Method for characterizing interfacial region mesoscopic traps of polymer nanocomposite dielectric

Abstract

The application discloses a method for characterizing mesoscopic traps in an interface region of a polymer nanocomposite dielectric, a three-dimensional structure model of the nanocomposite dielectric is constructed by using a Monte Carlo method, an electric field distribution of the nanocomposite dielectric under different conductivity distribution conditions of the interface region is calculated by using a high-throughput simulation to solve a steady-state charge conservation equation, effective conductivity of the nanocomposite dielectric is calculated according to an effective medium theory, and interface region mesoscopic conductivity distribution characteristics of the nanocomposite dielectric are obtained by inversion; the three-dimensional distribution characteristics are helpful to reveal variation rules of trap capturing effects of the interface region on carriers from a microscopic level, and a relationship between a condensed state structure and molecular motion of the interface region of the nanocomposite dielectric and macroscopic electrical properties is established. Theoretical support is provided for improving resistance, breakdown, energy storage and other performances of the nanocomposite dielectric from the perspective of trap regulation, so as to meet development requirements of high energy storage density pulse capacitors and other power equipment.

Description

Technical Field

[0001] This invention belongs to the field of high voltage and insulation technology, specifically relating to a method for characterizing mesoscopic traps in the interface region of polymer nanocomposite dielectrics. Background Technology

[0002] Pulsed power technology is widely used in defense fields such as laser weapons, high-power X-rays, high-power microwave technology, and Z-pinch. Pulsed capacitors are the main energy storage devices in pulsed power systems, and the development of pulsed power technology places higher demands on the energy storage density of pulsed capacitors. How to improve the breakdown and energy storage performance of thin-film dielectrics in pulsed capacitors is a key scientific problem that urgently needs to be solved. Developing high-breakdown-performance insulating dielectrics can provide the material basis for high-energy-density pulsed capacitors. Research on polymer nanocomposite dielectrics has pointed the way for the development of high-breakdown-performance insulating dielectrics. Doping nanoscale inorganic particles into a polymer matrix to form a nanoparticle / polymer interface region can change the accumulation and dissipation process of charge carrier energy in the polymer, reduce the energy of the charge carriers, and improve the breakdown field strength of the nanocomposite dielectric.

[0003] The superior performance of polymer nanocomposite dielectrics is closely related to the interface regions formed within them. The mesoscale conductivity and trap distribution characteristics of these interface regions are key influencing factors for high breakdown strength and high energy density in dielectric energy storage materials. With increasing doping content, the conductivity of nanocomposite dielectrics exhibits an anomalous decrease. This anomalous decrease is unrelated to the conductivity of the nanofillers. This anomalous phenomenon occurs with doping with highly insulating, semi-conductive, or conductive fillers. This anomalous decrease in conductivity is related to the interface regions, indicating the formation of deep traps in these regions, which reduce their conductivity. This suggests the existence of low-conductivity and deep-trap interface regions in nanocomposite dielectrics. However, existing testing equipment and techniques face the technical challenge of measuring extremely small current signals in dielectrics under small electrode systems. For example, a picoammeter can accurately measure a current of approximately 1 pA under applied voltage. Assume an external electric field of 500 kV·mm. -1 The electrode area used is 100nm. 2 Only when the conductivity of the dielectric is greater than 2 × 10⁻⁶ -5 S·m -1 Only a picoammeter can measure a current of 1 pA. Therefore, existing testing equipment and techniques cannot accurately obtain the mesoscale distribution characteristics of conductivity and traps in the interface region, and cannot clarify the formation mechanism of deep traps. As a result, quantitative research on the mesoscale conductivity and trap distribution characteristics in the interface region is still lacking, making it difficult to establish the relationship between the condensed-state structure and molecular motion in the interface region and macroscopic electrical properties. Summary of the Invention

[0004] The purpose of this invention is to provide a method for characterizing mesoscopic traps in the interface region of polymer nanocomposite dielectrics, so as to overcome the shortcomings of the prior art.

