JP4665614B2 - Polymer material design system - Google Patents

Description

The present invention relates to efficiently design to Resid stem polymeric materials suitable for the desired purpose.

  The main conventional methods for improving the macroscopic properties (friction properties, viscoelasticity, optical properties, etc.) of polymer materials are obtained by experimentally measuring the properties of the material using real polymer materials. A different real polymer material if the measured value does not meet a given target (eg, a polymer material that differs in at least one of the factors that may affect the properties, such as polymer structure or monomer composition) The above-mentioned properties of the material were experimentally measured again using, and this procedure was repeated until a satisfactory polymer material was obtained. However, it takes manpower and time to actually obtain various polymer materials and experimentally measure the macro characteristics of these materials. Moreover, since it is difficult to accurately control environmental conditions in actual experiments, the accuracy and reproducibility of the experiments tend to be insufficient.

  On the other hand, attempts have been made to predict macroscopic properties of materials by computer simulation based on molecular dynamics methods. In general, molecular dynamics tracks the movement of individual particles that make up a material. It is expected that the macroscopic properties of materials can be predicted from the trajectories (trajectories) of the movements of those particles. Patent document 1 is mentioned as a prior art document relevant to this kind of technique.

International Publication No. 97/06496 Pamphlet

However, it is inappropriate to simply apply such a molecular dynamics method in predicting the macro properties of polymer materials. This is taken into account to predict the very high number of atoms in a polymer material (usually at least 10 ³ or more, often 10 ⁴ or more) in a polymer material and to predict the macro properties of the polymer material This is related to the large scale of power time and length (in other words, the relaxation time is long). Under these circumstances, it is difficult to obtain useful results at realistic calculation costs even if it is attempted to predict the macro-characteristics of a polymer material by molecular dynamics simulation at the atomic level that tracks the trajectory of individual atoms. In order to reduce the calculation cost, a technique of handling one molecule (for example, benzene) modeled as one particle is also known. However, a model that represents a single molecule of polymer as a single particle cannot explain the “entanglement effect” that has an important effect on the macroscopic behavior of polymer materials. Patent Document 1 also describes that the time correlation function of a polymer can be estimated empirically from the molecular chain length of the polymer in order to shorten the calculation time. However, the estimation based only on the molecular chain length is insufficient in accuracy, and the balance between the usefulness of the obtained result and the calculation cost is insufficient.

  An object of the present invention is to provide a method for efficiently designing a polymer material having properties suitable for a desired application. Another object of the present invention is to provide a system for efficiently designing a polymer material having predetermined properties.

  One invention disclosed herein relates to a method of designing a polymeric material suitable for a desired application. The method includes obtaining a coarse-grained model of the polymer material using a predetermined set of parameters. In this coarse-grained model, the polymer contained in the polymer material has an adjacent mass point that represents two or more monomer units each having a finitely-extendable-nonlinear-elastic FENE) modeled as a bead-spring chain connected by a spring. The design method also includes predicting at least one property of the polymeric material using the coarse-grained model. Further, the method includes predicting the characteristics of another polymer material in which at least one of the parameters included in the parameter group is different from the polymer material. It also includes grasping (or monitoring) the influence of the parameter on the characteristics from these prediction results. The prediction of the characteristics can be performed by simulation (typically computer simulation) based on a molecular dynamics method (MD method). In a preferred embodiment, the property can be predicted by simulation based on a nonequilibrium molecular dynamics method (NEMD method).

  According to such a design method, parameters corresponding to polymer materials that are expected to exhibit good properties (ie, optimized or optimized polymer materials) without experimentally measuring the properties of the actual polymer material. You can find a combination of values. In addition, since the characteristics of the polymer material are predicted using the coarse-grained model in this way, it is possible to efficiently perform the characteristic prediction for many types of polymer materials having different parameter values. Therefore, useful results can be obtained while reducing the calculation cost.

  The design method can be applied to the design of polymer materials for various uses whose performance can be effectively improved by optimizing macro characteristics such as coefficient of friction, viscoelasticity, and optical characteristics. For example, suitable applications of a polymer material having a low coefficient of friction include a low-friction polymer part formed by molding the polymer material, a low-friction coating that is disposed on the surface of a member to form a low-friction surface, and the like. be able to. The method disclosed herein is suitable as a method for designing a polymeric material suitable as a component of a low friction coating. When designing a polymer material having characteristics of friction characteristics in this way, using the coarse-grained model, at least the friction coefficient of the polymer material (coarse-grained) expressed using a predetermined parameter is determined. It is good to predict.

In a preferred aspect of the invention disclosed herein, the predetermined parameter group includes at least the following parameters. One of these parameters is a chain length parameter that represents the chain length of the polymer contained in the polymer material. The other is a flexibility parameter that represents the flexibility (flexibility) of the polymer. The other is a density parameter that represents the density of the polymer material.
According to the parameter group including these parameters, a coarse-grained model including an accurate description of the “entanglement effect” of the polymer molecules contained in the polymer material can be obtained. In modeling, the chemical details of the polymer molecules constituting the polymer material (especially chemistry with a length scale below the persistence length described below, such as bond vibrations) are ignored or It is reflected in a simplified form in two or more parameters. By this, the macro characteristic (for example, friction coefficient) of the polymer material can be predicted efficiently and accurately.

The “chain length parameter” will be described in more detail.
The chain length of the polymer molecules contained in the polymer material (related to the molecular weight or degree of polymerization and proportional to the molecular weight or degree of polymerization for linear homopolymers or linear random copolymers) is the relaxation time of the polymer material (Relaxation time) and response speed to external force, etc. By using such chain length parameters, the macro properties of the polymer material can be accurately and efficiently simulated.

In one preferred embodiment of the invention disclosed herein, the polymer chain length is parameterized as dimensionless quantities represented by the number N _b of mass points (beads) contained in a single polymer chain. (Refer to Examples described later). This makes it possible to obtain a universal model in which the polymer chain length is expressed as a dimensionless quantity. The polymer chain length (dimensionless amount) in such a universal model is obtained by applying a reference amount (details will be described later) according to the type of polymer to a certain length (chain length of the polymer). Can be converted. Therefore, from one universal model, the chain length (dimensional quantity) of various polymers corresponding to the chain length (dimensionalless quantity) of the universal model can be obtained.

Incidentally, the number N _b of beads per Kusariichi present polymers, e.g., number of monomer units contained in a single polymer chain N (i.e., the degree of polymerization of the polymer) of the characteristic ratio of the polymer (Characteristic ratio, C _∞ ) divided by (ie, N _b = N / C _∞ ). Therefore, characteristic ratio C _∞ can be said to represent the number of monomer units in the mass of each. ). This characteristic ratio C _∞ is an amount introduced to map the actual shape of the polymer chain onto a random walk chain of a certain step length, and in a random walk of step length a and number N of steps, The square R ² of the end-to-end distance R in the path follows the number of steps. That is, R ² = Na ² . The square of the end-to-end distance R per molecular weight of a real polymer (R ² / M), the atomic bond length a between monomer units, and the monomer mass m ₀ are determined experimentally (eg, light scattering or Through neutron scattering). Here, also in the coarse-grained model, the relationship of R ² = N _b b ² between the number N _b (number of steps) of the mass points per polymer chain and the distance b (step length) between these mass points. Should be kept. Therefore, b can be calculated by b ² = R ² / N from the molecular weight M = Nm ₀ and R ² / M = (N _b / M) b ² = m ₀ b ² . The characteristic ratio is defined by C _∞ = b ² / a ² . Here, a is a bond length between monomer units (chemical monomers) in an actual polymer, and b is a length (between mass points) estimated from an end-to-end distance per molecular weight experimentally measured for the polymer. Bond length).

