer of graphite b. The graphite b has a plate shape in which 30 to 40 carbon six-membered rings a are bonded on a single plane. It is not realistic to incorporate all of these as models for calculation. Therefore, the inventors have found that the structure of carbon black is approximated by a graphite structure, modeled and set as a carbon model.

  And it discovered that the adsorption energy of each said compound model and a carbon model was each calculated using a first principle calculation. Thereby, the adsorption energy of each compound constituting the rubber and the carbon black can be evaluated.

  As described above, the present invention can accurately calculate the adsorption energy between the compound constituting the rubber and the carbon black using the first principle calculation while reducing the calculation load, and thus the mechanical characteristics of the rubber. It aims at providing the evaluation method of the rubber material which is useful for evaluation.

  The invention according to claim 1 of the present invention is a method for evaluating a rubber material including at least rubber and carbon black, the compound specifying step of specifying at least two compounds constituting the rubber, and the specified A compound model setting step for determining a compound model for simulation based on each molecular structure for a compound, and a carbon model setting step for determining a carbon model obtained by modeling a graphite structure in which carbon atoms are arranged in a hexagon on a reference plane And an adsorption energy calculation step for obtaining an adsorption energy for the combination of the carbon model and all the compound models using a first principle calculation.

  The invention according to claim 2 is the rubber material evaluation method according to claim 1, wherein the compound has 10 or less carbon atoms.

  According to a third aspect of the present invention, the rubber includes isoprene rubber (IR), butadiene rubber (BR), styrene butadiene rubber (SBR), butyl rubber (IIR), brominated butyl rubber (BrIIR), epoxidized natural rubber (ENR). ), Nitrile rubber (NBR) or ethylene propylene diene rubber (EPDM), wherein the compound contains at least one of a benzene ring, ethylene, ethane, propylene, isobutane, epoxy or hydrogen cyanide. Alternatively, the evaluation method of the rubber material according to 2.

  According to a fourth aspect of the present invention, the adsorption energy calculating step includes a first step of calculating the total energy of the entire system including the carbon model and the compound model using first-principles calculation; A second stage for calculating the total energy of the compound model using the first principle calculation, and a third stage for calculating the total energy of the compound model alone using the first principle calculation, The rubber material evaluation method according to any one of claims 1 to 3, wherein the adsorption energy is calculated by subtracting the sum of the total energy of the carbon model and the total energy of the compound model from energy. .

  In the invention according to claim 5, the first stage sets a unit cell comprising a carbon model having a finite size and a single compound model whose relative position is determined with respect to the carbon model. 5. The rubber material evaluation method according to claim 4, comprising a unit cell setting step and a step of calculating the total energy of the entire system from an overall model in which periodic boundary conditions are applied to the unit cell.

  According to a sixth aspect of the present invention, the carbon model is composed of only one layer of graphite structure, and the unit cell is included in a region obtained by projecting the carbon model in a direction perpendicular to the reference plane. The rubber material evaluation method according to claim 5, comprising the compound model, wherein the overall model is obtained by repeating the unit cell along the reference plane.

  According to a seventh aspect of the present invention, the carbon model has at least two layers of a graphite structure in which dangling bonds extending in a certain direction and parallel to the reference plane are provided at an end, and the unit cell is 6. The compound model according to claim 5, further comprising a compound model that faces a dangling bond of the carbon model at a distance from the dangling bond of the carbon model at a distance in a direction perpendicular to the reference plane. This is a method for evaluating a rubber material.

  The invention according to claim 8 is the rubber material evaluation method according to claim 7, wherein the overall model is obtained by repeatedly arranging the unit cells in a direction perpendicular to the predetermined direction of the dangling bonds. .

  The invention according to claim 9 is the rubber material evaluation method according to claim 7 or 8, wherein a functional group is bonded to the dangling bond.

