Method and apparatus for analyzing the young's modulus of the interfacial region of a polymer nanocomposite dielectric

Abstract

The application discloses a method and device for analyzing the Young's modulus of an interface region of a polymer nanocomposite dielectric, wherein the method uses a Monte Carlo method to construct a three-dimensional structure model of the polymer nanocomposite dielectric, simulates a stress and strain field and an effective Young's modulus of the polymer nanocomposite dielectric with high throughput, simulates the effective Young's modulus of the polymer nanocomposite dielectric with high throughput in combination with an effective medium theory, and inversely obtains a Young's modulus distribution characteristic of the interface region. The method establishes a correlation between the mesoscopic characteristics of the interface region and macroscopic mechanical properties, provides theoretical and method support for research and development of high-performance electrical insulating materials, and is helpful to development of dielectric capacitors with high breakdown strength and energy storage density.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of high voltage and insulation, and particularly relates to a method for characterizing the mesoscopic Young's modulus distribution characteristics of an interface region of a polymer nanocomposite dielectric. BACKGROUND

[0002] Polymer dielectric thin film materials are widely used in energy storage capacitors, frequency inverters, electronic transformers and other equipment. With the continuous increase of voltage level and the development of energy storage devices towards miniaturization and intelligentization, higher requirements are put forward for polymer dielectric materials, and dielectric materials with high breakdown strength and energy storage density are urgently needed. The breakdown strength of dielectric materials is related to mechanical strength. When a direct current voltage is applied to the electrodes on both sides of the dielectric material, the material will be subjected to Coulomb force and then mechanical deformation. If the Young's modulus and mechanical strength of the material are larger, the Coulomb force that the material can withstand is larger, which helps to prevent the material from being mechanically damaged and thus improves the breakdown strength of the material.

[0003] The interface region is formed by the interaction between nanoparticles and the polymer matrix, and there are chemical bonds such as covalent bonds, ionic bonds and hydrogen bonds in the interface region. Strong interaction between the matrix and the nanofiller is beneficial to the improvement of the Young's modulus of the polymer nanocomposite dielectric and has higher breakdown strength. Therefore, clarifying the distribution characteristics of the mesoscopic Young's modulus of the interface region is a key factor in the study of high breakdown strength and high energy storage materials.

[0004] Existing instruments and equipment are difficult to effectively characterize the mesoscopic characteristics of different regions in the interface region of the polymer nanocomposite dielectric, which seriously limits the study of the mesoscopic Young's modulus distribution characteristics of the interface region and makes it difficult to establish the relationship between the mesoscopic characteristics of the interface region and the macroscopic performance. SUMMARY

[0005] The application converts the mesoscopic Young's modulus distribution characteristics of the interface region into an inverse problem of the Navier-Cauchy equation, proposes a method for the mesoscopic Young's modulus of the interface region of the polymer nanocomposite dielectric based on the Navier-Cauchy equation inversion, and establishes an effective correlation between the mesoscopic characteristics of the interface region and the macroscopic mechanical properties, thereby providing theoretical and methodological support for the development of high-performance polymer nanocomposite dielectric materials.

[0006] To achieve the above purpose, the polymer nanocomposite dielectric interface region Young's modulus analysis method provided by the application comprises the following steps:

[0007] Step 1, obtaining the Young's modulus of the polymer nanocomposite dielectric through experiments, and establishing a three-dimensional structure model of the polymer nanocomposite dielectric, wherein the three-dimensional structure model of the polymer nanocomposite dielectric comprises a polymer matrix, a nanofiller and an interface region;

[0008] Step 2, taking the Young's modulus distribution of the polymer nanocomposite dielectric interface region as the input data set, substituting into the Navier-Stokes equation, calculating the displacement, strain, stress distribution of the polymer nanocomposite dielectric, and then calculating the effective Young's modulus of the interface region in the three-dimensional structure model of the dielectric according to the strain and stress of the polymer nanocomposite dielectric by the effective medium theory;

[0009] Step 3, comparing the effective Young's modulus obtained in step 2 with the Young's modulus obtained in step 1 to determine the appropriate interface region characteristic parameters in the three-dimensional structure model of the dielectric, and calculating the mesoscopic Young's modulus distribution characteristics of the interface region of the polymer nanocomposite dielectric according to the interface region characteristic parameters.

[0010] Further, in step 1, a three-dimensional structure model of the polymer nanocomposite dielectric is established by using the Monte Carlo method, and the Young's modulus of the polymer matrix and nanofiller region is set to the experimental result.

[0011] Further, in step 1, a gradually descending Sigmoid function is used to describe the variation law of the Young's modulus of the interface region.