[0005] A method for characterizing mesoscopic traps in the interface region of polymer nanocomposite dielectrics includes the following steps:

[0006] S1, a three-dimensional structural model of the nanocomposite dielectric was constructed using the Monte Carlo method;

[0007] S2, taking the interface region size and mesoscopic conductivity of the nanocomposite dielectric as input, uses high-throughput simulation to solve the steady-state charge conservation equation to calculate the electric field distribution of the nanocomposite dielectric under different interface region conductivity distributions, and then calculates the effective conductivity of the nanocomposite dielectric based on the effective dielectric theory;

[0008] S3. By comparing the obtained effective conductivity with the conductivity experimental results, the mesoscopic conductivity distribution characteristics of the interface region of the nanocomposite dielectric are obtained by inversion.

[0009] S4. The relationship between the mesoscale trap energy level and conductivity in the interface region is derived from the Mayer compensation behavior that depends on the conductivity temperature. Then, the mesoscale distribution characteristics of the trap energy level in the interface region are obtained based on the mesoscale conductivity distribution characteristics of the nanocomposite dielectric interface region.

[0010] Preferably, the quantity of nanofiller per unit volume can be calculated by the doping ratio and the shape parameters of the nanoparticles. Then, the Monte Carlo method can be used to construct a three-dimensional structural model of an amorphous polymer-based nanocomposite dielectric containing three phases: polymer matrix, nanofiller, and interface region.

[0011] Preferably, the volume crystallinity of the semi-crystalline polymer is calculated based on the X-ray diffraction test results, and then the volume occupied by the amorphous region is calculated. The corrected volume percentage of the nanofiller is obtained by dividing the doping volume fraction of the nanofiller by the volume percentage of the amorphous region. Then, the Monte Carlo method is used to construct a three-dimensional structural model of the semi-crystalline polymer-based nanocomposite dielectric containing the three phases of amorphous region, nanofiller, and interface region.

[0012] Preferably, when establishing the three-dimensional structural model, the spatial step size is set to 1-2 nm, and each dimension of the three-dimensional structural model is divided into 300-500 parts, with a corresponding total length of 300 nm-1 μm. This size of three-dimensional space is much smaller than the amorphous region between spherulites, allowing the structural model to be confined to the amorphous region between spherulites. After establishing the three-dimensional structural model of the amorphous region in the semi-crystalline polymer, the doping content of the nanofiller needs to be recalculated. Because there is basically no nanofiller in the spherulites, this volume needs to be removed. The volume crystallinity of the semi-crystalline polymer can be calculated based on the X-ray diffraction test results, and then the volume occupied by the amorphous region can be calculated. Finally, the corrected nanofiller volume percentage is obtained by dividing the nanofiller doping volume fraction by the volume percentage of the amorphous region.

[0013] Preferably, the conductivity of the interface region of the nanocomposite dielectric is set to a radial distribution in the Sigmoid function space so that the conductivity between the interface region and the polymer matrix can be smoothly transitioned.

[0014] Preferably, σ interface0 / σ matrix Within the defined interval, select n points using a logarithmic division method, r0 / r nano Within a certain interval, n points are selected by linearly dividing the interval into equal parts.

[0015] Preferably, an external electric field is applied to the polymer nanocomposite dielectric, and the steady-state charge conservation equation for the change of conductivity gradient is solved using the finite volume formula Jacobi iteration method to obtain the internal potential and electric field distribution of the polymer nanocomposite dielectric in steady state.

[0016] Preferably, the macroscopic effective conductivity is calculated using the effective dielectric theory, for the conductivity distribution parameters r0 and σ in the interface region of the polymer nanocomposite dielectric. interface0 Given an n×n input dataset, calculate n 2 Group macroscopic effective conductivity.

[0017] Preferably, by combining the mesoscopic distribution characteristics of conductivity in the interface region of polymer nanocomposite dielectrics and the fact that conductivity follows Mayer compensation, an analytical expression for the mesoscopic distribution of trap energy levels in the interface region is derived.