  In the present invention, at least two compounds are identified from rubber, and a compound model for simulation is set based on the molecular structure of each identified compound. The compound model can reduce the molecular weight compared to the whole rubber. In the present invention, a carbon model having a graphite structure in which carbon atoms are arranged in a hexagonal shape on a plane is set. Such a carbon model can represent the surface of carbon black. By using these models, it is possible to calculate the energy state (electron density distribution) using the first principle calculation by reducing the total number of atoms. In the present invention, in the adsorption energy calculation step, the adsorption energy for the combination of the carbon model and all the compound models is obtained. Based on the calculated adsorption energy between individual compound models and carbon models, the dispersibility and uneven distribution of carbon black can be predicted or evaluated.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
FIG. 1 shows a computer apparatus 1 that is used in carrying out the rubber material evaluation method of the present invention. The computer device 1 includes a main body 1a, a keyboard 1b and a mouse 1c as input means, and a display device 1d as output means. Although not shown, the main body 1a is provided with a processing unit (CPU), a ROM, a working memory, a mass storage device such as a magnetic disk, and CD-ROM and flexible disk drives 1a1 and 1a2. The mass storage device stores processing procedures (programs) for executing various calculations described later. Preferably, a plurality of computer devices 1 are used for parallel processing.

FIG. 2 shows an example of the processing procedure of the evaluation method.
In the present embodiment, first, a compound specifying step for specifying at least two compounds constituting the rubber from the rubber to be evaluated is performed (step S1). In other words, the rubber is virtually decomposed into its constituent compounds. The standard for specifying the compound is not particularly limited, but it is preferable that the compound is decomposed to a size to which the first-principles calculation described later can be applied. Preferably, it can be based on the number of carbon atoms or molecular weight. Specifically, when based on the number of carbon atoms, the number of carbon atoms of each compound is desirably 10 or less, more preferably 8 or less. Further, when the molecular weight is used as a reference, the molecular weight of each compound is desirably 150 or less, more preferably 120 or less.

  In the compound specifying step, it is desirable that all compounds constituting the rubber are specified in the rubber, but two or more typical compounds constituting the rubber may be specified. Can fully evaluate the performance of rubber materials. In the latter case, a part of the compound constituting the rubber is omitted.

  Here, a pneumatic tire is considered as an example of an industrial product using a rubber material. Typical rubbers used for this are isoprene rubber (IR), butadiene rubber (BR), styrene butadiene rubber (SBR), butyl rubber (IIR), brominated butyl rubber (BrIIR), epoxidized natural rubber (ENR), nitrile. Examples include rubber (NBR) or ethylene propylene diene rubber (EPDM). These rubbers are generally composed of a benzene ring, a compound of ethylene, ethane, propylene, isobutane, epoxy or acrylonitrile. Table 1 shows an example in which a compound is specified from each rubber.

  Next, in the present embodiment, a compound model setting step for determining a compound model for simulation based on each molecular structure is performed for each compound (step S2). FIG. 3 shows one ethylene model 2A obtained by modeling ethylene as a compound model 2 by visualization. FIG. 2A is a plan view of the ethylene model 2A, FIG. 2B is a front view, and FIG. 2C is a perspective view.

The ethylene model 2A is modeled three-dimensionally based on the molecular structure (CH ₂ = CH ₂ ) included in ethylene. That is, the constituent atoms and their relative positions are defined equal to that of the actual compound (ethylene in this example). Modeling means an operation of specifying the type and arrangement of constituent atoms such as the carbon atom model 3 and the hydrogen atom model 4 and storing them in the computer device 1 as numerical data.

  The ethylene model 2A includes a carbon atom model 3 that models two carbon atoms, and a hydrogen atom model 4 that models four hydrogen atoms. In the ethylene model 2A, the center of gravity (center) of each of the carbon atom model 3 and the hydrogen atom model 4 is located on a single reference plane P1. In this example, the reference plane P1 is shown in parallel with the XY plane. In this way, the compound model 2 is given one plane as a reference.

FIG. 4 and FIG. 5 show one propylene model 2B modeling propylene as another example of the visualized compound model 2. 4A is a plan view of the propylene model 2B, FIG. 4B is a front view, and FIG. 5 is a perspective view thereof. The propylene model 2B is modeled three-dimensionally based on the molecular structure (CH (CH ₃ ) = CH ₂ ) provided by propylene. That is, the propylene model 2B includes three carbon atom models 3 and six hydrogen atom models 4. In the propylene model 2B, each of the three carbon atom models 3 has a center of gravity located on a single reference plane P1. Each atomic species and relative position (lattice constant) of each carbon atom model 3 and hydrogen atom model 4 is set equal to that of the molecular structure of propylene and the like and stored in the computer apparatus 1.

  In the above two examples, the bond 5 showing the bond of the atomic model is shown. This is merely drawn for easy understanding of the positional relationship between atoms, and is not essential for modeling. Although not shown, other compounds can be modeled in the same manner as in the above example based on the molecular structure of each compound.