[0012] Further, the process of step 2 is:

[0013] S2.1, constructing the equilibrium differential equation of the polymer nanocomposite dielectric;

[0014] S2.2, constructing the geometric equation and constitutive equation of the polymer nanocomposite dielectric;

[0015] S2.3, substituting the geometric equation into the constitutive equation to obtain the relationship between stress and displacement derivative;

[0016] S2.4, substituting the relationship between stress and displacement derivative into the equilibrium differential equation to obtain the relationship between the second derivative of displacement and body force, i.e. the differential form of the Navier-Stokes equation;

[0017] S2.5, converting the Navier-Stokes equation set into integral form and using the divergence theorem to obtain its weak solution form, and obtaining the displacement-discretized Navier-Stokes equation according to its weak solution form;

[0018] S2.6, updating the displacement-discretized Navier-Stokes equation displacement by displacement;

[0019] S2.7, given the initial displacement, then solving the Navier-Stokes equation by using the program Jacobi iteration method; updating the displacement by displacement through the program Jacobi iteration, then calculating the source term through the displacement, and then performing the next iteration; then substituting the displacement obtained by iteration into the geometric equation to calculate the strain, and then calculating the stress through the constitutive equation;

[0020] S2.8, calculating the effective Young's modulus of the polymer nanocomposite material according to the stress and strain by using the effective medium theory;

[0021] S2.9, calculating the effective Young's modulus of the polymer nanocomposite material according to the stress and strain by using the effective medium theory; Y interface0 / Y matrix taking the effective Young's modulus of the polymer nanocomposite material as the dependent variable, obtaining r 0 / r nano taking the effective Young's modulus of the polymer nanocomposite material as the dependent variable, obtaining Y matrix the Young's modulus of the polymer matrix, Y interface0 the Young's modulus of the interface region close to the surface of the nanoparticles, r 0 the parameter of the Sigmoid function, r nano the radius of the nanoparticles; taking the effective Young's modulus of the polymer nanocomposite material as the dependent variable, obtaining n 2 a contour map of the effective Young's modulus; comparing the contour map of the effective Young's modulus with the experimental results obtained in step 1, obtaining the parameter range of the Sigmoid function of the mesoscopic Young's modulus of the interface region.

[0022] Further, in step S2.6, the displacement quantity of the Navier-Stokes equation discretized by the displacement quantity is updated one by one by using the program Jacobian iteration method.

[0023] Further, the process of step 3 is:

[0024] taking the value of the horizontal coordinate of the point with the maximum curvature in the contour map r 0 / r nano and the value of the vertical coordinate Y interface0 / Y matrix as the parameter of the Sigmoid function of the mesoscopic Young's modulus of the interface region, substituting it into the gradually descending Sigmoid function to obtain the distribution characteristics of the Young's modulus of the interface region of different polymer nanocomposite dielectric materials.

[0025] Further, step 3 further includes: substituting the obtained parameter of the Sigmoid function of the Young's modulus of the interface region of the polymer nanocomposite dielectric material into the Navier-Stokes equation to calculate the distribution characteristics of the strain and stress inside the polymer nanocomposite dielectric material.

[0026] A polymer nanocomposite dielectric material interface region Young's modulus analysis device, comprising:

[0027] A building module is configured to store the Young's modulus of the polymer nanocomposite dielectric obtained by experiment and to establish a three-dimensional structure model of the polymer nanocomposite dielectric, the three-dimensional structure model of the polymer nanocomposite dielectric including a polymer matrix, a nanofiller and an interface region;

[0028] An effective Young's modulus calculation module is configured to take the Young's modulus distribution of the interface region of the polymer nanocomposite dielectric as an input data set, substitute the Young's modulus distribution into a Navier-Cauchy equation, calculate the displacement, strain and stress distribution of the polymer nanocomposite dielectric, and then calculate the effective Young's modulus of the interface region in the three-dimensional structure model of the dielectric according to the strain and stress of the polymer nanocomposite dielectric by effective medium theory.

[0029] An interface region mesoscopic Young's modulus distribution characteristic calculation module is configured to compare the effective Young's modulus with the Young's modulus obtained by experiment to determine the appropriate interface region characteristic parameter in the three-dimensional structure model of the dielectric, and to calculate the interface region mesoscopic Young's modulus distribution characteristic of the polymer nanocomposite dielectric according to the interface region characteristic parameter.

[0030] A computer device includes a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the polymer nanocomposite dielectric interface region Young's modulus analysis method when executing the computer program.

[0031] A computer readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the polymer nanocomposite dielectric interface region Young's modulus analysis method are implemented.