[0018] Preferably, the mesoscopic distribution characteristics of the trap energy levels in the interface region of the polymer nanocomposite dielectric can be derived from the mesoscopic distribution characteristics of the conductivity in the interface region of the polymer nanocomposite dielectric.

[0019] Compared with the prior art, the present invention has the following beneficial technical effects:

[0020] This invention presents a method for characterizing mesoscopic traps in the interface region of polymer nanocomposite dielectrics. It employs the Monte Carlo method to construct a three-dimensional structural model of the nanocomposite dielectric. Using the interface region size and mesoscopic conductivity of the nanocomposite dielectric as input, high-throughput simulation is used to solve the steady-state charge conservation equation to calculate the electric field distribution of the nanocomposite dielectric under different interface region conductivity distributions. Based on effective dielectric theory, the effective conductivity of the nanocomposite dielectric is calculated, and the mesoscopic conductivity distribution characteristics of the interface region are obtained through inversion. This invention utilizes three-dimensional distribution characteristics to help reveal the variation law of the carrier trapping effect of the interface region at the microscopic level. It allows for quantitative research on the mesoscopic conductivity and trap distribution characteristics of the interface region of polymer nanocomposite dielectrics, establishing the relationship between the condensed-state structure and molecular motion of the interface region of nanocomposite dielectrics and their macroscopic electrical properties. This provides theoretical support for improving the resistance, breakdown, and energy storage performance of nanocomposite dielectrics from the perspective of trap control, thereby meeting the development needs of power devices such as high-energy-density pulse capacitors. Attached Figure Description

[0021] Figure 1 This is a logic block diagram in an embodiment of the present invention.

[0022] Figure 2 (a) is a three-phase model of nanofiller, interface region and polymer matrix in an embodiment of the present invention. Figure 2(b) is a schematic diagram of the Sigmoid distribution function of the conductivity of the interface region in an embodiment of the present invention.

[0023] Figure 3 (a) shows the polypropylene / alumina conductivity test results in an embodiment of the present invention. Figure 3 (b) is the conductivity temperature dependence curve in an embodiment of the present invention.

[0024] Figure 4 The image shows the X-ray diffraction pattern of the polypropylene / alumina nanocomposite dielectric in an embodiment of the present invention.

[0025] Figure 5 This is a three-dimensional distribution diagram of polypropylene / alumina nanoparticles with different doping contents in an embodiment of the present invention.

[0026] Figure 6 The above are simulation results of the macroscopic effective conductivity of polypropylene / alumina with different doping contents in the embodiments of the present invention.

[0027] Figure 7 In this embodiment of the invention, the effective conductivity of the polypropylene / alumina nanocomposite dielectric (a) is within σ. interface0 / σ matrix and r0 / r nano (b) Contour map of the plane; (c) Conductivity distribution of the interface region; (d) Thickness of the interface region.

[0028] Figure 8 This is a three-dimensional distribution diagram of the conductivity of polypropylene / alumina nanocomposite dielectrics with different doping contents in the embodiments of the present invention.

[0029] Figure 9 This describes the mesoscopic distribution characteristics of trap energy levels in the interface region of the polypropylene / alumina nanocomposite dielectric in this embodiment of the invention.

[0030] Figure 10 (a) shows the conductivity test results of polypropylene / magnesium oxide in an embodiment of the present invention. Figure 10 (b) The conductivity temperature dependence curve in the embodiment of the present invention.

[0031] Figure 11 The image shows the X-ray diffraction pattern of the polypropylene / magnesium oxide nanocomposite dielectric in an embodiment of the present invention.

[0032] Figure 12 (a) Figure 12 (b) Figure 12 (c) Figure 12 (d) Figure 12 (e) shows the three-dimensional distribution of polypropylene / magnesium oxide nanoparticles with doping contents of 0.5wt%, 1wt%, 2wt%, 3wt%, and 5wt%.

[0033] Figure 13 (a) Figure 13 (b) Figure 13 (c) Figure 13 (d) Figure 13 (e) shows the simulation results of the macroscopic effective conductivity of polypropylene / magnesium oxide with doping contents of 0.5wt%, 1wt%, 2wt%, 3wt%, and 5wt%.