  Next, in the present embodiment, a carbon model setting step for determining a carbon model is performed (step S3). 6 and 7 show the visualized carbon model 6. FIG. 6A is a plan view thereof, FIG. 6B is a front view thereof, and FIG. 7 is a perspective view thereof. In the carbon model 6 of this embodiment, the carbon atom model 3 is arranged in a hexagonal shape on a plane, and is composed only of a graphite structure. Specifically, the center of gravity of the spherical carbon atom model 3 is on a single reference plane P2, and they are arranged at the apexes of regular hexagons arranged in a honeycomb shape. Accordingly, the carbon model 6 is provided with one reference plane P2 as in the case of the compound model 2.

  In the present embodiment, in the carbon model 6, the lattice constant of the graphite structure is a = 2.456 angstroms, and the interlayer distance c of the graphite structure is c = 3.348 angstroms. Then, the atomic species (carbon atoms) and their arrangement (lattice constant, etc.) are stored in the computer device 1 for modeling. As described above, carbon black can be said to be a spherical shape in which graphite laminates are gathered. If it is modeled as it is, the calculation load increases significantly and the first principle calculation cannot be applied. For this reason, in the present invention, carbon black is substituted for the carbon model 6 having a graphite structure.

  Next, in the present embodiment, an adsorption energy calculation step is performed in which the adsorption energy for the combination of the carbon model 6 and all the compound models 2 is determined using first principle calculation (step S4).

  In the adsorption energy calculation step, first, one compound model 2 is arbitrarily selected from the plurality of compound models 6. Next, the adsorption energies of the selected compound model 2 and carbon model 6 are calculated. When the calculation of the adsorption energy is finished, another one of the compound models 2 is selected, and the adsorption energy between this and the carbon model 6 is calculated in the same manner. By repeating such a procedure, the adsorption energies of all the compound models 2 and the carbon models 6 can be obtained.

The calculation of the adsorption energy between the carbon model 6 and one arbitrarily selected compound model 2 is a first calculation in which the total energy of the entire system including the carbon model 6 and the compound model 2 is calculated using the first principle calculation. A second stage in which the total energy of the carbon model 6 alone is calculated using the first principle calculation, and a third stage in which the total energy of the compound model 2 alone is calculated using the first principle calculation. The adsorption energy is calculated by subtracting the sum of the energy of the single carbon model 6 and the energy of the single compound model 2 from the energy of the entire system as shown in the following formula (1).
Adsorption energy = Total energy of the whole system-[(Total energy of carbon model alone) + (Total energy of compound model to be adsorbed)]
... Formula (1)

  In the first stage, as shown in FIGS. 8 and 9, for example, a carbon model 6 having a finite size and one compound model 2 (in this example, the relative position of which is determined) are determined. A unit cell setting step for setting a unit cell 7 consisting of ethylene model 2A) is performed. 8A is a plan view showing an example of the unit cell 7, FIG. 8B is a front view thereof, and FIG. 9 is a perspective view thereof. The unit area of the unit cell 7 is indicated by the symbol U.

  In the first principle calculation described later, a periodic boundary condition is used. Since the periodic boundary condition eliminates the influence of the boundary and represents a system having a substantially infinite size, it is considered that one boundary Ua of the unit cell 7 is connected to a boundary Ub on the opposite side of the system ( The same applies to the boundaries Uc and Ud.) The unit cell 7 of the carbon model 6 is continuously repeated in the XY plane direction, that is, the X direction and the Y direction, and the above boundary conditions are given, whereby a pseudo-uniform and infinite graphite structure (graphite) is calculated. Surface structure) and a compound adsorbed thereto are formed in a pseudo manner.

  If the compound model 2 is larger than the unit cell 7 of the carbon model 6, the periodic boundary condition cannot be applied. Therefore, the region U of the unit cell 7 is determined in consideration of the size of the compound model 2 to be adsorbed. In this embodiment, the largest compound among the compounds to be evaluated is a benzene ring. Accordingly, the region U of the unit cell 7 can include a benzene ring model therein.