The value of the characteristic ratio C _∞ for various polymers, for example can be easily obtained from the following known literature (I) ~ (III).
(I). RS Porter and JF Johnson, Chem. Rev. 66 (1966)
(II). J. Brandrup and EH Immergut (eds), Polymer Handbook (Wiley-Interscience, New York, 2nd ed., 1975).
(III) SM Aharoni, Macromolecules 16 1867 (1978).
Table 1 shows a part of the characteristic ratio _C∞ described in these documents. The method disclosed here can be implemented by adopting the value of the characteristic ratio C _∞ described in these documents or Table 1 as necessary.

Here, the meanings of the symbols in Table 1 are as follows.
l _p : persistence length [Å],
m _b : mass [g / mol] of particles (physical monomer),
a: bond length between monomer units (chemical monomers) [モ ノ マ ー],
E: binding energy between particles (physical monomers) [meV],
C _∞ : characteristic ratio,
R _Θ : measured value of the rotation radius of the polymer chain N _b : number of particles (physical monomer) contained in one polymer chain,
A: cross section of the polymer chain (tube cross-section)
N _c : critical molecular weight.
The bottom column of Table 1 shows values of various parameters for a typical model polymer (FENE model polymer) often used in this technical field.

  If the number of beads per polymer chain is too large or too small, the accuracy of simulation (and thus usefulness) may tend to decrease. The invention disclosed here is preferably applied to, for example, a polymer that is modeled with the number of beads per polymer chain being about 3 to 400 (more preferably about 5 to 50). In terms of a dimensional quantity, it can be preferably applied to a polymer having an average chain length in the range of about 10 to 500 nm (more preferably in the range of about 50 to 300 nm).

Next, the “flexibility parameter” will be described.
This flexibility parameter can be expressed, for example, using the persistence length l _p of the polymer. The persistence length l _p is defined in one aspect as a tangent-tangent correlation along the actual polymer backbone. Based on the scattering experiment, the sustained length according to this definition is
Can be obtained. Here, t _p is at position p on the outer shape of the polymer, is a unit vector of the tangent to the outer shape of the polymer chains. T _{p + s} is a unit vector of a tangent to the outer shape of the polymer chain at a position p + s (s is an arbitrary position) on the outer shape of the polymer.
Further, the persistence length l _p is calculated from the following equation from the characteristic ratio C _∞ and the bond length a between monomers:
(See Table 1).
The persistence length is an index representing the length of the polymer chain that maintains linearity (that is, the stiffness of the polymer chain). The greater the persistence value, the higher the rigidity of the polymer chain (and hence the bending). Or low flexibility). The persistence length of the polymer is determined by its chemical properties, and phenomena on a length scale below the persistence length (such as bond vibrations between atoms) contribute little to the macro behavior (eg, coefficient of friction) of the polymer material. Therefore, the macro characteristics of the polymer material can be accurately and efficiently simulated by parameterizing the flexibility of the polymer using this sustained length.

As the flexibility parameter used in the method disclosed herein, a dimensionless quantity (l _p / b) obtained by dividing the sustained length l _p of the polymer by the bond length b between the mass points of the polymer can be adopted. (See examples below). Thereby, a universal model in which the flexibility of the polymer is expressed as a dimensionless quantity can be obtained. By using such a universal model, the flexibility (dimensional quantity) of various polymers corresponding to the flexibility (non-dimensional quantity) of the universal model can be obtained in the same manner as the above description of the chain length parameter. .

  Further, as the “density parameter”, for example, a dimensionless quantity represented by using the number of polymer molecules (number of polymer chains) included in the unit volume of the system to be simulated can be used. A dimensionless quantity expressed using the number of mass points included in the unit volume may be used. In a typical aspect of the method disclosed herein, the simulation is performed using a periodic boundary condition in at least one direction. A universal model in which the basic cell in the periodic boundary condition is the unit volume, and the density of the system is parameterized as a dimensionless quantity using the number of molecules or the number of mass points (beads) of the polymer contained therein. Can be obtained. By using the universal model, the density (dimensional quantity) of various systems corresponding to the density (non-dimensional quantity) of the universal model can be obtained in the same manner as the above description of the chain length parameter.

In the present invention , in order to predict the properties, a first wall comprising a surface having a polymer coating to which one end of the polymer chain is anchored, and a surface facing the surface having the polymer coating, the polymer coating comprising: the simulation and a second wall with a front surface that Yusuke in condition for relative movement at a predetermined shear rate (shear rate). By applying a force in the shear direction (external force) to the polymer material (polymer coating) in this way and simulating the entropy change (stress relaxation state), the macro characteristics of the polymer material (eg, time-dependent friction coefficient) ) Can be appropriately predicted.

  Predicting the coefficient of friction of a polymer material by simulation based on a molecular dynamics method includes obtaining a stress tensor from the trajectory of the mass included in the coarse-grained model, and shear stress of the stress tensor. Predicting the coefficient of friction of the polymer material from the ratio of the shear stress component and the normal stress component can be included. This stress tensor is obtained, for example, through a tensor-like virial expression from the time function of the configuration of each mass point (including position and moment information).

  In one preferred embodiment of the invention disclosed herein, the simulation is performed by controlling the normal force on a wall having a polymer coating (eg, the first wall). This normal force means a force (or load) applied in a direction perpendicular to the wall. It is preferable to perform the simulation under conditions controlled so that the normal force is equal to or less than a predetermined value or so that the normal force is within a predetermined range. By appropriately setting the value or range of the normal force, a more useful simulation result (for example, a predicted coefficient of friction) can be obtained according to the intended use of the polymer material. The value of the normal force can be controlled, for example, by adjusting the size of the basic cell in the y direction (direction perpendicular to the wall) in the periodic boundary condition (see an example described later).

  Another invention disclosed herein relates to a system for designing a polymer material suitable for a desired application using a coarse-grained model of the polymer material. The design system includes at least material parameters including a chain length parameter representing a chain length of a polymer contained in the polymer material, a density parameter representing a density of the polymer material, and a flexibility parameter representing the flexibility of the polymer. Means for obtaining. Further, it includes means for obtaining a simulation condition parameter including at least a time parameter indicating a length of time for performing the simulation, a temperature parameter indicating the temperature of the system for performing the simulation, and a cell size parameter indicating the size of the simulation box. . The design system also includes means for performing a simulation based on molecular dynamics on the coarse-grained model of the polymer material using those parameters. Also included is a means for outputting the simulation result. Here, in the coarse-grained model, the polymer is modeled as a bead-spring chain in which adjacent mass points each representing two or more monomer units are connected by a finite-elongation nonlinear elastic spring (FENE).

In the invention disclosed herein, the simulation may further include a first wall including a surface having a polymer coating to which one end of the polymer chain is tethered, and a surface facing the surface having the polymer coating. a second wall under the condition that the relative movement at a predetermined shear rate with a front surface that have a polymer coating. The share rate may be included in the simulation condition parameter as a share rate parameter representing the share rate. In another preferred embodiment, the simulation is performed by controlling a normal force to the first wall. The normal force may be included in the simulation condition parameter as a control normal force parameter that specifies a value or range of a normal force applied to the first wall.

  Hereinafter, preferred embodiments of the present invention will be described in detail. It should be noted that technical matters other than the contents particularly mentioned in the present specification and necessary for the implementation of the present invention can be grasped as design matters for those skilled in the art based on the prior art. The present invention can be carried out based on the technical contents disclosed in the present specification and the common general technical knowledge in the field.

  In the disclosed invention, a coarse-grained molecular model (coarse) is used to design a polymer material having properties suitable for the desired application (eg, low coefficient of friction). Visualization model). This parameter group is selected so that the flexibility, topology (polymer molecule length, branching, connectivity, etc.), excluded volume, etc. of the polymer molecules contained in the polymer material are appropriately reflected. This makes it possible to obtain a coarse-grained model that takes into account the influence of the “entanglement effect” of the polymer molecules contained in the polymer material. In modeling, the chemical details of the polymer molecules that make up the polymer material are ignored or reflected in a simplified form in one or more parameters included in the parameter group. . This makes it possible to calculate the dynamics by applying Newton's law and to predict the macro characteristics of the polymer material using statistical mechanical techniques. For example, one or more characteristics among viscosity, viscoelasticity, friction characteristics (friction coefficient), orientation, time-dependent characteristics, static characteristics, optical characteristics, and the like can be predicted.

