JP2010256300A - Method for creating polymer material model - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To efficiently create a polymer material model in a short period of time. <P>SOLUTION: A method includes the steps of: S1 connecting monomer models modeled from a polymer material, monomer, in numbers equal to a molecular weight between entanglement points of the polymer material and setting a unit models of a polymer chain wherein factitious reaction sites have been defined for the monomer models at both ends; S2 relaxing a structure of the unit model to set a random coil-like unit model; S3 arranging a plurality of unit models in a space to set a first polymer material model; S4 relaxing a structure of the first polymer material model and making adjacent two reaction sites combine the unit models getting closer to each other at a predetermined distance or below to grow into a polymer chain model; and S5 stopping the growth step in S4 when an average molecular weight of the polymer chain model contained in the polymer material model becomes almost equal to the average molecular weight of the analytical object polymer material. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a polymer material model creation method capable of efficiently creating a polymer material model used in computer simulation in a short time.

  In recent years, various simulations (numerical calculations) of polymer materials using computers have been proposed. In this type of simulation, molecular dynamics (MD) calculation is mainly performed.

  In molecular dynamics calculation, a material model in which particles consisting of many atoms or aggregates (including molecules) are arranged is set based on the molecular structure of the polymer material to be analyzed, and all the arranged particles are classical. Newton's equation of motion is applied as subject to dynamics. Then, the movement of all particles at each time is tracked.

  According to such molecular dynamics calculation, it is possible to accurately track the microscopic motion of particles. Therefore, it is possible to clarify the nature and movement of a substance without depending on the experimental results. Further, by adjusting the tracking time and the like, an accurate simulation result independent of the initial arrangement of particles can be obtained. Related technologies include the following.

JP 2007-107968 A JP 2006-282929 A

Generally, rubber and polymer materials have a long molecular chain structure intertwined in a complicated manner as shown in FIG. The entangled portion, that is, the molecular weight between the entanglement points K and K shows a substantially fixed value in each polymer material. This is generally called the molecular weight between entanglement points, and it has been found that it can be calculated from the following formula (1) by various experiments.
Entanglement molecular weight Me = ρ · R · T / G ₀ (1)
Where ρ is the density of the polymer, R is the gas constant, G _{0 is the} plateau elastic modulus, and T is the absolute temperature indicating the plateau elastic modulus.

  Therefore, in order to perform an accurate simulation of a polymer material, a polymer material model that correctly reproduces such entanglement of molecular chains, in other words, has the same molecular weight between the entanglement points as the polymer material to be analyzed. It is necessary to create a polymer material model having a polymer model.

  However, in the conventional polymer material model, for example, polymer chain models having a molecular weight (for example, about 100,000 to 300,000) of the polymer material to be analyzed are created in different shapes using the Monte Carlo method or the like. In addition, it is created by performing structural relaxation until it reaches a predetermined density. Such a polymer material model is not guaranteed to have the above-described molecular weight between entanglement points, but rather is considered not to have the molecular weight between entanglement points. In the simulation using such a polymer material model, there is room for further improvement in calculation accuracy.

  In addition, when a monomer model of a polymer material to be analyzed is set and a method of randomly growing the model using structural relaxation is used, the above problem may be solved. However, with this method, even if the latest computer is used, calculation time on the order of several years to several tens of years is required.

  The present invention has been devised in view of the above problems, and efficiently creates a polymer material model including a polymer chain model having a molecular weight between entangled points, and executes a highly accurate simulation. The main purpose is to provide a method for creating a polymer material model that is useful for the future.

  The invention described in claim 1 of the present invention is a method of creating a polymer material model for numerical analysis used in a computer, and a monomer model obtained by modeling a monomer of a polymer material to be analyzed is the high-level model. A step of setting a unit model of a polymer chain that is connected by a number equal to the molecular weight between the entanglement points of the molecular material and has fictitious reaction sites defined in the monomer models at both ends, and the unit model is structured by molecular dynamics calculation Relaxing and setting a random coil unit model; setting a first polymer material model by randomly arranging a plurality of the random coil unit models in a predetermined space; and When the structure of the first polymer material model is relaxed by molecular dynamics calculation and two adjacent reaction sites are less than or equal to a predetermined distance, The growth step of removing a reaction site and generating a bond to form a bond to grow it into a polymer chain model, and the average molecular weight of the polymer chain model included in the polymer material model is the polymer material to be analyzed And a step of stopping the growth step when the average molecular weight becomes substantially equal.