  The carbon model 6 of the unit cell 7 has a finite size. In this example, the carbon model 6 is composed of 24 carbon atom models 3. In this embodiment, the size of the unit area U of the unit cell 7 is a rectangular parallelepiped having an X direction distance: 3a, a Y direction distance: 2√3a, and a Z direction distance: 4c (c = 3.348 angstroms). That is, it has a size of 7.368 × 8.508 × 13.392 (unit: angstrom) in the X, Y, and Z directions. The unit cell 7 is composed of a carbon model 6 having a single graphite layer in the Z-axis direction from the viewpoint of calculation load. The actual interlayer distance of graphite is 3.348 angstroms. By separating this distance by four times, the influence between the upper and lower graphite layers can be ignored in giving a periodic boundary condition.

  In the unit cell 7 of this example, the reference plane P1 of the ethylene model 2A is parallel to the reference plane P2 of the carbon model 6 and faces the same at a distance r in a direction perpendicular to them. Further, the unit cell 7 of the present embodiment completely includes the ethylene model 2A inside the region where the carbon model 6 is projected in a direction perpendicular to the reference plane P2. Considering the carbon model 6 as a single graphite wall, this overall model is a model for simulating the adsorption energy between the graphite wall (surface) and the compound.

  Further, in the present embodiment, the relative positions of the ethylene model 2A and the carbon model 6 in the XY plane are shown in “site A” (site-A) shown in FIGS. 8 and 9 and in FIGS. 10 and 11. Consider two types of “site B” (site-B). When the site A is viewed in a direction perpendicular to the reference planes P1 and P2 (Z direction), the C = C bond of the ethylene model 2A is in the six-membered ring of the graphite model 6 and the diagonal line of the six-membered ring The layout is located above. On the other hand, the site B is determined as an arrangement in which the C═C bond of the ethylene model 2A is orthogonal to the CC bond of the carbon model 6 when viewed from the Z direction. However, the relative positions of the carbon model 6 and the compound model 2 are not limited to the above two types, and it goes without saying that various changes can be made.

  Next, the step of calculating the total energy (potential energy) of the entire system by first-principles calculation by applying periodic boundary conditions to the unit cell 7 is performed. FIG. 12 schematically shows an overall model M1 obtained by applying the periodic boundary condition. In the overall model M1 of this example, the unit cells 7 are repeatedly arranged along the reference plane P2 according to the periodic boundary condition. Specifically, the overall model M1 is obtained by the unit cells U being repeatedly connected in the X and Y directions and connected to each other. This gives a homogeneous and pseudo-infinitely large system on X2-Y2-Z2.

  The “first-principles calculation” that is the subject of this specification means a calculation that does not depend on the experimental results. For each model, the Schrodinger wave equation is solved based on quantum mechanics, and the interatomic interaction is calculated. Define. Further, specific examples of the first principle calculation include at least “molecular orbital calculation” or “band calculation”. In this embodiment, band calculation is adopted. In the present embodiment, the first principle calculation is used when calculating each energy of the unit cell, the carbon model 6 alone, and the compound model 2 alone. About adsorption energy, it calculates from said Formula (1) using each energy value obtained by the first principle calculation.

  Input information necessary for the band calculation is obtained by the above modeling. That is, only the types of atoms included in the model and their arrangement (lattice constant). By performing the band calculation, the electron density distribution and energy in the ground state of the input atom can be obtained. The energy is the sum of the potential energy of electrons by the nucleus, the kinetic energy of electrons, the coulomb energy between electrons, and the exchange correlation energy, and this value is minimum in the ground state. In the unit cell, it is desirable to change the distance r between the carbon model 6 and the compound model 2 within a predetermined range. In the present embodiment, the distance r is varied in the range of 6.5 to 12.654 (Bohr) (1 Bohr is 0.529 angstrom), and the total energy at each distance is calculated.

A general-purpose first-principles electronic state calculation program can be used for the band calculation. In this embodiment, “ABINIT v4.1.3” is used. The calculation conditions were as follows.
Pseudopotential: TM type GGA pseudopotential k point: 1 × 1 × 1
Cut-off energy: 60 (Ha)

  Table 2 shows the calculation results of the total energy of the entire system including the ethylene model 2A and the carbon model 6. Note that 1 [Ha] is 27.212 [eV].

  In the second and third stages, the total energy of the ethylene model 2A alone and the total energy of the carbon model 6 alone are obtained by the first principle calculation. In these stages, the input information in the band calculation is set as the atomic species of each model and their arrangement state, and the same process as in the first stage is performed. Table 3 shows the calculation results of the total energy of each of the ethylene model 2A and the carbon model 6.