  In the coarse-grained model, polymer molecules are modeled as bead-spring chains in which adjacent mass points are connected by FENE springs. Each polymer molecule includes a plurality of mass points, and each mass point represents a plurality of chemical units (typically monomer units). The mapping between the actual polymer and the coarse-grained polymer can be achieved using a conversion rule based on known or experimentally available basic data about the polymer. Such basic data may include the polymer's persistent length, end-to-end distance, molecular weight, density, and the like.

  The coarse-grained model is a many-body model characterized by the potential between mass points. A molecular dynamics method that has already been developed can be used as an effective method for solving this many-body problem (that is, calculating the dynamics and mechanical / chemical properties of this coarse-grained model). In order to derive the friction coefficient by calculation based on the molecular dynamics method, the following statistical physics method can be used.

That is, N mass points in the n dimension (each mass point has coordinates r _i and moments p _i , where i = 1,..., N and the space dimension n is 2 or 3. ) And the given two-body or many-body dynamical law F ({r}) = − ∇ _r V ({r}) is subject to some constraints (temperature or pressure, in some cases Follow Newton's equation of motion under flow constraints. These differential equations can be properly solved using a symplectic iteration scheme such as velocity Verlet method (eg Allen, MP, Tildesley DJ: Computer simulation of liquids, Clarendon Press, Oxford, 1987). From the solution of the fine fraction equation, the time function of the coordinates r _i and moments p _i with _{(r i (t), p} i (t)), to extract the macroscopic quantities as the time average of these trajectories it can.

For example, the microscopic Kirkwood equation for the stress tensor σ is expressed as follows:
In the above formula
It is a relative distance between the particles in position ^{r (i, α), =} 1 for N _c book chain contained in the system alpha, ..., a N _c, are included in each strand particle For the number N _b , i = 1,..., N _b . The total number (total number) N _s of particles contained in the system is represented by N _s = N _c N _b (here, for the sake of simplicity, the molecular weight distribution of the polymer chains contained in the system is monodispersed) Shall be.) In the example disclosed herein, one particle (mass) from represent a certain number of chemical units (monomer units), the number of particles N _b included in one strand is directly proportional to the molecular weight of the polymer. This value of N _b is related to the chemical nature of the polymer, and in particular depends on the flexibility (flexibility) of the polymer.
In the above formula, v ^{(i, α)} represents the intrinsic velocity of the particle i in the chain α. The quantity U in the above formula is the interaction potential between the site i in the chain α and the site j in the chain β. By definition, the term (i, α) = (j, β) is excluded from the equation. In the simulation disclosed here, the interaction potential differs between sites belonging to the same chain and between sites belonging to different chains. Between different chains, the particles interact through a Lennard-Jones repulsion potential (which ensures an excluded volume) that is symmetric in the radial direction of the chain. Particles that are adjacent to each other along the main chain in one chain receive an attractive force that is symmetrical in the radial direction of the chain, depending on the FENE potential. Neighboring particles also receive a bending potential depending on the given duration.

  The inventor solved the equation of motion to obtain the positions and velocities for all particles contained in the periodic simulation cell with volume V, and extracted the stress tensor from the above equation containing all these positions and velocities. This stress tensor includes the contribution of shear stress and normal stress (stress normal to the wall). The transient friction coefficient can be extracted from the trajectory as the ratio of the shear stress component and the normal stress component. The coefficient of friction is obtained by time averaging the transient coefficient of friction over a time range (eg, the entire simulation time). This coefficient of friction is defined as the ratio of shear stress to normal stress (or the ratio of shear force to load) in the stress tensor σ.

The calculation of trajectories r (i) and v (i) used to calculate the stress tensor above can also be used to calculate other macroscopic quantities such as optical tensors, structure factors, etc.
For example, the optical tensor n is defined by the following equation. Therefore, the optical tensor n can be obtained from the trajectory.

The structure factor (structure factor) S (q) may be measured transfer wave vector of the polymer chain having a mass per one N _b (wave vector transfer, neutron scattering deuterated polymer. ) Q is defined as follows. Therefore, the structure factor S (q) can be obtained from the trajectory.

These macroscopic quantities (optical tensor, structure factor, etc.) can be extracted from the simulation results for the coarse-grained model disclosed herein. Therefore, the simulation can predict the influence (anisotropy or dependence) of the polymer chain length, density, shear rate, etc., on these macroscopic quantities. On the other hand, the optical tensor n can be experimentally measured by birefringence and dichromatism, and the structure factor S (q) is proportional to the scattering intensity in the scattering experiment. Therefore, the effectiveness of the coarse-grained model used in the simulation can be confirmed by comparing the macroscopic amount extracted from the simulation result with the macroscopic amount obtained experimentally. For example, the end-to-end distance R can be obtained experimentally from the structure factor S. In the simulation, the end-to-end distance R can be extracted from S, but can also be obtained directly from the coordinates by the following equation.

Further, the rotation radius of the polymer chain can be obtained from the trajectory. The size of the simulation cell (simulation box) is preferably determined so as to be smaller than the radius of gyration. The size Lx in the x direction, the size Ly in the y direction, and the size Lz in the z direction of the simulation box are the number N _{s of} particles (physical monomers) included in the system, the bulk density (number density) of the polymer material, n = N _b / V (where N _b is the number of particles contained in one polymer chain, V = LxLyLz), the surface density of the polymer material σ = N _c / Lx / Ly (N _c is The number of polymer chains included in the system), and Lz. For example, by increasing the value of N _b , the box size can be selected so as to be always larger than the turning radius.

In one preferred embodiment of the invention disclosed herein, for a coarse-grained model of a polymer material obtained using a predetermined parameter group, a chain length parameter representing a chain length of a polymer included in the polymer material, the polymer The properties of the polymer material are predicted by molecular dynamics simulation using the bendability parameter representing the bendability and the density parameter representing the density of the polymer material. It is preferable to determine the parameters so that all the parameters constituting these parameter groups are dimensionless. For example, as the chain length parameter, the number N _b (dimensionless amount) of mass points contained in one polymer chain can be adopted. Further, as the flexibility parameter, a dimensionless quantity obtained by dividing the continuous length l _p of the polymer by the bond length b between the mass points of the polymer can be adopted. As the density parameter, a dimensionless quantity (a dimensionless bulk density) expressed by using the number of polymer chains included in a unit volume (for example, the volume V of the simulation cell) and / or the number of mass points included in the volume. ) Can be used. In addition, a dimensionless quantity (dimensionless surface density) expressed using the number of polymer chains included in a predetermined area may be used.

Thus, in the simulation using the parameter group consisting of dimensionless parameters, the result of the simulation is also obtained as a dimensionless quantity. Such a dimensionless quantity can be converted into a dimension quantity by multiplying it with an appropriate reference quantity. This reference amount is expressed in units of mass (m), energy (ε), and length (σ). These three amounts (dimension conversion factors) are different for each polymer, and can be determined, for example, from the FENE model polymer having the parameters shown in Table 1 as follows.
Further, based on the melting point T of the material, the energy ε can be estimated using the relationship of ε = Tk _b (k _b : Boltzmann constant). Ratios listed in Table 1
Is measured at the melting point T. Usually, these temperatures (material melting points) are in the range of 400-500K. For polytetrafluoroethylene, the measured temperature in the amount listed in Table 1 is 460K.