  The invention according to claim 2 is the method for producing a polymer material according to claim 1, wherein the growth step includes a process of reducing the volume of the space and accelerating the growth step with time.

  In the invention according to claim 3, the monomer model includes a hydrogen particle model in which hydrogen atoms are modeled, and a crosslinked body in which a crosslinking agent is modeled in the space of the polymer material model that has undergone the growth process. And further comprising a step of relaxing the structure by randomly arranging the models, and in the step of relaxing the structure, when the distance between the crosslinked body model and the hydrogen particle model is equal to or less than a predetermined distance, the hydrogen particle model The method for producing a polymer material according to claim 1, further comprising a cross-linking treatment in which a main chain atom of the polymer chain model and a cross-linked model are bonded to each other.

  According to a fourth aspect of the present invention, there is provided the polymer material model according to the third aspect, wherein in the crosslinking treatment, the bonding is performed on the condition that two hydrogen particle models approach the distance or less in the crosslinked body model. It is a creation method.

  Further, the invention according to claim 5 is characterized in that the crosslinking treatment includes the step of performing the bonding on the condition that only one hydrogen particle model approaches the distance or less in the crosslinked body model, and a predetermined time. The method for producing a polymer material according to claim 4, further comprising a step of prohibiting the crosslinked body model in which the bonding is performed until bonding with other main chain atoms until the passage.

  According to the present invention, the unit model equal to the molecular weight between the entanglement points of the polymer material to be analyzed is set as one unit, and the unit model is combined with each other and grown to set the polymer chain model. Accordingly, since each polymer chain model has the molecular weight between the entanglement points of the polymer material model, it is possible to perform a highly accurate simulation.

  Further, as in the invention described in claim 2, when unit models are combined and grown, when a reaction acceleration process for reducing the volume of the movable space is included with the passage of time, the reaction sites approach each other. Opportunities can be increased and the growth process can be performed in a short time.

  Further, as in the invention described in claim 3, when the crosslinking treatment is included, a polymer material model having a crosslinked structure can be efficiently created.

  Further, as in the invention of claim 4, the crosslinking treatment is performed by applying a hydrogen particle model of these polymer chain models to a crosslinked body model on condition that two hydrogen particle models are close to the distance or less. They can also be removed and their main chain atoms can be bonded via a cross-linked model.

  According to a fifth aspect of the present invention, the cross-linking treatment includes a step of performing the coupling on the condition that only one hydrogen particle model approaches the distance or less in the cross-linked model. The cross-linked product model in which this bonding is performed may be prohibited from bonding with other main chain atoms until a predetermined time elapses. According to this method, the crosslinking points can be more dispersed.

It is a perspective view of the polymer material model obtained by this embodiment. It is a structural formula of cis 1,4 polybutadiene. It is a flowchart which shows the process sequence of this embodiment. It is a partial top view of the unit model of this embodiment. FIG. 5 is a diagram showing the structure of the unit model of FIG. It is a perspective view of the 1st polymer material model. (A), (b) is a diagram explaining an effect | action when reaction sites approach. It is a perspective view in the middle of reaction of the 1st polymeric material model. It is a graph which shows the example of distribution of the molecular weight of the polymer chain in the 1st polymer material model. It is a flowchart which shows the process sequence of embodiment which produces the bridge | crosslinked polymeric material model. It is a perspective view of the 2nd polymer material model. (A), (b) is a diagram explaining the effect | action of a crosslinked body model. It is a perspective view of the bridge | crosslinked polymeric material model obtained by this embodiment. It is a schematic diagram of the polymer chain explaining the molecular weight between entanglement points.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
In the polymer material model creation method of this embodiment, for example, a polymer material model 1 as shown in FIG. 1 can be created. This model 1 is non-crosslinked, and is composed of a box-shaped cell 2 that partitions a minute space, and a large number of polymer chain models 3 arranged inside the cell 2.