  By substituting the calculation results of Table 2 and Table 3 into Equation (1), the adsorption energy can be calculated for each distance between the carbon model and the ethylene model 2A. Table 4 and FIG. 13 are graphs showing the relationship between the adsorption energy (eV) of the carbon model 6 and the ethylene model 2A and their distance (Bohr).

The graph shows the result of three-dimensional spline fitting performed on the calculation results in Table 4. From this result, the adsorption energy (minimum value) in the ground state is as follows.
<Adsorption energy of ethylene model and carbon model>
Site A: -0.01758 [eV] (distance r = 7.47 [Bohr])
Site B: -0.01586 [eV] (distance r = 7.67 [Bohr])

  By the procedure as described above, adsorption energy between the carbon model 6 and the compound model 2 (an ethylene model 2A in this example) at an arbitrary position can be obtained. And by applying these procedures to the model 2 of all the compounds obtained by the decomposition step, it is possible to obtain the adsorption energy of each compound constituting the rubber and carbon black.

14 and 15 show plan views of a unit cell 7 composed of a propylene model 2B and a carbon model 6 as another example of the compound model 2. The former shows the arrangement of the site A and the latter shows the arrangement of the site B, respectively. Each unit cell 7 includes the propylene model 2B in a region where the carbon model 6 is projected in a direction perpendicular to the reference plane P2. Further, FIG. 16 shows a front view of FIG. 15. As described above, a distance r is set between the reference planes P1 and P2, and the distance between the wall surface of the carbon model 6 and the propylene model 2B is changed variously. The adsorption energy was calculated. FIG. 17 shows a graph of this as described above. From this result, the adsorption energy in the ground state is as follows.
<Adsorption energy of propylene model and carbon model>
Site A: -0.02224 [eV] (distance r = 7.80 [Bohr])
Site B: -0.02070 [eV] (distance r = 7.95 [Bohr])

FIG. 18 shows the results of a similar calculation using Compound Model 2 as a benzene ring model obtained by modeling a benzene ring (C ₆ H ₆ ). In the unit cell 7, as shown in FIGS. 19A and 19B, the reference plane P2 (not shown here) of the carbon model 6 and the plane formed by the six-membered ring of the benzene ring model 2C are parallel to each other. Is arranged. Further, as shown in FIG. 19A, the site A has a 6-membered ring of the benzene ring model 2C right above the 6-membered ring of the carbon model 6, and the site B has a benzene ring as shown in FIG. 19B. The center of the six-membered ring of model 2C is located immediately above the carbon atom model 3 of carbon model 6. According to this result, the adsorption energy in the ground state is as follows.
<Adsorption energy of benzene ring model and carbon model>
Site A: -0.02425 [eV] (distance r = 8.03 [Bohr])
Site B: -0.02610 [eV] (distance r = 7.86 [Bohr])

Further, FIG. 20 shows the result of the same calculation performed by using the compound model 2 as an ethane model 2D obtained by modeling ethane (CH ₃ CH ₃ ). As shown in FIG. 21, the unit cell 7 has one side of an equilateral triangle whose apex is the reference plane P2 of the carbon model 6, the CC bond of the ethane model 2D, and the hydrogen atom model coupled to the carbon atom model on one side. Were set to be parallel. From this result, the adsorption energy in the ground state is as follows.
<Adsorption energy of ethane model and carbon model>
Site A: -0.01685 [eV] (distance r = 8.09 [Bohr])
Site B: -0.01876 [eV] (distance r = 7.92 [Bohr])

FIG. 22 summarizes the above results together with other compounds (hydrogen cyanide: HCN, epoxy: CH ₂ OCH ₂ , isobutane: CH ₃ —CH (CH ₃ ) ₂ ). The adsorption energy of each compound on the wall surface of the carbon model 6 has a shape similar to a typical interparticle interaction model in which a strong repulsive force works at a short distance and a gentle attractive force works at a long distance. Focusing on the energy minimum point considered to be the most stable position during adsorption, the adsorption energy of each compound is about 0.015 to 0.03 [eV], and the adsorption distance is 7.5 to 8.5 [Bohr]. ] Is distributed in the range of about.