[0032] Compared with the prior art, the present application has at least the following beneficial technical effects:

[0033] In polymer nanocomposite dielectric, the molecular chains in the interface region are bound by the nanofiller to form a more compact aggregate structure, which increases the difficulty of molecular motion and increases the Young's modulus of the interface region. According to the above characteristics, the stress and strain and effective Young's modulus of the polymer nanocomposite dielectric with different interface region properties are simulated in high throughput, the simulation results of the effective Young's modulus are compared with the experimental results of the Young's modulus, and the mesoscale distribution characteristics of the Young's modulus of the interface region are obtained by inversion. A Monte Carlo method is used to construct a geometric structure model of a polymer nanocomposite dielectric containing a polymer matrix, a nanofiller and an interface region, and a Sigmoid function is used to initialize the Young's modulus of the interface region. Different Young's modulus distributions of the interface region are used as input data sets, and the Navier-Cauchy equation is used to calculate the displacement, strain and stress distribution of the polymer nanocomposite dielectric, and the effective Young's modulus data set of the polymer nanocomposite dielectric is calculated by the effective medium theory. The simulation results of the Young's modulus are compared with the experimental results, the maximum curvature point in the simulation results is taken as the parameter of the Sigmoid function, the mesoscale Young's modulus distribution characteristics of the interface region of different polymer nanocomposite dielectrics are obtained, and the parameters of the Sigmoid function are substituted into the Navier-Cauchy equation to obtain the strain, stress and other distribution characteristics of the polymer nanocomposite dielectric. The present application can establish an effective correlation between the mesoscale characteristics of the interface region and the macroscopic mechanical properties, obtain the Young's modulus characteristics of the polymer nanocomposite dielectric, and provide theoretical and methodological support for the development of high-performance electrical insulation materials by studying the Young's modulus characteristics of different polymer nanocomposite dielectrics. It is helpful to develop dielectric capacitors with high breakdown strength and energy storage density.

[0034] Further, the present application can also obtain the strain, stress and other distribution characteristics of the polymer nanocomposite dielectric according to the Young's modulus characteristics, which is of great significance for material performance evaluation and optimization design.

[0035] Further, the present application uses finite volume program Jacobi iteration method and GPU acceleration algorithm to solve the Navier-Cauchy equation, which is fast, efficient, accurate and stable. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 is a flowchart of the present application;

[0037] Figure 2a is a two-dimensional schematic diagram of a polymer nanocomposite dielectric;

[0038] Figure 2b is a Sigmoid function form of the Young's modulus distribution of the interface region;

[0039] Figure 2c is a constant form of the Young's modulus distribution of the interface region;

[0040] Figure 2d Exponential function form of the Young's modulus distribution of the interface region;

[0041] Figure 3 Polyetherimide / alumina Young's modulus experimental results;

[0042] Figure 4 Three-dimensional distribution state of alumina filler with different doping contents in a 300x300x300nm polyetherimide cubic volume;

[0043] Figure 5 Effective Young's modulus simulation results of polyetherimide / alumina nanocomposite dielectric with different doping contents;

[0044] Figure 6 Effective Young's modulus of polyetherimide / alumina nanocomposite dielectric with different doping contents in the x-y plane Y interface0 / Y matrix and r 0 / r nano Contour map of the x-y plane;

[0045] Figure 7 Three-dimensional distribution of stress and strain of polyetherimide / alumina nanocomposite dielectric with different doping contents;

[0046] Figure 8 Distribution map of the Young's modulus of the interface region;

[0047] Figure 9 Module structure schematic diagram of the polymer nanocomposite dielectric interface region Young's modulus analysis device provided by the application. DETAILED DESCRIPTION

[0048] In order to make the purpose and technical scheme of the application more clear and convenient to understand. The application is further described in detail below in combination with the drawings and examples. The specific examples described herein are only used to explain the application, and are not used to limit the application.

[0049] The application converts the mesoscopic Young's modulus distribution characteristics of the interface region into an inverse problem of the Navier-Cauchy equation, and proposes an interface region mesoscopic Young's modulus method for the inverse of the Navier-Cauchy equation of the polymer nanocomposite dielectric. The three-dimensional distribution characteristics of the polymer nanocomposite dielectric, such as strain and stress, can be obtained. An effective correlation between the mesoscopic characteristics of the interface region and the macroscopic mechanical properties is established, which provides theoretical and methodological support for the research and development of high-performance electrical insulation materials, and helps to develop dielectric capacitors with high breakdown strength and energy storage density.

[0050] Example 1

[0051] Reference Figure 1 The present invention provides a method for inverting and analyzing the Young's modulus of the interface region of polymer nanocomposite dielectrics, comprising the following steps:

[0052] Step 1: The Young's modulus of the polymer nanocomposite dielectric was obtained experimentally, and a three-dimensional structural model of the polymer nanocomposite dielectric (hereinafter referred to as the dielectric three-dimensional structural model) was established using the Monte Carlo method.

[0053] Step 2: Using the Young's modulus distribution of the interface region of the polymer nanocomposite dielectric as the input dataset, substitute it into the Navier-Cauchy equation, and use the finite volume program Jacobi iteration method and GPU accelerated computing method to calculate the displacement, strain, and stress distribution of the polymer nanocomposite dielectric. Then, the effective Young's modulus of the interface region in the three-dimensional structure model of the dielectric is obtained by calculation through effective dielectric theory.