  The polymer material model 1 is a numerical value in which various parameters including coordinates of each node for specifying the shape and position of the cell 2 and the polymer chain model 3 are stored in a storage device of a computer (not shown). It is data. In FIG. 1, what was visualized based on these numerical data is shown. In such a polymer material model 1, for example, physical quantities such as stress and / or strain when deformed by applying an external force are numerically calculated by a computer. Then, by evaluating these physical quantities, it is useful for predicting the development or performance of the polymer material. The computer is not particularly limited, but a supercomputer with high calculation processing capability is preferably used.

  In the present embodiment, cis-1,4 polybutadiene (hereinafter simply referred to as polybutadiene) is taken as an example of a polymer material to be analyzed. However, it goes without saying that a polymer material model can be created for other polymer materials in the same procedure.

As shown in FIG. 2, polybutadiene is obtained by polymerizing a monomer {— [CH ₂ —CH═CH—CH ₂ ] —} composed of a methylene group (—CH ₂ —) and a methine group (—CH—). can get.

  FIG. 3 shows a flowchart of a processing procedure for creating such a polymer material model 1 of polybutadiene. In this embodiment, first, based on the molecular structure of the polybutadiene to be analyzed, the unit model 4 of the polymer chain is created in the storage device of the computer (step S1).

  As shown in FIG. 4, the unit model 4 includes a monomer model 5 obtained by modeling butadiene, which is a polybutadiene monomer, connected by a number n equal to the molecular weight Me between the entanglement points of the polybutadiene and positioned at both ends. Each of the monomer models 5e is created on the assumption that an imaginary reaction site R is defined. In addition, the molecular weight Me between entanglement points is calculated from the above-mentioned formula (1).

The monomer model 5 of the present embodiment is configured by a “Full Atom model” in which all atoms (C and H) are handled as the particle model 6 in a computer simulation. However, for example, it may be modeled according to the “United Atom Model” in which hydrogen atoms are not treated as positive. In this case, CH and CH ₂ are each handled as an aggregate of atoms incorporating the effect of hydrogen atoms.

  The particle model 6 included in the unit model 4 is handled as a mass point of an equation of motion in computer simulation based on molecular dynamics calculation. That is, parameters such as mass, volume, diameter, charge and / or initial coordinates are defined in the particle model 6. Each of these parameters is stored in the computer as numerical information as described above.

  Further, a bond chain 7 is defined between the particle models 6 and 6. The bond chain 7 specifies and constrains the relative position of the particle model 6 and is input to a computer device as vector information, for example.

  Each monomer model 5 has a three-dimensional structure, a bond length that is a bond length between the particle models 6 and 6, and a bond angle that is an angle formed by three consecutive particle models 6 through the bond chain 7. In the four particle models 6 that are continuous through the bonding chain 7, dihedral angles formed by three adjacent particles are defined. Each monomer model 5 changes the bond length, bond angle, and dihedral angle by receiving an external force or an internal force according to the custom. Thereby, the unit model 4 can change the three-dimensional structure.

  The modeling as described above can be processed using, for example, software called J-OCTA manufactured by Japan Research Institute, Ltd.

  The reaction site R is a fictitious particle. This reaction site R is provided as a connection point when the two unit models 4 are connected to grow the length. This will be described in detail later.

  Next, the computer performs a process of relaxing the structure of the unit model 4 by molecular dynamics calculation and transforming it into a random coil-shaped unit model 8 as shown in a simplified manner in FIG. 5 (step S2).

  In this structural relaxation, molecular dynamics calculation is performed on one unit model 4 that is initialized almost straightly as shown in FIG. 4 under a predetermined relaxation time and relaxation conditions under omnidirectional free boundary conditions. Accordingly, the unit model 4 that is straightly initialized is freely moved according to classical mechanics, and the coupling length, the coupling angle, and the dihedral angle are changed, and the random coil-shaped unit model 8 as shown in FIG. Transforms into This process is useful for eliminating the artificial influence at the time of initial setting of the unit model 4 and achieving stabilization or quasi-stabilization of the model.