  As for the value of adsorption energy, since no reliable experimental value has been reported at present, comparative verification cannot be performed. However, N.Jacobson (2001) et al., First-principles calculation results on adsorption of hydrogen molecules on the graphite wall (N.Jacobson, B.Tegner, E.Schroder, P.Hyldgaard, and BIlumdqvist, Applied Physics Reports 2001-35 ), The adsorption energy is about 0.02 [eV] and the adsorption distance is about 6.2 [Borh]. Therefore, the calculated value of the present embodiment is in agreement with the order of the experimental value, and can be determined as a sufficiently reliable value.

  Further, comparing the sites A and B in the calculation results of the adsorption energy of each compound model 2, the adsorption energy is smaller in the arrangement in which the carbon atom model of the compound model 2 is located at the center of the carbon 6-membered ring of the carbon model 6. There was a tendency to increase (in absolute value). Therefore, in the actual adsorption of each compound on the wall surface of graphite, it is considered that the arrangement with less overlap between carbon atoms is more stable. This can be seen from the fact that in the example of the propylene model, the adsorption energy is higher at the site A where the double bond having a shorter bond distance is arranged at the center of the carbon 6-membered ring. However, the difference in adsorption energy between sites is very small compared to the difference between each compound model. Therefore, it is considered that the influence of the difference between the sites can be ignored as a model of the interparticle interaction constructed when the coarse-grained molecular dynamics calculation is performed.

  FIG. 23 shows a graph in which the vertical axis represents the adsorption energy and the horizontal axis represents the molecular weight of each compound model 2. For molecules composed solely of carbon and hydrogen, the adsorption energy tends to be proportional to the molecular weight.

  As described above, according to the present invention, the rubber to be evaluated is virtually decomposed into each compound, and the adsorption energy between each compound and carbon black is examined, whereby the adsorption energy between the rubber and carbon black is indirectly measured. Can be evaluated. Therefore, in order to obtain a blend capable of improving the dispersibility of carbon black, the adoption, substitution, etc. of a compound having a large adsorption energy can be studied. In addition, by studying the use, substitution, and the like of compounds with similar adsorption energies, it is possible to prevent the uneven distribution of carbon black and the like, which is very useful for actual rubber compounding design. For example, in a pneumatic tire, by controlling the uneven distribution of carbon black in the blend rubber, it is possible to improve the wear resistance, grip force, rolling resistance, and the like in a balanced manner.

Next, another embodiment of the present invention will be described.
As schematically shown in FIG. 24, when the carbon model 6 is considered as a graphite wall, the embodiment calculates and evaluates the adsorption energy Ea between the graphite wall surface of the carbon model 6 and the compound model. . However, since the unit cell 7 has an infinitely continuous graphite wall surface, the graphite side surface cannot be obtained. For this reason, the system which calculates the adsorption energy Eb between a graphite side surface and a compound cannot be obtained. In this embodiment, a model is provided for calculating and evaluating the adsorption energy between the graphite side and the compound model. This can be realized by changing the setting of the unit cell 7 as follows.

  First, as shown in FIGS. 25 and 26, the carbon model 6 is set to have a two-layer graphite structure including a first model portion 6a and a second model portion 6b. The first model portion 6a and the second model portion 6b have respective reference planes P2a and P2b in which the carbon atom model 3 is arranged in a hexagon. The reference plane P2a and the reference plane P2b are parallel to each other and are defined in parallel with the ZX plane in this embodiment. Each reference plane P2a, P2b has a distance R (R ≠ 0) in the Y direction and is separated from the other.

  In addition, the arrangement of atoms in the first and second model parts 6a and 6b is symmetric so that the arrangement of atoms in one model part is equal to the arrangement of atoms in the other model part when the arrangement of atoms is rotated 180 degrees around the Z axis. Have sex. Specifically, the first and second model parts 6a and 6b are composed of a plurality of carbon atom models 3 arranged at the apexes of a regular hexagon that draws a honeycomb, and at least one end in the Z direction, in this example, Z And dangling bonds 9 which are provided at both ends in the direction and are unbonded hands.

  All the dangling bonds 9 extend in a certain direction (Z direction in this example). In this example, there are six dangling bonds 9, and a hydrogen atom model 8 is bonded to all of them. The graphite side surface can be expressed by such a dangling bond 9 and an atomic model other than carbon bonded thereto. As shown in FIGS. 27A and 27B, the dangling bond 9 may be bonded with an OH group model 10 including an oxygen atom model 11 and a hydrogen atom model 8 instead of the hydrogen atom model. good. Furthermore, various functional groups other than these, for example, an arbitrary group such as a COOH group or a COO group can be bonded.