[0054] Step 3: Compare the effective Young's modulus obtained in Step 2 with the Young's modulus obtained in Step 1 to determine the interface region characteristic parameters in the appropriate three-dimensional dielectric structure model. Based on the interface region characteristic parameters, calculate the mesoscopic Young's modulus distribution characteristics of the interface region of the polymer nanocomposite dielectric.

[0055] Step 1 specifically involves:

[0056] A three-dimensional structural model of the polymer nanocomposite dielectric was established using the Monte Carlo method. The three-dimensional model of the dielectric includes the polymer matrix, nanofillers, and interface regions, such as... Figure 2a As shown. The nanofiller is contained within the polymer matrix, with the interface region between the nanofiller and the polymer matrix.

[0057] Interfacial characteristics are crucial for regulating the properties of polymer nanocomposite dielectrics. These characteristics are distributed across a microscale range of a few nanometers to tens of nanometers, and complex coupling relationships exist between these characteristics. The three-dimensional dielectric structure model established in this invention can effectively separate the mesoscopic characteristics of different regions within the interfacial area. The spatial step size is typically set to 1-2 nm, and the mesh is divided into 200-400 parts across the three dimensions. The length, width, and height of the three-dimensional structure model are equal, all ranging from 200 nm to 800 nm.

[0058] The Young's modulus of the polymer matrix and nanofiller regions was set to the experimentally obtained results. The Young's modulus distribution in the interfacial region of polymer nanocomposite dielectrics may take various forms, such as the Sigmoid function form, the constant form, and the exponential function form. Figure 2b -d is shown. Where, the constant form ( Figure 2c) can cause a large difference in Young's modulus between the interfacial region and the polymer matrix. There will be distortion in strain between the interfacial region and the polymer matrix. Since the interfacial region and the polymer matrix are aggregated from the same molecular chains, only the aggregation structure is slightly different, it is not likely that there is a large difference in Young's modulus between the two. The exponential function form of the interfacial region Young's modulus distribution can make the Young's modulus between the interfacial region and the polymer matrix transition smoothly, but it can cause the interfacial region to extend very far, which is not consistent with the mesoscale experimental results. The sigmoid function form of the interfacial region Young's modulus distribution can make the Young's modulus between the interfacial region and the polymer matrix transition smoothly, and the thickness of the interfacial region is in a reasonable range. Therefore, it is most reasonable to set the Young's modulus of the interfacial region of the polymer nanocomposite dielectric to be in the form of a sigmoid function. Figure 2d Figure 2b

[0059] Since nanodoping generally increases the Young's modulus of the polymer nanocomposite dielectric, the Young's modulus of the interfacial region will be greater than that of the matrix. The possible change rule is that the surface of the nanoparticles binds the molecular chains, resulting in the largest Young's modulus of the interfacial region near the surface of the nanoparticles. The binding of the molecular chains in the interfacial region gradually weakens along the radial direction away from the nanoparticles, and the Young's modulus gradually decreases. The molecular chains far away from the nanoparticles will not be affected by the binding action of the nanoparticles, and the Young's modulus here is the same as that of the matrix. The change rule of the Young's modulus of the interfacial region is described by a gradually decreasing sigmoid function:

[0060]

[0061] wherein, Y interface (r) Ei is the Young's modulus of the interfacial region, Y matrix E0 is the Young's modulus of the polymer matrix, Y interface0 E1 is the Young's modulus of the interfacial region near the surface of the nanoparticles, Δ Y interface0 ΔE1 is the difference in Young's modulus between the interfacial region near the surface of the nanoparticles and the polymer matrix, i.e. Δ Y interface0 = Y interface0 - Y matrix , r nano R is the radius of the nanoparticles, r 0 is the parameter of the sigmoid function, r r is the distance between the interfacial region at a certain position and the spherical center of the nanoparticles.

[0062] The step 2 is specifically:​​

[0063] Assuming that polymer nanocomposite dielectrics are in x , y , z The lengths of the directions are respectively L x , L y , L z For materials with a positive Poisson's ratio, when its x When the direction is stretched, y-z The area of ​​the material on a plane will decrease. For isotropic polymer nanocomposite dielectrics, under conditions of small deformation and constant volume, it is possible to obtain... x Direction generates displacement Δ u Afterwards, y and z Displacement Δ in the direction v and Δ w The following relationship must be satisfied:

[0064]

[0065] In the simulation model, for the sake of simplicity, it is assumed that... L y and L z If they are equal, then the displacement Δ v and Δ w They are equal. We can obtain Δ. v and Δ w The expression:

[0066]

[0067] The equilibrium differential equation is:

[0068]