  In the simulation of structural relaxation, the integration time step, temperature, and / or relaxation time can be arbitrarily determined. For example, necessary and sufficient conditions are set so that the potential energy and stress of the unit model 4 do not substantially change. Such structural relaxation can be processed using, for example, the software described above.

  Next, as shown in FIG. 6, a first high-frequency structure is formed in which a plurality of random coil-shaped unit models 8 having a relaxed structure are randomly arranged inside a cell 2 that partitions a predetermined three-dimensional space. The molecular material model 1a is set (step S3). This processing can also be executed by a computer according to a random number function or the like.

  The cell 2 is a boundary that determines the movable range of the polymer chain model 3, and as described above, the node coordinates of the vertex of the computer are stored. The cell 2 corresponds to a minute portion of the polybutadiene to be analyzed. The cell 2 of this embodiment is defined as a minute cube having a side of 400 nm (nanometer). However, it is not limited to such an aspect, and can be defined in various shapes and / or sizes.

Moreover, the number of the random coil-shaped unit models 8 arranged in the cell 2 is set so that the density in the cell 2 is 0.1 g / cm ³ or less, for example. Further, the unit models 8 are arranged so as not to contact each other. This helps to prevent another atom from coming into the same space and to prevent entanglement before the reaction. Therefore, the cell 2 needs to be formed to be somewhat large as an initial state. In addition, it is not preferable to increase the density because the unit models 8 are likely to come into contact with each other when the unit models 8 are randomly arranged on the computer.

  Next, in the computer, the structure of the first polymer material model 1a is relaxed based on the molecular dynamics calculation, and unit models 8 and 8 satisfying a predetermined condition are combined at the reaction site R to form the polymer chain model 3 A growth process is performed to grow (step S4). The structure relaxation ensemble of this embodiment is performed by NPT, but the ensemble is not particularly limited.

  For structural relaxation, as in step S2, molecular dynamics calculation is performed by a computer to freely move a plurality of initially arranged unitary random coil units 8 within a movable range within the cell 2. Further, in the computer, each position of the unit model 8 that moves is sequentially calculated. Then, as partially shown in FIG. 7 (a), the two random coil-shaped unit models 8 and 8 that move freely by structural relaxation approach each other, and their reaction sites R and R are predetermined. When the distance (in this example, the center-to-center distance) becomes L or less, the computer performs a process of growing these unit models 8 and 8 by combining them.

  Specifically, as shown in FIG. 7B, the computer removes the reaction sites R and R satisfying the above conditions from the unit model 8 and generates a bond (bonding part) B to generate two unit models. The process of combining 8 is performed. Bond B is given the same atomic properties as the main backbone skeleton with reaction site R attached. That is, the bond B of this embodiment is equivalent to a single bond of C and C at the base of the reaction site R. In addition, conditions are defined in advance so that the bonding between the reaction sites at both ends of one unit model 8 is prohibited. Thereby, one longer polymer chain model 3 in which two random coil-shaped unit models 8 are combined can be formed. FIG. 8 shows a first polymer material model 1a during the reaction of the growth process.

  Then, by repeating the growth process described above, the polymer chain model 3 of this embodiment grows sequentially with the reaction site R as a bonding point and the unit model 8 as one unit. For this reason, the polymer chain model 3 grows in a state where the molecular weight between the entanglement points is maintained.

  In the process of the unit model 8 growing one after another at the reaction site R, it is unlikely that molecular chains are entangled at positions other than the reaction site R. This is because the unit model 8 itself has a sufficiently packed density, so that even if another unit model 8 comes into contact therewith, there is no force for entanglement. In addition, the random coil-shaped unit model 8 has been subjected to structural relaxation in advance, and thus tends to maintain a rounded shape although it is deformed.

  Also, such a growth process usually tends to require a lot of calculation time. In particular, in the initial state, in order to arrange the unit model 8 so as not to contact, the cell 2 is formed large, and thus such a tendency becomes remarkable. In the present embodiment, in order to shorten the calculation time of the growth process by the computer, a reaction acceleration process for reducing the volume of the space of the cell 2 with time is performed.