28 to 30 show an example of the unit cell 7 of the present embodiment.
28 is a front view of the unit cell 7, FIG. 29 is a plan view thereof, and FIG. 30 is a perspective view thereof. The unit cell shows an example constituted by the carbon model 6 shown in FIG. 27 and the ethylene model 2A. The same thing as the said embodiment is applicable to ethylene model 2A.

  In the unit cell 7, the ethylene model 2A is set outside a region obtained by projecting the carbon model 6 in a direction perpendicular to the reference plane P2a (or P2b). The ethylene model 2A is set so as to face the dangling bond 9 at a distance in the direction in which the dangling bond 9 extends, that is, the Z direction. Therefore, as shown in FIG. 28, the reference plane P1 of the ethylene model 2A is separated from the carbon model 6 in the Z direction. The distance r between them (r ≠ 0) is shown as the distance in the Z direction between the center of gravity G of the oxygen atom model 11 in the OH group model 10 and the reference plane P1 of the ethylene model 2A. In the adsorption energy calculation step, the distance r is changed variously as in the above-described embodiment. As shown in FIG. 29, the center of the C = C bond of the ethylene model 2A is defined on the center of gravity (upward in the Z-axis direction) of the oxygen atom model 11 of the second model portion 6b.

  Periodic boundary conditions are applied to such unit cells 7 so that the dangling bonds 9 are repeatedly arranged in a direction perpendicular to the certain direction (Z direction). That is, as shown in FIG. 29, by repeatedly arranging the unit cells 7 in the X and Y directions, an overall model M1 as shown in FIG. 31 is obtained. Such an overall model M1 simulates continuous graphite side faces. By obtaining such a model, the adsorption energy between the graphite side surface and the compound can be calculated and evaluated. This can evaluate the influence of the functional group couple | bonded with the dangling bond of the graphite side surface about adsorption energy. Thus, the adsorption energy can be evaluated not only on the surface of graphite but also on the side surface by setting the unit cell and applying the periodic boundary condition.

FIG. 32 is a graph showing the relationship between the adsorption energy (eV) between the carbon model 6 and the ethylene model 2A based on such a model and their distance (Bohr). From this result, it is understood that the adsorption energy (minimum value) in the ground state is as follows.
<Adsorption energy between ethylene model and carbon model (side)>
No OH group: -0.02168 [eV] (distance r = 6.87 [Bohr])
With OH group: -0.00693 [eV] (distance r = 8.09 [Bohr])

33 to 34 are graphs showing the relationship between the adsorption energy (eV) of the carbon model 6 and the propylene model 2B and their distance (Bohr). From this result, it is understood that the adsorption energy (minimum value) in the ground state is as follows.
<Adsorption energy of propylene model and carbon model (side)>
No OH group: -0.02305 [eV] (distance r = 7.13 [Bohr])
With OH group: -0.01223 [eV] (distance r = 8.52 [Bohr])

  The shape of the adsorption energy curve with respect to the side surface of the graphite wall body is similar to the result in the case of the wall surface of the graphite wall body described above. It can also be confirmed that the adsorption energy changes significantly depending on the presence or absence of OH groups bonded to the dangling bonds 9.