[0069] In the formula, f is the body force vector along the coordinate axis. x , y , z directional components are used f x , f y , f z Representation. Stress tensor Along the coordinate axis x , y , z The stress can be decomposed into one normal stress and two shear stresses. along x The axis is decomposed into a normal stress. σ x, along the y axis decomposes into a normal stress σ y , along the z axis decomposes into a normal stress σ z , on a plane normal to the x axis, the shear stress decomposes into two components parallel to the y axis and the z axis, denoted by τ xy , τ xz , y x yx , z yz , τ zx , τ zy , z xy , x yx , y xz , τ zx , τ yz , τ zy . τ τ τ τ τ

[0070] The geometric equations of polymer nanocomposite dielectrics (the relationship between particle displacement and strain) are:

[0071]

[0072] In the formula, the components of normal strain along the x , y , z directions are ε x , ε y , ε z , and the components of shear strain along the x , y , z directions are​​​​​​ε xy 、 ε yz 、 ε zx , displacement vector U along x 、 y 、 z the component in the direction of u 、 v 、 w .

[0073] The constitutive equation for isotropic elastic body is the generalized Hooke's law:

[0074]

[0075] where, Y E is the Young's modulus, µ ν is the Poisson's ratio of the material.

[0076] For convenience, the constitutive equation is written as follows:

[0077]

[0078] where, c 11 = c 22 = c 33 = Y (1 -μ ) / (1 +μ )(1 - 2 μ ), c 12 = c 13 = c 23 = Yμ / (1 +μ )(1-2 μ ), c 44 = c 55 = c 66 = Y / 2(1 +μ )。

[0079] Substituting the geometric equation into the constitutive equation, the relationship between stress and displacement derivative can be obtained:

[0080]

[0081] Substituting the relationship between stress and displacement derivative into the equilibrium differential equation, the relationship between the second displacement derivative and body force can be obtained, which is the differential form of Navier-Cauchy equation:

[0082]

[0083] Converting Navier-Cauchy equation group into integral form and using divergence theorem, the weak solution form of Navier-Cauchy equation can be obtained:

[0084]

[0085] Where Ω is the spatial region.

[0086] The polymer nanocomposite dielectric is divided into n x n x n cubic cells with side length h . The parameters c , u , v and w are discretized as c i,j,k , u i,j,k , v i,j,k and w i,j,k , respectively.

[0087] The left side of the first equation in Navier-Cauchy weak solution form equation group can be discretized as

[0088]

[0089] Where , x , y and z are the unit vectors in , c 11 , c 44 , c 66 directions, respectively.

[0090] Combining like terms, the discretized Navier-Cauchy equation u can be obtained

[0091]

[0092] The parameters in the equation are

[0093]

[0094] The left side of the second equation in the Navier-Cauchy weak solution form equation group can be discretized as

[0095]

[0096] Merging the like terms can obtain v Discretized Navier-Cauchy equation

[0097]

[0098] The parameters in the equation are respectively

[0099]

[0100] The left side of the third equation in the Navier-Cauchy weak solution form equation group can be discretized as

[0101]

[0102] Merging the like terms can obtain w Discretized Navier-Cauchy equation:

[0103]

[0104] The parameters in the equation are respectively:

[0105]

[0106] Then, the programmed Jacobi iteration method is used to update the displacement in equations (12), (15) and (18) one by one u , v , w .

[0107]

[0108] The superscript n represents the physical quantity in the iteration of the n th time, and the superscript n +1 represents the physical quantity in the iteration of the n +1 th time.

[0109] Given the initial displacement, i.e., when n =0 is u , v and w , then the programmed Jacobi iteration method is used to solve the Navier-Cauchy equation. The displacement is updated one by one through the programmed Jacobi iteration u , v , wThen the source term is calculated by the displacement, and the next iteration is performed. The error of the displacement before and after iteration is calculated, if the error does not reach the set precision, the iteration is continued, if the set precision is reached, the iteration is stopped, at this time the displacement numerical solution of the required precision is obtained. Next, the displacement obtained by iteration is substituted into the geometric equation to calculate the strain, and then the stress is calculated by the constitutive equation.

[0110] The stress expression in the direction of the applied stress is:

[0111] (21)

[0112] After obtaining the stress and strain, the effective Young's modulus of the polymer nanocomposite material can be calculated by the effective medium theory .

[0113] (22)

[0114] wherein, σ x is the stress in the direction of the applied force; ε x is the strain in the direction of the applied force; ε y and ε z is the strain component in the plane perpendicular to the direction of the applied force; μ is the Poisson's ratio.