  In the reaction acceleration process, for example, the pressure at the time of starting the growth process is set to, for example, 0.1 atm. Thereafter, each time a predetermined time step elapses, the cell 2 is isotropically reduced and the pressure is reduced. For example, it is desirable to increase by 0.1 atm. As a result, the movement range of the unit model 8 or the polymer chain model 3 is narrowed, and the movement of the unit model 8 is activated, thereby increasing the growth opportunity and accelerating the reaction of the growth process. It should be noted that even if the pressure inside the cell is increased too much, the calculation accuracy may be lowered. Therefore, the upper limit is preferably about 10 atmospheres. Note that it is not preferable that the pressure of the cell S is increased at once, because an abnormal force acts and the unit models 8 may be nested in a place other than the reaction site R.

  Further, in the computer, the molecular weight of each polymer chain model 3 (including the remaining unit model 8) is calculated and stored in the storage device during the growth process. FIG. 9 shows the relationship between the molecular weight and the number of individual polymer material models during the growth process. As described above, by growing the polymer chain model 3 while performing structure relaxation, a molecular weight distribution substantially following a Gaussian distribution can be obtained in the first polymer material model 1a.

  Then, the growth process is stopped when the average molecular weight of one polymer chain model calculated from the individual molecular weights has grown to a state where it is substantially equal to the average molecular weight of the polymer material to be analyzed (step) Y in S5). Thereby, the polymer material model 1 as shown in FIG. 1 is obtained. In FIG. 1, the line types of the polymer chain model 3 are made different for easy understanding. On the other hand, in the case of N in step S5, the growth process in step S4 is continuously performed.

  In the case of this embodiment, the average molecular weight of the polybutadiene to be analyzed is 300,000, and the average molecular weight of the polymer chain model 3 included in the polymer material model 1a is in the range of 90 to 110%, that is, about 230,000 to 330,000. The growth process is stopped when it is included in the range. As described above, the phrase “substantially equal” does not need to be exactly matched, and an error of at least about ± 10% is allowed.

  The polymer material model 1 obtained by the above preparation method is a material model for analysis close to the actual polymer structure because the polymer chain model 3 grows while maintaining the molecular weight between the entanglement points. Therefore, a highly accurate simulation can be executed using such a polymer material model. In addition, after finishing this growth process, the computer performs a process of replacing the remaining reaction site R with the bond B.

  The production method of the present invention can also be applied to a model of a crosslinked polymer material. An example of a procedure for creating such a model is shown in FIG.

  In this embodiment, first, a second polymer material model 1b (FIG. 11) in which a crosslinked body model D is randomly arranged in the cell 2 of the polymer material model 1 obtained in step S6 is defined. (Step S7).

  The crosslinked body model D of the present embodiment is expressed by particles and is handled as a mass point in the simulation. This crosslinked body model D models a crosslinking agent added to an actual polymer material, for example, a sulfur compound such as monosulfide, disulfide, or polysulfide. Further, the crosslinked body model D is randomly arranged so as not to overlap with the polymer chain model 3. In addition, the compounding quantity of the crosslinked body model D can be defined arbitrarily.

  Next, the structure relaxation of the second polymer material model 1b in which the crosslinked body model D is arranged is performed again by the computer. Thereby, the relative position of the crosslinked body model D and the polymer chain model 3 can be changed. In the structure relaxation, as shown in FIG. 12A, it is determined whether or not the particle model 6 of two hydrogen atoms of the polymer chain model 3 has approached a predetermined distance K or less in the crosslinked body model D. (Step S9) When approaching, the particle model 6 of those hydrogen atoms is deleted, and the carbon particle model that is the main main chain atom is passed through the bridge model D as shown in FIG. (Step S10). Then, it is determined whether or not all the cross-linked models D have reacted as described above (step S11). If the result is true, the process ends. On the other hand, if the result is false, step S8 and subsequent steps are repeated.