[0034] Figure 14 (a) The effective conductivity of the polypropylene / magnesium oxide nanocomposite dielectric in the embodiments of the present invention is within σ. interface0 / σ matrix and r0 / r nano Contour map of a plane, Figure 14 (b) shows the conductivity distribution of the interface region, and Figure 14(c) shows the thickness of the interface region.

[0035] Figure 15 (a) Figure 15 (b) Figure 15 (c) Figure 15 (d) Figure 15 (e) shows the three-dimensional distribution of conductivity of polypropylene / magnesium oxide composite dielectrics at 0.5wt%, 1wt%, 2wt%, 3wt%, and 5wt%, respectively.

[0036] Figure 16This describes the mesoscopic distribution characteristics of trap energy levels in the interface region of the polypropylene / magnesium oxide nanocomposite dielectric in this embodiment of the invention. Detailed Implementation

[0037] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0038] like Figure 1 As shown, the present invention provides a method for characterizing mesoscopic traps in the interface region of polymer nanocomposite dielectrics, comprising the following steps:

[0039] S1, a three-dimensional structural model of a nanocomposite dielectric containing nanofillers, a polymer matrix, and an interface region was constructed using the Monte Carlo method;

[0040] For amorphous polymers, under conditions of thorough and uniform mixing, the nanofillers can be considered uniformly dispersed within the polymer matrix. After doping with nanofillers to form a polymer nanocomposite dielectric, it will contain a three-phase structure comprising the polymer matrix, nanofillers, and interface regions. The quantity of nanofillers per unit volume can be calculated using the doping ratio and the shape parameters of the nanoparticles. Then, the Monte Carlo method can be used to construct a three-dimensional structural model of the amorphous polymer-based nanocomposite dielectric containing the polymer matrix, nanofillers, and interface regions, as shown below. Figure 2 As shown in (a).

[0041] For semi-crystalline polymers, after doping with nanofillers, the nanofillers are mainly concentrated in the amorphous region because the production of spherulites will displace the nanofillers.

[0042] Nanofillers are added to semi-crystalline polymer melts or solutions. Under thorough stirring, the nanofillers are uniformly distributed in the melt or solution state. After the polymer and nanofillers are thoroughly mixed, the polymer melt is cooled below the crystallization temperature, initiating nucleation and forming crystalline regions within the polymer. Studies show that during polymer crystallization, a negative pressure region forms at the spherulite growth front. The pressure gradient force pulls the nanofillers away from the crystalline region, causing them to accumulate at the spherulite growth front. Therefore, after the crystallization process, the nanofillers are mainly enriched in the amorphous regions between the spherulites.

[0043] Since there are virtually no nanofillers within the spherulites, their conductivity remains unaffected. Therefore, the change in the macroscopic conductivity of the polymer nanocomposite dielectric can be considered primarily attributable to structural changes in the amorphous region. In semi-crystalline polymers, only the three phases—amorphous region, nanofiller, and interface region—need to be considered. To exclude the volume of the crystalline region, the nanofiller doping content in the polymer nanocomposite dielectric needs to be recalculated. The volumetric crystallinity of the semi-crystalline polymer is calculated based on X-ray diffraction results, and then the volume occupied by the amorphous region is calculated. The corrected nanofiller volume percentage is obtained by dividing the nanofiller doping volume fraction by the amorphous region volume percentage. Then, a three-dimensional structural model of the semi-crystalline polymer-based nanocomposite dielectric, including the amorphous region, nanofiller, and interface region, is constructed using the Monte Carlo method.