[0115] is the stress in the direction of the applied force; Y interface0 / Y matrix and r 0 / r nano In the set interval, linearly divide n points. Take Y interface0 / Y matrix as the row, and r 0 / r nano as the column, to form a n × n input variable matrix, and n 2 kind of interface zone Young's modulus distribution diagram. Taking this interface zone Young's modulus distribution as the input data set, substituting it into the Navier-Cauchy equation, setting the boundary conditions according to the experimental conditions, using the finite volume Jacobi iteration method and GPU acceleration algorithm to calculate the displacement, strain and stress distribution of the polymer nanocomposite dielectric, and then calculating the n 2Effective Young's modulus of polymer nanocomposite dielectric under interface region Young's modulus distribution

[0116] The effective Young's modulus of the polymer nanocomposite dielectric under the interface region Young's modulus distribution is obtained. Y interface0 / Y matrix As the abscissa, r 0 / r nano As the ordinate, the effective Young's modulus of the polymer nanocomposite dielectric as the dependent variable, the following equation can be obtained n 2 A contour map of the effective Young's modulus. Comparing the contour map of the effective Young's modulus with the experimental results in step 1, the parameters of the interface region mesoscopic Young's modulus Sigmoid function r 0 and Y interfacc0 range.

[0117] The step 3 is specifically:

[0118] In the contour map, the value of the abscissa of the point with the maximum curvature r 0 / r nano and the value of the ordinate Y interface0 / Y matrix As the parameters of the interface region mesoscopic Young's modulus Sigmoid function, they are substituted into equation 1 to obtain the interface region Young's modulus distribution characteristics of different polymer nanocomposite dielectrics. Substituting the obtained parameters of the interface region mesoscopic Young's modulus Sigmoid function of the polymer nanocomposite dielectric into the Navier-Cauchy equation (i.e. equations 12, 15 and 18), the strain, stress and other distribution characteristics inside the polymer nanocomposite dielectric can be calculated.

[0119] Example 1: Interface region Young's modulus distribution characteristics of polyetherimide / alumina nanocomposite dielectric

[0120] (1) Basic data

[0121] The Young's modulus of polyetherimide is 1.45 GPa, the Poisson's ratio is 0.39, and the density is ; the Young's modulus of Al2O3 is 150 GPa, the Poisson's ratio is 0.23, and the density is , and the particle size of the nanoparticles is set to 10 nm.

[0122] (2) The Young's modulus of polyetherimide / alumina nanocomposite dielectric with different doping concentrations is obtained by experimental testing, and the test results are shown in Figure 3As the doping content of nanoparticles increases, Young's modulus first increases and then decreases, reaching its maximum value when the doping content is 3wt%.

[0123] (3) A three-dimensional cube with dimensions of 300 nm was constructed using Matlab scientific software. Subsequently, based on the different properties of the matrix phase, doped phase, and interface region, the random distribution of alumina with different doping contents in the polyetherimide matrix was simulated using the Monte Carlo method, and a three-dimensional structural model was constructed, such as... Figure 4 As shown. Set the iteration error to 10. -20 .

[0124] (4) Set the interface area for Young's modulus input dataset and solve the equilibrium differential equation, geometric equation, constitutive equation and effective Young's modulus calculation formula (22) to obtain the effective Young's modulus corresponding to the dataset.

[0125] The Young's modulus of the polymer nanocomposite dielectric interface region was set as a Sigmoid function, with the adjustment parameter of the Sigmoid function being the Young's modulus near the nanoparticles in the interface region. Y interface0 and interface area thickness r 0. Settings Y interface0 / Y matrix The range is 0-5. r 0 / r nano The interval is 0-1, and 20 points are taken using a linear division method. Y interface0 / Y matrix For the purpose of action, with r 0 / r nano By using the columns to form a 20×20 input variable matrix, 400 different Young's modulus distributions in the interface region can be obtained.

[0126] Set boundary conditions according to the experimental conditions. x With an initial directional displacement of 1 nm, the displacement, strain, and stress distribution of the polymer nanocomposite dielectric were calculated using the finite volume formula Jacobi iteration method and a GPU-accelerated algorithm. The effective Young's modulus of the nanocomposite was then calculated using effective dielectric theory. Y eff .

[0127] Figure 5 Simulation results of the effective Young's modulus of polyetherimide / alumina nanocomposite dielectrics with different doping contents are presented. The results show that the effective Young's modulus of the polymer nanocomposite dielectric is mainly affected by the thickness of the interface region. r 0 and Young's modulus of the interface regionY interface0 Modulation. For the same sample, with the increase of the thickness and Young's modulus of the interface region, the effective Young's modulus of the sample increases continuously.

[0128] (4) The mesoscopic distribution characteristics of the Young's modulus of the polymer nanocomposite dielectric interface region

[0129] The calculated 400 effective Young's moduli are compared with the experimental results, Figure 6 The contour map of the effective Young's modulus of the polyetherimide / alumina nanocomposite dielectric with different doping contents when the simulation results are equal to the experimental results is taken Figure 6 The maximum curvature point of each curve in the interface region Y interface0 And r 0 as the parameters in the Sigmoid function of the Young's modulus distribution of the interface region, and further determine the mesoscopic distribution characteristics of the Young's modulus of the interface region.