The dimension conversion factor depends on the SI physical quantity. For example, the dimensionless quantity η ^* [SI unit: kg ¹ m ⁻¹ s ⁻¹ ] with respect to the viscosity is
Can be converted into a dimensional viscosity η.
Further, the dimensionless quantity t ^* [SI unit: s, that is, kg ⁰ m ⁰ s ¹ ] relating to time is given by
Can be converted into a time t having a dimension.
More generally, the SI unit is
The dimensionless quantity Q ^* can be converted into a dimensional quantity by the following equation.
Note that 1K = 1.38066 × 10 ⁻²³ J = 8.61735 × 10 ⁻⁵ eV.

Table 1 gathers data on persistence length, characteristic molecular weight, shape and size for various polymers. For example, the dimension conversion factor of polytetrafluoroethylene (PTFE) is obtained as follows using the data in Table 1. Here, N _c ^FENE represents the Nc values of FENE model polymers shown in Table 1, l _p ^FENE shows a l _p value of FENE model polymers shown in Table 1.
As a result, the dimensionless shear stress τ ^* = 1 (SI unit: kg ¹ m ⁻¹ s ⁻² , and thus α = 1, β = −1, γ = −2 in the above conversion formula) is the actual shear stress. τ = τ ^* × m ^{1 + (-2/2)} × σ ^{-1 + ( -2 )} × ε ^{-(-2) / 2} = τ ^* × σ ^-3 ε ¹ = 0.8 [MPa] To be calculated. Further, it is calculated that T ^* = 1 as a dimensionless temperature (simulation parameter) corresponds to an actual temperature T = εT ^* = 460 [K]. The normal stress (normal stress) of 1 MPa is equal to 1 N / mm ² .

Further, the surface density (number of mass points per unit area) in the simulation code can be set to, for example, σ ^* _surf (dimensionless quantity) = 0.5. Here, the physical unit of the surface density is m ⁻² (kg ⁰ m ⁻² s ^0. That is, in the above conversion formula, α = 0, β = −2, γ = 0). The surface density σ _surf = σ ^* _surf × m ^{0 + 0/2} × σ ^{−2 + 0} × ε ^−0/2 = 0.5 × σ ⁻² is obtained. As calculated above, for PTFE σ = 20Ｆ, the actual surface density (expressed in dimensional quantities) of PTFE corresponding to this dimensionless surface density is σ _surf = 0.5 × 20. ^-2 [Å- ² ] = 0.00125 [Å- ² ].

  As a method of obtaining an actual polymer corresponding to a suitable combination of parameter values found by design, a method of selecting an existing polymer material (commercially available product, etc.) that fits well with the combination of parameter values is adopted. Can do. In addition, a polymer material that is well suited to such a suitable combination of parameter values may be newly produced. Alternatively, it is also possible to obtain a polymer material that is more suitable for a combination of the above-mentioned preferable parameter values by optimizing the composition, production conditions, etc. of the existing polymer material. Such adaptation of the parameter values can be achieved by adjusting one or more of the molecular weight, topology, flexibility, surface density of the polymer material, bulk density, etc. included in the polymer material, for example.

  The molecular weight of the polymer is adjusted by the polymerization conditions such as polymerization temperature, type and amount of polymerization catalyst, monomer concentration, presence / absence and use of chain transfer agent, presence / absence and type of solvent, polymerization atmosphere, polymerization pressure, etc. (To better match the target parameter value combination). The polymer topology (existence and degree of branching, etc.) is the type of monomer, the copolymerization ratio when two or more monomers are used, polymerization temperature, type and amount of polymerization catalyst, monomer concentration, chain transfer It can be adjusted according to the presence or absence and the type of agent used. The flexibility of the polymer depends on the type of monomer, the copolymerization ratio when two or more monomers are used, the polymerization mode (for example, the ratio of cis / trans / vinyl bond in polybutadiene), the stereoregularity of the polymer ( tacticity) and the like. The polymerization mode and stereoregularity can be adjusted by polymerization conditions such as the type of polymerization catalyst and the type of solvent.

  The density of the polymer material can be adjusted by subjecting the polymer material to a heat treatment under predetermined conditions (combination of temperature and time). Usually, it is preferable to perform the heat treatment in a temperature range between the glass transition temperature and the melting point of the polymer contained in the polymer material. It is also possible to adjust the density of the polymer material according to the temperature profile when the polymer material is cooled from the molten state. As another method for adjusting the density of the polymer material, there can be exemplified a method in which an external force is applied to the polymer material. For example, a process of isotropically pressing the polymer material, a process of applying anisotropic (for example, uniaxial or biaxial) tensile stress, compressive stress, or shear stress to the polymer material alone or as appropriate Can be used in combination. By appropriately selecting the conditions for performing these treatments, the bulk density or surface density of the polymer material, or both, can be adjusted.

  The method disclosed herein is, for example, a polymer material containing one or more of the polymers exemplified below (typically a polymer material substantially composed of one or more of these polymers). Can be applied to any design. Preferably, it is applied to the design of a polymer material containing one of these polymers (more preferably a polymer material substantially composed of the polymer).

[Polymer having a main chain composed of carbon-carbon bonds]
Polyolefins such as polyethylene, polypropylene, poly 1-butene and polyisobutylene.
Polymers obtained by polymerization of conjugated dienes, for example, polyconjugated dienes such as polyisoprene and polybutadiene. The bonding mode of the main chain may be any of cis, trans and vinyl, and these bonding modes may be mixed at an arbitrary ratio.
Polyaromatic vinyls such as polystyrene, poly α-methylstyrene, and poly m-methylstyrene.
Halogenated hydrocarbons such as polytetrafluoroethylene.
Poly (meth) acrylic acid esters such as polymethyl acrylate, polymethyl methacrylate, polybutyl methacrylate, polyhexyl methacrylate, poly 2-ethylbutyl methacrylate, polyoctyl methacrylate and polydodecyl methacrylate.
Other vinyl polymers such as polyacrylic acid, polyvinyl acetate, polyvinyl alcohol, polyacrylamide, polyvinyl chloride and the like.

[Polymer having main chain containing ester bond]
Polydecamethylene adipic acid, polydecamethylene succinic acid, polydecamethylene sebacic acid, polybisphenol A carbonate, polyethylene terephthalate and the like.
[Polymer having a main chain containing an ether bond]
Polyoxyethylene, polyoxypropylene, polyoxytetramethylene, polyoxy-2,6-dimethyl-1,4-phenylene and the like.
[Polymer having main chain containing amide bond]
Polyε-caprolactam, polyhexamethylene adipamide (ie, 6,6-nylon) and the like.
[Polymer having main chain containing siloxane bond]
Polydimethylsiloxane and the like.

  The method disclosed herein can be preferably applied to the design of a polymer material suitable as a component of a polymer material that exhibits favorable friction characteristics (friction coefficient, conditions causing stick-slip phenomenon, etc.) according to a desired application. . For example, it is suitable as a method for designing a polymer material for polymer coating that is arranged on the surface of a member made of another material (metal material, ceramic material, resin material, etc.) and adjusts its friction behavior. An example of a preferable application object is a polymer material for a polymer coating (low friction coating) for reducing the friction of the surface of a piston and / or valve of an internal combustion engine. Another example is a polymer coating applied to the surface of the brake disc and / or brake pad.

The present invention can be implemented, for example, using a system configured as follows.
<Example 1>
In the following, an example of a system for designing a polymer material suitable as a component of a low friction coating will be described. This system performs a simulation on the polymer material using a coarse-grained model of the polymer material obtained using a predetermined parameter group described later. In the coarse-grained model, the polymer contained in the polymer material is described as a bead-spring chain in which adjacent mass points, each representing two or more monomer units, are connected by a finite stretch nonlinear elasticity (FENE) spring.