[0044] For semi-crystalline polymer-based nanocomposite dielectrics, both spherulites and amorphous regions exist between the two electrodes. When the semi-crystalline polymer comes into contact with the electrodes, a contact barrier is formed, and the contact barrier in different regions is related to the aggregated structure of the polymer. For polypropylene and low-density polyethylene, the conduction band of the crystalline region is higher than that of the amorphous region. Therefore, the barrier at the interface between the electrode and the crystalline region is high, making charge injection difficult; the barrier at the interface between the electrode and the amorphous region is low, making charge injection easy. Assuming that the spherulites and amorphous regions in the semi-crystalline polymer are connected in parallel, then the current collected by the electrode in steady state is mainly determined by the current in the amorphous region. After doping with nanofillers, the nanofillers are displaced during spherulite production, and they mainly accumulate in the amorphous regions. Since there are virtually no nanofillers within the spherulites, their conductivity is largely unaffected. Therefore, the change in the macroscopic conductivity of semi-crystalline polymer-based nanocomposite dielectrics is mainly attributed to the structural changes in the amorphous regions. The problem of considering four phases—the crystalline region, the amorphous region, the nanofiller, and the interface region—in semi-crystalline polymers can be simplified to a three-phase problem by using the logical deduction above and existing experimental results. This reduction significantly decreases the complexity of the research problem.

[0045] To distinguish between nanofillers and interface regions ranging from tens to hundreds of nm in the polymer nanocomposite dielectric structure model, the spatial step size was set to 1-2 nm. In the three-dimensional structural model, each dimension was divided into 300-500 parts, with a corresponding total length of 300 nm-1 μm.

[0046] Because the charge injection barrier between the electrode and the crystalline region is higher than that between the electrode and the amorphous region, most of the charge is injected into the amorphous region. A significant energy barrier exists between the amorphous and crystalline regions; a large amount of energy is required for charge to enter the crystalline region from the amorphous region. Therefore, charge tends to transport in the amorphous region. Consequently, the three-dimensional structural model of the semi-crystalline polymer-based nanocomposite dielectric containing the interface region is simplified, considering only the polymer matrix, nanofiller, and interface region. Therefore, the same method can be used to construct three-dimensional structural models of amorphous polymer-based nanocomposite dielectrics and semi-crystalline polymer-based nanocomposite dielectrics to study the mesoscopic conductivity and trap distribution characteristics of the interface region.

[0047] S2, taking the interface region size and mesoscopic conductivity of the nanocomposite dielectric as input, uses high-throughput simulation to solve the steady-state charge conservation equation to calculate the electric field distribution of the nanocomposite dielectric under different interface region conductivity distributions, and then calculates the effective conductivity of the nanocomposite dielectric based on the effective dielectric theory;

[0048] The conductivity of the interface region of the nanocomposite dielectric is set to a radial distribution in the Sigmoid function space to achieve a smooth transition in conductivity between the interface region and the polymer matrix, while maintaining a reasonable interface region thickness. The Sigmoid function includes the conductivity σ near the surface of the nanofiller in the interface region. interface0 The two independent variables, r0 and the interface thickness adjustment parameter, are used to adjust the conductivity distribution characteristics of the interface region.

[0049] like Figure 2 As shown in (b), the conductivity distribution in the interface region is represented by the Sigmoid function:

[0050]

[0051] In the formula, r is the length extending outward from the center of the nanoparticle. nano Let r be the radius of the nanoparticle, r0 be the interface thickness adjustment parameter, and σ be the radius of the nanoparticle. matrix σ is the electrical conductivity of the polymer matrix. interface σ represents the electrical conductivity of the interface region at different distances from the nanoparticles. interface0 The conductivity of the interface region near the surface of the nanofiller is given.

[0052] The Sigmoid function contains the conductivity σ of the interface region near the surface of the nanofiller. interface0 The two independent variables, α and r0, which are used to adjust the interface thickness, can be used to regulate the conductivity distribution characteristics of the interface region. The ratio of the conductivity of the interface region to the conductivity of the polymer matrix is ​​α. c The thickness of the interface region is set to extend from the surface of the nanofiller to α. c The position equals 95%.

[0053]

[0054] In the formula, d interface The thickness of the interface area.

[0055] The constitutive equation for dielectric current density is:

[0056] j(r)=σ(r)E(r) (3)

[0057] In the formula, r is the three-dimensional spatial coordinate in the polymer nanocomposite dielectric, j is the current density at different spatial locations, σ is the conductivity at different spatial locations, and E is the electric field strength at different spatial locations.