[0130] (5) The distribution characteristics of the interface region

[0131] According to the displacement, strain and stress distribution of the polymer nanocomposite dielectric obtained in the foregoing, data visualization is performed using Paraview software, as shown in Figure 7 , which respectively reflects the stress and strain distribution of the polymer nanocomposite dielectric. When an external force is applied, the normal stress of the interface region is the smallest, followed by the matrix, and the nanoparticles are the largest; the normal strain of the nanoparticles is the smallest, followed by the interface region, and the matrix is the largest; the shear stress and shear strain around the nanoparticles show central symmetry distribution, and the normal shear stress and shear strain are basically perpendicular to the negative shear stress and shear strain.

[0132] The Sigmoid curve of the Young's modulus distribution of the interface region in the polymer nanocomposite dielectric with different doping contents is shown in Figure 8 . With the increase of the doping content, the constraint effect and the influence of adjacent nanoparticles on the aggregation behavior of the molecular chains in the interface region increase, and the interface region becomes thinner.

[0133] Example 2

[0134] Referring to Figure 9 , a polymer nanocomposite dielectric interface region Young's modulus analysis device comprises:

[0135] A construction module is configured to store the Young's modulus of the polymer nanocomposite dielectric obtained by experiment, and to establish a three-dimensional structure model of the polymer nanocomposite dielectric, wherein the three-dimensional structure model of the polymer nanocomposite dielectric comprises a polymer matrix, a nanofiller and an interface region.

[0136] An effective Young's modulus calculation module is configured to take the Young's modulus distribution of the interface region of the polymer nanocomposite dielectric as an input data set, substitute the data set into the Navier-Stokes equation, calculate the displacement, strain and stress distribution of the polymer nanocomposite dielectric, and then calculate the effective Young's modulus of the interface region in the three-dimensional structure model of the dielectric according to the strain and stress of the polymer nanocomposite dielectric by the effective medium theory.

[0137] An interface region mesoscopic Young's modulus distribution characteristic calculation module is configured to compare the effective Young's modulus with the experimentally obtained Young's modulus to determine the appropriate interface region characteristic parameter in the three-dimensional structure model of the dielectric, and calculate the interface region mesoscopic Young's modulus distribution characteristic of the polymer nanocomposite dielectric according to the interface region characteristic parameter.

[0138] Embodiment 3

[0139] The computer device provided by the application comprises a memory and a processor connected electrically, wherein the memory stores a computer program capable of running on the processor, and the processor implements the polymer nanocomposite dielectric interface region Young's modulus inversion analysis method of embodiment 1 when executing the computer program.

[0140] The computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the application.

[0141] The processor can be a central processing unit (CPU), and can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0142] The memory can be used to store the computer program and / or modules, and the processor realizes various functions of the polymer nanocomposite dielectric interface region Young's modulus inversion analysis device / terminal device by running or executing the computer program and / or modules stored in the memory, and calling the data stored in the memory.

[0143] In addition, each functional unit in each embodiment of the application can be integrated in one processing unit, or each unit can exist physically, or two or more units can be integrated in one unit.

[0144] Embodiment 4

[0145] If the functions are realized in the form of software function units and sold or used as independent products, they can be stored in a nonvolatile computer readable storage medium executable by a processor. Based on this understanding, the technical solutions of the present application or the parts of the prior art or the parts of the technical solutions can be embodied in the form of software products. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in various embodiments of the present application. The aforementioned storage medium includes a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various media that can store program codes.

[0146] The above is only to illustrate the technical idea of the present application, and cannot limit the protection scope of the present application. Any modification made according to the technical idea of the present application on the basis of the technical solutions falls within the protection scope of the claims of the present application.

Claims

1. A method for analyzing the Young's modulus of the interfacial region of polymer nanocomposite dielectrics, characterized in that, Includes the following steps: Step 1: Obtain the Young's modulus of the polymer nanocomposite dielectric through experiments, and establish a three-dimensional structural model of the polymer nanocomposite dielectric. The three-dimensional structural model of the polymer nanocomposite dielectric includes a polymer matrix, nanofillers, and interface regions. Step 2: Using the Young's modulus distribution of the interface region of the polymer nanocomposite dielectric as the input dataset, substitute it into the Navier-Cauchy equation to calculate the displacement, strain, and stress distribution of the polymer nanocomposite dielectric. Then, based on the strain and stress of the polymer nanocomposite dielectric, calculate the effective Young's modulus of the interface region in the three-dimensional structure model of the dielectric through the effective dielectric theory. Step 3: Compare the effective Young's modulus obtained in Step 2 with the Young's modulus obtained in Step 1 to determine the interface region characteristic parameters in the appropriate three-dimensional dielectric structure model. Based on the interface region characteristic parameters, calculate the mesoscopic Young's modulus distribution characteristics of the interface region of the polymer nanocomposite dielectric.

2. The method for analyzing the Young's modulus of the interface region of polymer nanocomposite dielectrics according to claim 1, characterized in that, In step 1, a three-dimensional structural model of the polymer nanocomposite dielectric is established using the Monte Carlo method, and the Young's modulus of the polymer matrix and nanofiller regions is set to the experimental results.