  This design system handles a polymer coating in which one end of a polymer chain contained in the polymer material is anchored to the surface of a wall (eg, a metal wall). Therefore, the simulation is performed under the condition that a first wall having a surface having the polymer coating and a second wall having a surface facing the coating surface and having or without the polymer coating exist. . The first wall and the second wall can be moved relative to each other. The design system consists of (1) a system in which both the first and second walls have a polymer coating, ie a symmetrical polymer coating (brush-brush sliding), and (2). Simulations can be performed for a system with a polymer coating and a second wall without a polymer coating, ie an asymmetric polymer coating (brush-mica slip). The design system also has the capability to simulate (3) a system with a symmetric polymer coating and further solvent, and (4) a system with an asymmetric polymer coating and further solvent. . In the coarse-grained model, individual molecules contained in the solvent are represented as mass points. These solvent particles interact with polymer beads according to the laws of mechanics (in this example introducing the Lennard-Jones potential).

  Such simulations can monitor the amount of friction coefficient, squared force fields, bond length dispersion, shear stress, normal stress, snapshots, and the like. This design system further has a function of creating a moving image based on the obtained simulation result.

  As shown in FIG. 1, the design system includes an input device 10 having a display and a keyboard, a computer 20 connected to the input device 10 and having an arithmetic device 22 and a storage device 24, and a display and a computer connected to the computer 20. And an output device 30 having a keyboard. As the input device 10 or the output device 30, for example, a general computer user terminal can be used. In a preferred embodiment, the input device 10 is also used as the output device 30. The storage device 24 stores source code of a program that implements each function described above via the arithmetic device 22. In addition, the storage device 24 can store simulation results performed in the past, parameter groups input in the past, source code edited by the user, and the like.

In this design system, simulation conditions can be set by the following parameters.
[Simulation time]
Set the true simulation time in seconds. Moreover, it is good also as a structure which replaces with true simulation time and inputs physical simulation time (time which actually calculates). However, since the physical time required for the calculation depends on the basic design (architecture) of the computer used, it is usually more convenient to specify the true time than the physical time.

[System temperature (dimensionless quantity)]
The temperature of the system to be simulated is set to T = 1 (the actual system temperature corresponds to about 400K). In order to obtain useful results, it is necessary to set the temperature so that the polymer contained in the polymer material does not undergo excessive alteration (thermal decomposition, crosslinking reaction, etc.) when the actual polymer material is placed at that temperature. preferable. Usually, depending on the intended use of the polymer material to be designed, it is appropriate to set the temperature at or near the temperature at which the polymer material is actually used.

[Simulation box size (Dimensionless amount)]
In this design system, a three-dimensional system having a periodic boundary condition with respect to the flow direction (x direction) is handled. In the source code of the program used here, the setting is fixed so that the flow direction (x direction) is the direction from the left to the right of the screen. The vertical direction of the screen is the flow gradient direction (flow gradient direction, y direction). The size of the simulation box corresponds to the size of the basic cell in the periodic boundary condition. Here, the size of the simulation box (referred to as X, Y, and Z box sizes, respectively) is set for each of the x direction, the y direction, and the z direction. In the example disclosed here, each box size is parameterized as a dimensionless quantity using the length of the basic cell.
X box size: defined as a number obtained by dividing the size of the simulation box with respect to the flow direction (x direction) by the basic cell length.
Y box size: defined as a number obtained by dividing the size of the simulation box with respect to the direction of flow inclination (y direction) by the basic cell length.
Z box size: Defined as the number of simulation boxes divided by the basic cell length for the flow vorticity direction (z direction). A normal snapshot shows a state viewed from the z direction.

[Share rate]
The share rate (shear rate) represents a velocity gradient. Here, the share rate is set as a value obtained by dividing the x component of the velocity at the upper end of the simulation cell by the cell size (dimension amount) in the vertical direction (y direction). Share rate = 0 means that the system is in a dormant state. Further, the shear rate = 1 means that the surface to which the polymer adheres (the surface of the wall) moves by an amount corresponding to the diameter of one polymer chain per unit time. In other words, the length of one unit time is determined by the chemistry of the polymer.

[Control normal force (dimensionless quantity)]
The simulated system is characterized by a stress tensor. This stress tensor is determined through a tensorial virial formula from the polymer and solvent particle configuration at any time step. The program code of the present system has a function of evaluating a normal pressure (normal pressure) in the flow tilt direction (vertical direction or y direction) from the stress tensor. More specifically, normal force is defined as the yy component of the stress tensor. In this system, the simulation can be performed under conditions in which the magnitude of the normal pressure (or load) is appropriately controlled according to the use (type of application) of the polymer material. For example, the value of the normal force during simulation can be kept constant (this is a typical situation when experimentally measuring the frictional force). The control normal force may be set to a value corresponding to a load that is preferably selected as a measurement condition when experimentally measuring the coefficient of friction of the polymer material. it can. The value of the control normal force is adjusted dynamically during the simulation run starting from the initial configuration. That is, when the input value of the control normal force is not zero, the value of the control normal force is adjusted by changing the Y box size until the desired control normal force is reached during the simulation. When the input value of the control normal force is zero, the simulation is performed without considering the control normal force. That is, this parameter is optional.

In this design system, a coarse-grained model of the polymer material can be obtained using the following parameter group.
[Polymer chain length (dimensionless amount)]
In this design system, the chain length of a polymer contained in the polymer material (here, a linear polymer is described as an example) is parameterized as the number of mass points (beads) contained per molecule of polymer. As described above, the number of mass points is determined by dividing the degree of polymerization of the polymer (in the case of a homopolymer, the molecular weight of the polymer / the molecular weight of the monomer) by the characteristic ratio _C∞ . When the molecular weight of the polymer contained in the system is monodisperse, the number of mass points per polymer chain (ie, the chain length parameter used in the design system) is a positive integer. In a system including a polydisperse polymer, an average value of the number of mass points included in each polymer chain may be used.

[Density (Dimensionless amount)]
In this design system, the density (number density) of the polymer material is parameterized by the number of molecules of the polymer (having the above chain length) contained in the basic cell. The surface density of the polymer material is expressed as the number of polymer chains (number of polymers per surface area) included per area of a plane (xy plane) defined by the x direction and z direction of the simulation box. The bulk density of the polymer material is expressed as the number of mass points included in the simulation box (number density of mass points).

[Polymer flexibility (dimensionless amount)]
In this design system, the flexibility (flexibility) of the polymer contained in the polymer material is parameterized as a value obtained by dividing the sustained length l _p of the polymer by the bond length b between the mass points of the polymer. For perfectly flexible polymers, l _p approaches zero (theoretical perfect flexibility when <t _p , t _{P + S} > = 0). As the polymer stiffness increases, the value of the flexibility parameter increases.

[Packing fraction (dimensionless amount)]
The packing fraction is a parameter representing the ratio of the mass of the solvent particles to the total number of mass points existing in the system (total number of mass points of the polymer chain and solvent particles), and is a value between 0 and 1. Can take. The total number of mass points present in the system depends on the previously selected density parameter (number of polymer chains) and chain length parameters. This parameter is effective when a simulation is performed on a system including solvent particles. That is, this parameter is optional and the packing fraction = 0 in a system that does not include solvent particles. On the other hand, packing fraction = 1 means that there is no polymer chain in the system (a system with only a solvent).

Hereinafter, a procedure for predicting the characteristics of a polymer material (particularly, a polymer material suitable for low friction coating) using the present design system will be described with reference to FIGS. 1 and 2.
First, select one of four simulation modes: (1). Symmetric polymer coating, (2). Asymmetric polymer coating, (3). Symmetric polymer coating + solvent, (4). Asymmetric polymer coating + solvent ( Step 102). This selection can be performed by, for example, inputting numbers 1 to 4 corresponding to the above (1) to (4) from a keyboard in an interactive window displayed on the display of the input device 10. Here, the case where a symmetric polymer coating is selected as the simulation mode will be mainly described.