[0058] When the current reaches steady state, the divergence of the current density is equal to 0, which is the steady-state charge conservation equation:

[0059]

[0060] Let the electric field E be expressed as electric potential. negative gradient The steady-state charge conservation equation can be transformed into the form of the generalized Poisson equation:

[0061]

[0062] Assuming an electric field is applied along the x-direction to the polymer nanocomposite dielectric, the electric field distribution inside the composite dielectric reaches equilibrium at steady state, and the external current also reaches steady state. The steady-state charge conservation equation for the conductivity gradient is solved using the finite volume formula Jacobi iteration method to calculate the potential and electric field distribution. Then, the macroscopic effective conductivity is solved according to the effective dielectric theory, whose expression is:

[0063]

[0064] In the formula, E x Let j represent the electric field intensity along the x-direction at different spatial locations. x Let σ be the current density along the x-direction at different spatial locations. eff The effective conductivity of the polymer nanocomposite dielectric is given by . <> represents the calculated spatial average.

[0065] S3, by comparing the obtained effective conductivity with the experimental results, the mesoscopic conductivity distribution characteristics of the interface region of the nanocomposite dielectric are obtained.

[0066] An external electric field is applied to the polymer nanocomposite dielectric, and the steady-state charge conservation equation is solved using the finite volume formula Jacobi iteration method to obtain the internal potential and electric field distribution of the polymer nanocomposite dielectric in steady state.

[0067] The macroscopic effective conductivity is calculated using the effective dielectric theory, and the conductivity distribution parameters r0 and σ in the interface region of the polymer nanocomposite dielectric are analyzed. interface0 Given an n×n input dataset, calculate n 2 The macroscopic effective conductivity was determined. Then, the simulated effective conductivity values ​​were compared with the experimental conductivity results to invert and determine the mesoscopic distribution characteristics of conductivity in the interface region of the polymer nanocomposite dielectric.

[0068] σ interface0 / σ matrix Within the defined interval, select n points using a logarithmic division method, r0 / r nano Within a certain interval, n points are linearly divided into equal parts. This involves using the interface thickness adjustment parameter r0 and the conductivity σ near the nanofiller surface in the Sigmoid function representing the interface conductivity distribution. interface0 These two parameters are set as an n×n input dataset, and n can be calculated for each polymer nanocomposite dielectric sample. 2 The macroscopic conductivity is used to form an n×n output dataset.

[0069] S4. The relationship between the mesoscale trap energy level and conductivity in the interface region is derived from the Mayer compensation behavior that depends on the conductivity temperature. Then, the mesoscale distribution characteristics of the trap energy level in the interface region are obtained based on the mesoscale conductivity distribution characteristics of the nanocomposite dielectric interface region.

[0070] From the Mayer compensation behavior of the conductivity of polymer nanocomposite dielectrics, we can deduce that the shape distribution parameters of the exponential function-type trap density-energy level distribution remain unchanged. That is, the shape distribution parameters of the trap density-energy level distribution in the interface region are the same as those in the polymer matrix; only the deepest trap energy level changes. Combining the mesoscopic distribution characteristics of the conductivity in the interface region of the polymer nanocomposite dielectric with the Mayer compensation behavior, an analytical expression for the mesoscopic distribution of trap energy levels in the interface region can be derived.

[0071] Based on the mesoscopic distribution characteristics of conductivity in the interface region of polymer nanocomposite dielectrics, the mesoscopic distribution characteristics of trap energy levels in the interface region of polymer nanocomposite dielectrics can be derived.

[0072] 1) The trap density-energy level distribution is an exponential function.

[0073] The temperature dependence of the conductivity of polymer nanocomposite dielectrics follows the Mayer compensation rule.

[0074]

[0075] In the formula, σ M The macroscopic conductivity obtained from the test is T, where T is the test temperature. MN To compensate for the temperature of Meyer, k BU is the Boltzmann constant. T For the trap energy level, σ 00 It is a pre-factor.