It is a perspective view which shows an example of the computer apparatus used by this embodiment. It is a flowchart which shows the process sequence of this embodiment. The ethylene model is shown, (A) is a plan view, (B) is a front view, and (C) is a perspective view. A propylene model is shown, (A) is a top view, (B) is a front view. It is a perspective view of a propylene model. A carbon model is shown, (A) is a top view, (B) is a front view. It is a perspective view of a carbon model. A unit cell (site A) is shown, (A) is a plan view, and (B) is a front view. FIG. A unit cell (site B) is shown, (A) is a plan view, and (B) is a front view. FIG. It is a diagram explaining application of the periodic boundary condition to a unit cell. It is a graph which shows the adsorption energy of a carbon model and an ethylene model. It is a top view of the unit cell (site A) which consists of a carbon model and a propylene model. It is a top view of the unit cell (site A) which consists of a carbon model and a propylene model. It is the front view. It is a graph which shows the adsorption energy of a carbon model and a propylene model. It is a graph which shows the adsorption energy of a carbon model and a benzene ring model. The top view of the unit cell of a carbon model and a benzene ring model is shown, (A) shows the site A, (B) shows the site B, respectively. It is a graph which shows the adsorption energy of a carbon model and an ethane model. The top view of the unit cell of a carbon model and an ethane model is shown, (A) shows the site A, (B) shows the site B, respectively. It is a graph which shows collectively the adsorption energy of a carbon model and a typical compound model. It is a graph which shows the relationship between the molecular weight of a compound model, and adsorption energy. It is the schematic explaining the positional relationship of a graphite wall body and a compound. The carbon model is shown in another embodiment, in which (A) is a front view of the first model portion, and (B) is a front view of the second model portion. (A) is the front view of the carbon model of other embodiment, (B) is the perspective view. It is a front view of the carbon model of other embodiment. It is a front view of the unit cell of other embodiments which consists of the carbon model and an ethylene model. FIG. FIG. It is a perspective view of the whole model. It is a graph which shows the adsorption energy of a carbon model and an ethylene model. It is a perspective view of the unit cell which consists of a carbon model and a propylene model. It is a graph which shows the adsorption energy of a carbon model and a propylene model. (A) is a block diagram of carbon black, (B) is a plan view of graphite.

Explanation of symbols

1 Computer Device 2 Compound Model 2A Ethylene Model 2B Propylene Model 2C Benzene Ring Model 2D Ethane Model 3 Carbon Atom Model 4 Hydrogen Atom Model 6 Carbon Model 7 Unit Cell M1 Overall Model P1 Reference Plane of Compound Model P2 Reference Plane of Carbon Model

Claims (9)

A method for evaluating a rubber material containing at least rubber and carbon black,
A compound specifying step of specifying at least two compounds constituting the rubber;
A compound model setting step for determining a compound model for simulation based on the molecular structure of each of the identified compounds;
A carbon model setting step for determining a carbon model that models a graphite structure in which carbon atoms are arranged in a hexagonal shape on a reference plane;
A method for evaluating a rubber material, comprising: an adsorption energy calculation step for obtaining an adsorption energy for a combination of the carbon model and all the compound models using a first principle calculation.   The method for evaluating a rubber material according to claim 1, wherein the compound has 10 or less carbon atoms. The rubber is isoprene rubber (IR), butadiene rubber (BR), styrene butadiene rubber (SBR), butyl rubber (IIR), brominated butyl rubber (BrIIR), epoxidized natural rubber (ENR), nitrile rubber (NBR) or ethylene. Propylene diene rubber (EPDM),
The rubber compound evaluation method according to claim 1, wherein the compound contains at least one of a benzene ring, ethylene, ethane, propylene, isobutane, epoxy, or hydrogen cyanide. The adsorption energy calculation step includes a first step of calculating the total energy of the entire system including the carbon model and the compound model using a first principle calculation;
A second stage of calculating the total energy of the carbon model alone using first-principles calculations;
A third step of calculating the total energy of the single compound model using first-principles calculation,
4. The rubber according to claim 1, wherein the adsorption energy is calculated by subtracting the sum of the total energy of the single carbon model and the total energy of the single compound model from the total energy of the entire system. Material evaluation method. The first stage includes a unit cell setting step for setting a unit cell consisting of a carbon model having a finite size and one compound model whose relative position is determined with respect to the carbon model;
5. The method for evaluating a rubber material according to claim 4, further comprising: calculating a total energy of the entire system from an overall model in which periodic boundary conditions are applied to the unit cell. The carbon model consists of only one layer of graphite structure,
The unit cell includes one of the compound models included in a region obtained by projecting the carbon model in a direction perpendicular to the reference plane.
In addition, the overall model can be obtained by repeating the unit cell along the reference plane. The carbon model has at least two layers of a graphite structure provided with dangling bonds extending in a certain direction parallel to the reference plane at an end portion;
The unit cell includes a compound model that is outside a region obtained by projecting the carbon model in a direction perpendicular to the reference plane and faces a dangling bond of the carbon model at a distance in the fixed direction. The method for evaluating a rubber material according to claim 5.   8. The rubber material evaluation method according to claim 7, wherein the overall model is obtained by repeatedly arranging the unit cells in a direction perpendicular to the predetermined direction of the dangling bonds.   The method for evaluating a rubber material according to claim 7 or 8, wherein a functional group is bonded to the dangling bond.

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