  Next, material parameters are input (step 104) and simulation condition parameters are input (step 106). Step 104 and step 106 may be performed in parallel or sequentially. When performing in order, either step 104 or step 106 may be performed first. In the present system, an interactive window for inputting material parameters and simulation condition parameters is displayed on the display of the input device 10 according to the mode selected in step 102. If a solvent-free system is selected in step 102, this window includes the simulation time, polymer chain length, density (number density), share rate, system temperature, simulation box size (X, Y, Each box size), polymer flexibility, and control normal force parameters are provided. This interactive window also has a column for selecting whether to generate a moving image by a number (1: Yes, 2: No). When a system including a solvent is selected in step 102, a window having a column for inputting a packing fraction will be displayed. Since default parameters are input in advance in the input fields for each parameter, there is no need to input them again if there is no need to change them.

  When the input of these parameters is completed, the program code is executed (step 108). When the job is completed, the simulation result is displayed on the display of the output device 30 (here, common to the display of the input device 10) (step 110). The simulation result can be printed out from a printer connected to the computer 20 or can be stored in the storage device 24.

3 to 8 show simulation results obtained by executing the program code with the input values of the above-described parameters as values shown in Table 2 (hereinafter referred to as “parameter set A”). FIG. 3 shows a snapshot of the system, where the horizontal axis represents the shear direction (x direction) and the vertical axis represents the normal direction (y direction). In FIG. 3, “σ = 0.25” is a dimensionless quantity (σ ^* _surf ) representing the surface density of the polymer material, and the number of polymer chains in the xy plane of the simulation box is represented by the surface area (dimensionless quantity). ) Divided by the number density. When the polymer contained in the polymer material is PTFE and converted to an actual surface density (dimensional quantity) using the above-described dimension conversion factor, σ _surf = σ ^* _surf × σ ⁻² = 0. 25 × 20 ⁻² = 0.000625Å ⁻² (As described above, the length dimension conversion factor σ = 20Å for PTFE). In FIG. 3, “n = 0.36737” is a number representing the bulk density of the polymer material, and the number of mass points included in the simulation box is divided by the volume of the simulation box (dimensionless amount). It is what I asked for. When the polymer is PTFE, the above bulk density (n = 0.30637) is converted to an actual density (dimensional quantity), which is about 8 × 10 ⁻³ g / cm ³ .

FIG. 4 is a graph in which normal stress (dimensionless amount) is plotted against time. FIG. 5 is a graph plotting shear stress versus time. FIG. 6 is a graph in which the ratio (time-dependent friction coefficient) between shear stress and normal stress over time is plotted against time. FIG. 7 is a diagram showing the spatial distribution (state of stress concentration) of the square of the force field (<F ² >), where the horizontal axis is X and the vertical axis is Y, and the space is divided vertically and horizontally. The magnitude of the stress applied to is displayed by color coding. A color sample showing the correspondence between this color, the value of <F ² >, and the color is shown at the right end of the figure. The numbers shown in this color sample are dimensionless quantities representing the value of <F ² >. In the case where the polymer is PTFE, when <F ² > = 1000, 2000, 3000 in this color sample is converted into actual stress (dimension amount), 3.9 × 10 ⁻³ eV / Å ² , 7.8, respectively. It corresponds to × 10 ⁻³ eV / Å ² and 11.7 × 10 ⁻³ eV / Å ² .

FIG. 8 is a graph showing the dispersion of bond lengths at a certain point in time, where the horizontal axis represents the bond length and the vertical axis represents the frequency. In FIG. 8, “max bond length = 1.0536” is a number representing the limit elongation length of a finite elongation non-linear elasticity (FENE) spring.
Is a dimensionless quantity calculated by In the case where the polymer is PTFE, this value is converted to an actual length (dimensional amount), which is about 21 cm. The coarse-grained model used here considers the possibility of polymer chains (bonds between mass points) breaking and chain breaks due to excessive stress concentration, etc. So those phenomena were not observed.

9 to 14 show that the program code is executed for the parameter set B (the values other than the density parameter are the same as the parameter set A) in which the value of the density parameter is changed to 20 among the parameters included in the parameter set A It is the simulation result obtained by. FIG. 9 shows a snapshot of the system. In FIG. 9, “σ = 0.5” is a number representing the surface density of the polymer material (similar to the case of parameter set A), and when converted to the actual surface density (dimensional quantity), the polymer is In the case of PTFE, it is about 0.00125 / cm ² . In FIG. 9, “n = 0.36737” is a number representing the bulk density of the polymer material (similar to the case of parameter set A), and the actual density (dimension) is obtained when the polymer is PTFE. In terms of amount, it is about 8 × 10 ⁻³ g / cm ³ . From comparison between FIG. 3 (parameter set A) and FIG. 9 (parameter set B), it can be seen that changing the input value of the density parameter from 10 to 20 is reflected as an increase in surface density and bulk density.

FIG. 10 is a graph plotting normal stress against time. FIG. 11 is a graph plotting shear stress versus time. FIG. 12 is a graph in which the ratio (time-dependent friction coefficient) between shear stress and normal stress over time is plotted against time. FIG. 13 is a diagram showing the spatial dispersion of the square of the force field (<F ² >). FIG. 14 is a graph showing the dispersion of bond lengths at a certain point in time. In FIG. 14, “max bond length = 1.233” is a number representing the limit elongation length of a finite elongation nonlinear elasticity (FENE) spring, which is a dimensionless amount calculated by the above formula. When the polymer is PTFE, when this value is converted into the actual length (dimensional amount), it is about 24.5 mm. Thus, changing the density parameter also changes the maximum bond length. In this simulation condition, neither polymer chain breakage nor breakage was observed.

  In this way, by predicting the characteristics of each of a plurality of parameter sets in which at least one of the material parameters is different (for example, the parameter sets A and B have different density parameters), the different parameters are obtained. It is possible to grasp the influence of the above on the characteristics. Based on such knowledge, it is possible to efficiently find (design) a polymer material exhibiting better characteristics.

<Example 2>
For the polytetrafluoroethylene (PTFE) of Ge ⁰ = 0.4 MPa having the characteristic values shown in Table 1, the value of the flexibility parameter is gradually changed in the parameter set C shown in Table 3 using the design system of Example 1. The program code was executed repeatedly (optimization loop). The simulation results obtained in this manner are calculated by using the value of the flexibility parameter as the horizontal axis and the friction coefficient predicted by the simulation (the time-dependent friction coefficient is calculated as a time average between 10 ⁻⁶ seconds and 1 second after the start of the simulation. The dimensionless amount obtained in this manner is shown in FIG. From the figure, it can be seen that the coefficient of friction is lowest when the value of the flexibility parameter is around 5. The value of the flexibility parameter at this time is about 100 mm when converted into the actual duration (dimensional quantity) of PTFE.

<Example 3>
For the same PTFE as in Example 2, by using the design system of Example 1 and adjusting the value of the density parameter in parameter set D shown in Table 4, the surface density parameter (dimensionless amount) should be changed little by little. Repeated execution of the program code. At this time, by adjusting the friction coefficient, the bulk density n was maintained at 0.7 (dimensionless amount) regardless of the value of the surface density parameter. The simulation results thus obtained are shown in FIG. 16 with the surface density parameter value as the horizontal axis and the friction coefficient value predicted by the simulation as the vertical axis. From the figure, it can be seen that the coefficient of friction is lowest when the dimensionless surface density parameter σ ^* _surf is near 0.16. The value of the surface density parameter σ ^* _surf at this time is converted to the actual surface density (dimensional quantity) of PTFE: σ _surf = σ ^* _surf × σ ⁻² = 0.16 × 20 ⁻² = 0.004Å ^{− 2} (as mentioned above, σ = 20Å for PTFE). It can also be seen that when the dimensionless surface density parameter σ ^* _surf exceeds 0.25, the friction coefficient increases rapidly. The value of the surface density parameter σ ^* _surf at this time is 0.25 × 20 ⁻² = 0.000625Å− ² when converted to the actual surface density (dimensional quantity) of PTFE. In the case of PTFE, one unit on the horizontal axis (non-dimensional surface density) in FIG. 16 is converted to 0.0025Å ⁻² of the actual surface density (dimensional quantity).