  By performing such processing, a crosslinked polymer material model 1c as shown in FIG. 13 can be set.

  In the above-described embodiment, when the particle model 6 of two hydrogen atoms approaches a single crosslinked body model D within a certain distance, these are combined. For this reason, for example, the so-called intramolecular cross-linking in which two hydrogen particle models 6h in one polymer chain model 3 are cross-linked frequently occurs, and the cross-linking points are concentrated at a specific position. May not be reproducible. In order to prevent such intramolecular crosslinking, for example, the following embodiment can be adopted.

  That is, in this process, the computer is coupled to the crosslinked body model D when only one hydrogen atom particle model 6 approaches the distance K or less. Then, until a predetermined time elapses after bonding, the crosslinked model D that has been bonded is given a condition for prohibiting bonding even when the particle model 6 of another hydrogen atom approaches. Then, after a predetermined time has elapsed, the above condition is released from the crosslinked model D, and the above bonding is allowed. That is, when one particle model 6 of one hydrogen atom approaches again below the distance K, it is combined with the particle model 6. In addition, although the said fixed time is not specifically limited, For example, about 1000-10000 steps (about 0.3-0.8 nanosecond in time) are desirable.

  According to this method, the cross-linked model D bonded to the particle model 6 of one hydrogen atom can move in the cell 2 without a binding reaction with the particle model 6 of another hydrogen atom for a while. . Therefore, the probability that the cross-linked model D is bonded to the hydrogen atom particle model 6 of the other polymer chain model 3 is increased. Thereby, the probability of the above-mentioned intramolecular crosslinking is reduced, and the crosslinking points can be dispersedly arranged.

  Although the embodiment of the present invention has been described above, it is needless to say that the present invention can be modified and implemented in various modes without being limited to the above-described embodiment.

1 Polymer Material Model 2 Cell 3 Polymer Chain Model 4 Unit Model 5 Monomer Model 6 Particle 7 Bonded Chain 8 Unit Model B Bond D Crosslinked Model R Reaction Site

Claims (5)

A method of creating a polymer material model for numerical analysis used in a computer,
A monomer model obtained by modeling the monomer of the polymer material to be analyzed is connected in a number equal to the molecular weight between the entanglement points of the polymer material, and a polymer chain in which fictitious reaction sites are defined in the monomer models at both ends. Setting the unit model;
The unit model is structurally relaxed by molecular dynamics calculation to set a random coil unit model;
A step of randomly setting a plurality of the random coil-shaped unit models in a predetermined space to set a first polymer material model;
The structure of the first polymer material model is relaxed by molecular dynamics calculation, and when two adjacent reaction sites are less than or equal to a predetermined distance, the reaction sites are deleted and a bond is generated to form a bond. A growth process to grow into a polymer chain model by
A step of stopping the growth step when an average molecular weight of a polymer chain model included in the polymer material model becomes substantially equal to an average molecular weight of the polymer material to be analyzed. How to create a molecular material model.   The method for producing a polymer material according to claim 1, wherein the growth step includes a process of accelerating the growth step by reducing the volume of the space with time. The monomer model includes a hydrogen particle model obtained by modeling a hydrogen atom,
And further comprising a step of relaxing the structure by randomly arranging a crosslinked body model obtained by modeling a crosslinking agent in the space of the polymer material model that has undergone the growth step, and
In this structural relaxation step, when the distance between the crosslinked body model and the hydrogen particle model is equal to or less than a predetermined distance, the hydrogen particle model is deleted and the main chain atoms and the crosslinked body model of the polymer chain model are deleted. The method for producing a polymer material according to claim 1, comprising a cross-linking treatment for binding to the polymer material.   4. The method of creating a polymer material model according to claim 3, wherein the cross-linking treatment is performed on the cross-linked body model on the condition that two hydrogen particle models are close to the distance or less. The cross-linking treatment is performed on the cross-linked body model on the condition that only one hydrogen particle model approaches the distance or less, and
5. The method for producing a polymer material according to claim 4, further comprising the step of prohibiting the cross-linked model that has been bonded to bond with other main chain atoms until a predetermined time elapses.

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