3. The method for analyzing the Young's modulus of the interface region of polymer nanocomposite dielectrics according to claim 1, characterized in that, In step 1, a gradually decreasing Sigmoid function is used to describe the variation of Young's modulus in the interface region.

4. The method for analyzing the Young's modulus of the interface region of polymer nanocomposite dielectrics according to claim 1, characterized in that, The process of step 2 is as follows: S2.1 Construct the equilibrium differential equation for polymer nanocomposite dielectrics; S2.2 Constructing the geometric and constitutive equations for polymer nanocomposite dielectrics; S2.3 Substituting the geometric equations into the constitutive equations, we obtain the relationship between stress and displacement derivatives; S2.4 Substitute the relationship between stress and displacement derivative into the equilibrium differential equation to obtain the relationship between the second derivative of displacement and body force, which is the differential form of the Navier-Cauchy equation. S2.

5. Convert the Navier-Cauchy equations into integral form and use the divergence theorem to obtain their weak solution form. Based on their weak solution form, obtain the Navier-Cauchy equations with discretized displacements. S2.

6. Update the displacement values ​​of the Navier-Cauchy equations, which are discretized from the displacement values, one by one; S2.

7. Given an initial displacement, solve the Navier-Cauchy equation using the Jacobi iterative method. Update the displacement one by one through the Jacobi iterative method, calculate the source term using the displacement, and then proceed to the next iteration. Substitute the displacement obtained from the iterative solution into the geometric equation to calculate the strain, and then calculate the stress using the constitutive equation. S2.

8. Based on stress and strain, the effective Young's modulus of the polymer nanocomposite material is calculated using the effective medium theory. S2.9, will Y interface0 / Y matrix As the x-axis, r 0 / r nano The vertical axis is , Y matrix This represents the Young's modulus of the polymer matrix. Y interface0 This represents the Young's modulus of the interface region near the surface of the nanoparticles. r 0 is the parameter of the Sigmoid function. r nano Let be the radius of the nanoparticle; and let the effective Young's modulus of the polymer nanocomposite dielectric be the dependent variable, then we obtain... n 2 Contour plots of effective Young's modulus; compare the contour plots of effective Young's modulus with the experimental results obtained in step 1 to obtain the parameter range of the possible interface region mesoscopic Young's modulus Sigmoid function.

5. The method for analyzing the Young's modulus of the interface region of polymer nanocomposite dielectrics according to claim 4, characterized in that, In step S2.6, the displacement values ​​of the Navier-Cauchy equation, which discretizes the displacement values, are updated one by one using the Jacobi iteration method.

6. The method for analyzing the Young's modulus of the interface region of polymer nanocomposite dielectrics according to claim 4, characterized in that, The process of step 3 is as follows: Select the x-coordinate value of the point of maximum curvature in the contour map. r 0 / r nano and the value of the ordinate Y interface0 / Y matrix As parameters of the Sigmoid function for the mesoscopic Young's modulus in the interface region, substituting them into the gradually decreasing Sigmoid function yields the distribution characteristics of the Young's modulus in the interface region of different polymer nanocomposite dielectrics.

7. The method for analyzing the Young's modulus of the interface region of polymer nanocomposite dielectrics according to claim 5, characterized in that, Step 3 further includes: substituting the parameters of the Young's modulus Sigmoid function of the obtained polymer nanocomposite dielectric into the Navier-Cauchy equation to calculate the strain and stress distribution characteristics inside the polymer nanocomposite dielectric.

8. A device for analyzing the Young's modulus of the interface region of a polymer nanocomposite dielectric, characterized in that, include: A construction module is used to store the Young's modulus of the polymer nanocomposite dielectric obtained experimentally and to establish a three-dimensional structural model of the polymer nanocomposite dielectric, wherein the three-dimensional structural model of the polymer nanocomposite dielectric includes a polymer matrix, nanofillers and interface regions. The effective Young's modulus calculation module is used to calculate the displacement, strain, and stress distribution of the polymer nanocomposite dielectric by substituting the Young's modulus distribution of the interface region into the Navier-Cauchy equation, and then calculating the effective Young's modulus of the interface region in the three-dimensional structure model of the dielectric based on the strain and stress of the polymer nanocomposite dielectric through the effective medium theory. The module for calculating the mesoscopic Young's modulus distribution characteristics of the interface region is used to compare the effective Young's modulus with the experimentally obtained Young's modulus to determine the interface region characteristic parameters in a suitable three-dimensional dielectric structure model, and to calculate the mesoscopic Young's modulus distribution characteristics of the polymer nanocomposite dielectric based on the interface region characteristic parameters.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method for analyzing the Young's modulus of the interface region of polymer nanocomposite dielectrics as described in any one of claims 1-7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for analyzing the Young's modulus of the interface region of polymer nanocomposite dielectrics as described in any one of claims 1-7.

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