<Example 4>
For the same PTFE as Example 2, using the design system of Example 1, the program code can be changed by slightly changing the value of the chain length parameter (number of mass points per polymer chain) in the parameter set E shown in Table 5. Repeated to run. The simulation results obtained in this way are shown in FIG. 17 with the value of the chain length parameter as the horizontal axis and the value of the friction coefficient predicted by the simulation as the vertical axis. From the figure, it can be seen that the coefficient of friction decreases as the value of the chain length parameter increases. The value of the chain length parameter at this time is about 2500 to 4000 when converted into the actual molecular weight of PTFE. It can also be seen that when the chain length parameter is lower than 10, the friction coefficient suddenly increases. The value of the chain length parameter at this time is about 1300 when converted to the actual molecular weight of PTFE. In the case of PTFE, one unit of the horizontal axis (dimensionless friction coefficient) in FIG. 17 is converted to 626 g / mol of an actual friction coefficient (dimensional amount).

<Example 5>
Plural types of PTFE having different material parameters were prepared. Test pieces No. 1 to No. 4 were prepared by coating these PTFEs on the surface of the stainless steel plate.
[Test piece No.1]
Test piece No. 1 was coated with PTFE appropriately selected from commercially available products (hereinafter, this material is referred to as “PTFE (1)”). The measured value (experimental value) of the persistence length of this PTFE (1) was about 20 cm, and the measured value (experimental value) of the surface density was about 0.00125 cm- ² . This test piece No. 1 was simulated using the design system of Example 1 with the parameter set F shown in Table 6. The share rate parameter = 1.2 × 10 ⁻⁴ (dimensionless amount) in this parameter set corresponds to the actual share rate = 10 cm / second.
The obtained simulation results are shown in FIG. 18 with time as the horizontal axis and time-dependent friction coefficient (dimensionless amount) as the vertical axis. The continuous lines in FIGS. 18 to 25 are obtained by weighting and averaging a large number of data (plots) obtained by the simulation.

Further, simulation was performed in the same manner as the parameter set F (parameter set F ′) except that the share rate parameter was changed from 1.2 × 10 ⁻⁴ to 2.4 × 10 ⁻⁴ . The share rate parameter = 2.4 × 10 ⁻⁴ (dimensionless amount) in the parameter set F ′ corresponds to the actual share rate = 20 cm / second.
The obtained simulation results are shown in FIG. 19 with time on the horizontal axis and time-dependent friction coefficient (dimensionless amount) on the vertical axis.

[Test piece No.2]
In the parameter set F ′ (that is, the share rate = 20 cm / second), the relationship between the flexibility parameter and the friction coefficient was grasped by repeating the program code while changing the flexibility parameter little by little. In addition, the relationship between the density parameter and the friction coefficient was grasped by repeating the execution of the program code by changing the density parameter little by little in the parameter set F ′. From these relationships, a combination of a flexibility parameter and a density parameter, which is expected to achieve the lowest friction coefficient, was found. Of the commercially available PTFE, PTFE having a sustained length that fits as well as the flexibility parameter and a surface density that fits as well as the density parameter (hereinafter, this material is referred to as “PTFE (2)”). ) Was selected. Test piece No. 2 was produced by coating this PTFE (2) on a stainless steel plate.

The test piece No. 2 was simulated using the design system of Example 1 with the parameter set G shown in Table 7. The share rate parameter = 1.2 × 10 ⁻⁴ (dimensionless amount) in this parameter set corresponds to the actual share rate = 10 cm / second. Further, the simulation was performed in the same manner as the parameter set G (parameter set G ′) except that the share rate parameter was changed from 1.2 × 10 ⁻⁴ to 2.4 × 10 ⁻⁴ . The share rate parameter = 2.4 × 10 ⁻⁴ (dimensionless amount) in this parameter set G ′ corresponds to the actual share rate = 20 cm / second.
The obtained simulation results are shown in FIG. 20 (share rate = 10 cm / second) and FIG. 21 (share rate = 20 cm / second) with time as the horizontal axis and time-dependent friction coefficient (dimensionalless amount) as the vertical axis.

[Test piece No.3]
From commercially available PTFE, PTFE having a slightly longer duration than PTFE (2) used for the production of test piece No. 2 (hereinafter, this material is referred to as “PTFE (3)”) was selected. Test piece No. 3 was produced by coating this PTFE (3) on a stainless steel plate.
The test piece No. 3 was simulated using the design system of Example 1 with the parameter set H shown in Table 8. The share rate parameter = 1.2 × 10 ⁻⁴ (dimensionless amount) in this parameter set corresponds to the actual share rate = 10 cm / second. Further, a simulation was performed in the same manner as the parameter set H (parameter set H ′) except that the share rate parameter was changed from 1.2 × 10 ⁻⁴ to 2.4 × 10 ⁻⁴ . The share rate parameter = 2.4 × 10 ⁻⁴ (dimensionless amount) in this parameter set H ′ corresponds to the actual share rate = 20 cm / second.
The obtained simulation results are shown in FIG. 22 (share rate = 10 cm / second) and FIG. 23 (share rate = 20 cm / second), with time on the horizontal axis and time-dependent friction coefficient (dimensionless amount) on the vertical axis.

[Test piece No.4]
PTFE having a slightly higher surface density than PTFE (2) used for the production of test piece No. 2 (hereinafter, this material is referred to as “PTFE (4)”) was selected from commercially available PTFE. Test piece No. 4 was produced by coating this PTFE (4) on a stainless steel plate.
This test piece No. 4 was simulated using the design system of Example 1 with the parameter set I shown in Table 9. The share rate parameter = 1.2 × 10 ⁻⁴ (dimensionless amount) in this parameter set corresponds to the actual share rate = 10 cm / second. Further, the simulation was performed in the same manner as the parameter set I (parameter set I ′) except that the share rate parameter was changed from 1.2 × 10 ⁻⁴ to 2.4 × 10 ⁻⁴ . The share rate parameter = 2.4 × 10 ⁻⁴ (dimensionless amount) in the parameter set I ′ corresponds to the actual share rate = 20 cm / second.
The obtained simulation results are shown in FIG. 24 (share rate = 10 cm / second) and FIG. 25 (share rate = 20 cm / second), with time on the horizontal axis and time-dependent friction coefficient (dimensionless amount) on the vertical axis.

[Comparison of test pieces No.1 to No.4]
For the test pieces No. 1 to No. 4 produced above, the friction coefficient was actually measured (actual measurement). A ball-on-plate friction tester (CSM, Ball-on-Plate Tribometer) was used to measure the friction coefficient. The measurement conditions are as follows.
Load: 5N
Load resolution: 10 mN,
Rotating pin radius: 5mm,
Ball material: Steel,
Ball radius: 0.5mm,
Measurement temperature: room temperature.
By adjusting the rotation speed, the friction coefficient at a moving speed (share rate) of 10 cm / second (low speed) and 20 cm / second (medium speed) was measured. The measurement was performed intermittently, and the value obtained by averaging the instantaneous friction coefficients obtained in this manner over time was used as the friction coefficient of each test piece. The test results obtained are shown in Table 10.