[0076] The temperature dependence of conductivity follows the Mayer compensation rule, indicating that the trap energy levels and trap density of polymer nanocomposite dielectrics have the following relationship.

[0077] u T =k B T MN ln(N0 / N T (8)

[0078] In the formula, N0 is the trap density in the extended state, N T For energy level u T The density of traps.

[0079] Equation (8) shows that the trap density-energy level distribution is an exponential function distribution.

[0080]

[0081] In the formula, T MN The shape distribution parameter represents the density-level distribution of an exponential function trap.

[0082] 2) The shape and distribution parameters of the exponential function type trap density-level distribution remain unchanged.

[0083] Only when the conductivity at most locations within the polymer nanocomposite dielectric follows the Mayer compensation rule can the macroscopic conductivity σ be guaranteed. M This rule applies. Expressing mesoscopic conductivity as a function of position yields the relationship between conductivity at different locations and the trap energy level and temperature:

[0084]

[0085] When the sample temperature equals T MN At that time, the spatial average conductivity of the sample is equal to σ. 00 We can obtain:

[0086]

[0087] Taking the logarithm of both sides of the above equation, we get:

[0088]

[0089] Due to the trap energy levels u at various locations in the polymer nanocomposite dielectric T Always greater than 0, therefore, only T at each position MNFor all r to be equal to a constant, equation (12) can hold. This proves a new law that the shape distribution parameters of the trap density-energy level distribution in the interface region remain unchanged, while only the trap energy levels change.

[0090] 3) Analytical expression for the mesoscopic distribution of trap energy levels in the interface region

[0091] Based on the fact that the shape distribution parameters of the trap density-energy level distribution in the interface region remain unchanged, and combining the mesoscopic distribution characteristics of conductivity in the interface region of the polymer nanocomposite dielectric with the Mayer compensation behavior of conductivity, the analytical expression for the mesoscopic distribution of trap energy levels in the interface region can be derived as follows:

[0092]

[0093] In the formula, u T(ir) For the trap energy levels at different locations in the interface region, u T(matrix) This represents the trap energy level of the polymer matrix.

[0094] Substituting the sigmoid equation for conductivity into the analytical expression for the trap energy level as a function of conductivity, the mesoscopic distribution of trap energy levels in the interface region can be quantitatively calculated:

[0095]

[0096] The shape parameters of the trap density-energy level distribution in polymer nanocomposite dielectrics are the same in the interface region and the polymer matrix. The shape parameters of the trap density-energy level distribution are related to the polymer composition. Since the interface region and the polymer matrix have the same molecular composition, the shape parameters of the trap density-energy level distribution do not change. The trap energy levels differ in the interface region and are related to the strength of the intermolecular interactions. The stronger the intermolecular interactions, the deeper the trap energy levels; the weaker the intermolecular interactions, the shallower the trap energy levels.

[0097] Example 1

[0098] Characterization of interfacial conductivity and trap energy level distribution of polypropylene / alumina nanocomposite dielectrics:

[0099] (1) The conductivity test results of polypropylene / alumina nanocomposite dielectrics with different doping concentrations at different temperatures are shown in the figure. Figure 3 (a) Figure 3 As shown in (b), temperature dependence analysis of conductivity revealed that the conductivity of polypropylene / alumina nanocomposite dielectric samples with different doping contents satisfies the condition that the extended lines of the Arrhenius fitting curves intersect at a single point, indicating that the temperature dependence of conductivity follows the Mayer compensation rule. The intersection point is T. MN For 414K, σ 00 3.16×10 -12 S·m -1The activation energy for electrical conductivity of the polypropylene matrix is ​​0.764 eV.