FIG. 26 collectively shows the simulation results (see FIGS. 18, 20, 22, and 24) for the test pieces No. 1 to 4 at a share rate of 10 cm / sec. FIG. 27 collectively shows the simulation results (see FIGS. 19, 21, 23, and 25) of these test pieces at a share rate of 20 cm / sec. 26 and 27 are compared with the actual measurement values shown in Table 10, and the order of the friction coefficient magnitudes of the test pieces No. 1 to 4 between the simulation results and the actual measurement values at any share rate. Can be seen to match. In addition, the test pieces No. 2 to 4 selected in consideration of a suitable combination of parameters obtained by simulation have a friction coefficient that is clearly lower than that of the test piece No. 1 in which commercially available products are appropriately selected. Indicated.
From these results, it was confirmed that by applying the polymer design method of the present invention, a polymer material satisfying desired characteristics (here, having a low coefficient of friction) can be efficiently designed. Moreover, according to the said polymer material design system, it was confirmed that this design method can be performed appropriately.

Specific examples of the present invention have been described in detail above, but these are merely examples and do not limit the scope of the claims. The technology described in the claims includes various modifications and changes of the specific examples illustrated above.
For example, in the above embodiment, an input device including a display and a keyboard is used as a means for acquiring material parameters and simulation condition parameters. However, a configuration including a mouse instead of the keyboard or a configuration using a touch panel display may be used. Further, it may be configured to input by voice. In the first embodiment, the description has been given of the mode in which the material parameters and the simulation condition parameters are acquired by inputting all the parameters (or accepting the default parameters). However, at least some parameters are stored in the storage device in advance. It is good also as an aspect which reads and acquires from the (registered) data.
In addition, the technical elements described in the present specification or the drawings exhibit technical usefulness alone or in various combinations, and are not limited to the combinations described in the claims at the time of filing. In addition, the technology illustrated in the present specification or the drawings achieves a plurality of objects at the same time, and has technical utility by achieving one of the objects.

In addition, the following are included in the content disclosed by this specification.
(1) A method of designing the characteristics of a polymer material in consideration of a small number of molecular structural elements by applying a coarse-grained model to polymer systems. In one preferred embodiment, the coarse grain model is applied to the polymer system ignoring the details of the chemical properties. Polymer-based material properties can be optimized independently of chemical details by considering an appropriate coarse-grained model. Here, the coarse-grained model is defined as a normal mechanical system, unlike a quantum mechanical system (a system with fluctuations). In a preferred embodiment, the characteristic frequencies of the dynamic system are lower than the atom-atom bond frequencies. In another preferred embodiment, the characteristic length of the dynamic system is longer than the bond length of the atom (more preferably longer than about 10 Å). The characteristic length can be, for example, the persistence length of the polymer chain.

(2) The method according to (1) above, wherein in the coarse-grained model, a polymer chain included in a polymer system is represented by an interacting mass point, and each mass point represents two or more monomer units. Such polymer systems can be characterized by dynamical rules between units (between mass points) with controlled bending flexibility and maximum elongation (maximum elongation length). In a preferred embodiment, the molecular weight and topology (architecture) of the polymer molecules are further controlled. Such a polymer system is composed of a plurality of polymer molecules and can be specified by the number density of the polymer and the composition of the polymer species. In a polydisperse system, the system can be characterized by the dispersion of the above parameters.

(3) Based on the coarse-grained model, design a coating polymer material (or polymer coating) with controlled properties such as viscosity, viscoelasticity, coefficient of friction, orientation, time dependence, static properties and optical properties. how to. In one preferred method, a coating polymer material with a controlled surface density is designed.

(4) A method for designing a low-friction polymer material (or a polymer contained in the polymer material) by applying the method according to any one of (1) to (3) above.

(5) By applying the method according to any one of (1) to (3) above, grasping a combination of parameter values expected to give suitable characteristics (for example, a low friction polymer material),
Converting the parameters included in the parameter value combination into a representation that indicates the molecular structure (eg, molecular weight, topology, density, etc.) of the polymer included in the polymer material, if necessary,
Providing a polymer having such a molecular structure;
A process for producing a polymeric material comprising

1 is a schematic diagram showing a schematic configuration of a design system of Example 1. FIG. It is a flowchart which shows the procedure which estimates the characteristic of a polymer material using the design system of Example 1. FIG. It is explanatory drawing which shows the simulation result (snapshot) about the parameter set A. It is explanatory drawing which shows the simulation result (normal stress) about the parameter set A. It is explanatory drawing which shows the simulation result (shear stress) about the parameter set A. It is explanatory drawing which shows the simulation result (time-dependent friction coefficient) about the parameter set A. It is explanatory drawing which shows the simulation result (spatial dispersion | distribution of the square of a force field) about the parameter set A. It is explanatory drawing which shows the simulation result (variation of coupling length) about the parameter set A. It is explanatory drawing which shows the simulation result (snapshot) about the parameter set B. It is explanatory drawing which shows the simulation result (normal stress) about the parameter set B. It is explanatory drawing which shows the simulation result (shear stress) about the parameter set B. FIG. It is explanatory drawing which shows the simulation result (time-dependent friction coefficient) about the parameter set B. It is explanatory drawing which shows the simulation result (spatial dispersion | distribution of the square of a force field) about the parameter set B. FIG. 10 is an explanatory diagram showing simulation results (coupling length dispersion) for parameter set B. It is a graph which shows the relationship between lasting length and a friction coefficient. It is a graph which shows the relationship between a surface density and a friction coefficient. It is a graph which shows the relationship between a bulk density and a friction coefficient. It is explanatory drawing which shows the simulation result (time-dependent friction coefficient in a share rate of 10 cm / sec) about sample No.1. It is explanatory drawing which shows the simulation result (time-dependent friction coefficient in a share rate of 20 cm / sec) about sample No.1. It is explanatory drawing which shows the simulation result (Time-dependent friction coefficient in a share rate of 10 cm / sec) about sample No.2. It is explanatory drawing which shows the simulation result (Time dependent friction coefficient in 20 cm / sec of share rates) about sample No.2. It is explanatory drawing which shows the simulation result (Time-dependent friction coefficient in a share rate of 10 cm / sec) about sample No.3. It is explanatory drawing which shows the simulation result (Time dependent friction coefficient in 20 cm / sec of share rates) about sample No.3. It is explanatory drawing which shows the simulation result (Time-dependent friction coefficient in a share rate of 10 cm / sec) about sample No.4. It is explanatory drawing which shows the simulation result (Time-dependent friction coefficient in 20 cm / sec of share rates) about sample No.4. It is explanatory drawing which shows collectively the simulation result (Time-dependent friction coefficient in a share rate of 10 cm / sec) about sample No. 1-4. It is explanatory drawing which shows collectively the simulation result (Time-dependent friction coefficient in a share rate of 20 cm / sec) about sample No. 1-4.

Explanation of symbols

10: input device 20: computer 22: arithmetic device 24: storage device 30: output device

Claims (2)

A system for designing a polymer material suitable for a desired application using a coarse-grained model of the polymer material,
At least the following:
A chain length parameter representing the chain length of the polymer contained in the polymer material;
A density parameter representing the density of the polymeric material; and
A flexibility parameter representing the flexibility of the polymer;
Means for obtaining a material parameter comprising:
At least the following:
A time parameter representing the duration of the simulation;
A temperature parameter representing the temperature of the system to be simulated; and
A cell size parameter representing the size of the simulation box;
Means for obtaining simulation condition parameters including:
Using these parameters, a coarse-grained model of the polymer material is modeled as a bead-spring chain in which adjacent mass points each representing two or more monomer units of the polymer are connected by a finite stretch nonlinear elastic spring. A means of performing a simulation based on molecular dynamics for the coarse-grained model,
Means for outputting the simulation results;
With
The means for performing the simulation comprises: a first wall comprising a surface having a polymer coating to which one end of the polymer chain is anchored; and a surface facing the surface having the polymer coating and having a polymer coating. Perform the simulation under the condition that the second wall moves relative to the predetermined share rate,
The simulation system parameter further includes a share rate parameter representing the share rate. Control the normal force on the first wall to perform the simulation,
The system of claim 1 , wherein the simulation condition parameter further comprises a control normal force parameter that specifies a value or range of normal force for the first wall.