[0100] (2) X-ray diffraction patterns of polypropylene / alumina nanocomposite dielectrics with different doping contents, as shown in the figure. Figure 4 The volume crystallinity was calculated, and then the volume occupied by the amorphous region was calculated. Next, the corrected volume percentages of the nanofiller were obtained by dividing the doping volume fraction of the nanofiller by the volume percentage of the amorphous region: 0.24% (PP / 0.5wt%Al2O3), 0.5% (PP / 1wt%Al2O3), 1.02% (PP / 2wt%Al2O3), 1.52% (PP / 3wt%Al2O3), and 2.71% (PP / 5wt%Al2O3).

[0101] 3) Establishment of a three-dimensional structural model of polypropylene / alumina nanocomposite dielectric:

[0102] A three-dimensional cubic structure model of polypropylene / alumina nanocomposite dielectric with different doping contents, containing a polymer matrix, nanofillers, and an interface region, was constructed using Matlab, as shown below. Figure 5 As shown, the alumina nanoparticles have a particle size of 20 nm. The spatial step size is 1 nm, and each dimension is divided into 300 parts, corresponding to a total length of 300 nm. The nanoparticles are uniformly distributed in the amorphous region.

[0103] 4) Set the interface area to input the conductivity dataset and solve for the corresponding macroscopic effective conductivity.

[0104] The conductivity distribution in the interface region is represented by the Sigmoid function, and the polymer conductivity is 7.875 × 10⁻⁶. -16 S·m -1 The electrical conductivity of the nanoparticles is 6 × 10⁻⁶. -13 S·m -1 r nano The value is 10 nm. The Sigmoid function contains the conductivity σ of the interface region near the surface of the nanofiller. interface0 The two independent variables, σ and the interface thickness adjustment parameter r0, can be used to adjust the conductivity distribution characteristics of the interface region. interface0 / σ matrix In 10 -5 Take 40 points between 1 and 0 using the logarithmic division method, r0 / r nano Divide the interval between 0 and 1 into 40 equal parts. σ can be... interface0 The input dataset is set to r0 as 40×40.

[0105] Applying 50 kV·mm along the x-direction to a nanocomposite dielectric -1The electric field was determined by solving the steady-state charge conservation equation for the conductivity gradient using the finite volume formula Jacobi iteration method to calculate the internal potential and electric field distribution of the nanocomposite dielectric. Then, the macroscopic effective conductivity was calculated using effective dielectric theory. Figure 6 Simulation results of the macroscopic effective conductivity of polypropylene / alumina nanocomposite dielectrics with different doping contents under 1600 different interface region conductivity distributions are presented. The results show that the interface region thickness r0 and σ, which characterizes the conductivity of the interface region, are important parameters. interface0 It is an important factor in regulating the effective electrical conductivity of nanocomposites. For the same sample, the effective electrical conductivity of the sample continuously decreases as the thickness of the interface region increases and the conductivity of the interface region decreases.

[0106] 5) Mesoscopic distribution characteristics of conductivity in the interfacial region of polymer nanocomposite dielectrics

[0107] The calculated macroscopic effective conductivity of 1600 types was compared with experimental results. Figure 7 (a) When the simulated and experimental results of the effective conductivity of polypropylene / alumina nanocomposite dielectrics with different doping contents are equal, the effective conductivity at σ interface0 / σ matrix and r0 / r nano A contour map of a plane, taking the σ value at the point of maximum curvature in the contour map. interface0 r0 is used as a parameter in the Sigmoid function for the conductivity distribution in the interface region, and the mesoscopic distribution characteristics of the conductivity in the interface region are further determined. The Sigmoid curves of the conductivity distribution in the interface region and the variation of the interface region thickness for polypropylene / alumina nanocomposite dielectrics with different doping contents are shown below. Figure 7 As shown in (b) and (c), the three-dimensional distribution of conductivity in the interface region is as follows: Figure 8 As shown, the thickness of the interface region decreases with increasing doping content. The conductivity of the nanofiller region, amorphous region, and interface region decreases sequentially, and the conductivity of the interface region transitions smoothly with that of the matrix.

[0108] 6) Mesoscopic distribution characteristics of traps in the interface region of polymer nanocomposite dielectrics:

[0109] The mesoscopic distribution characteristics of trap energy levels in the polypropylene / alumina interface region with different doping contents were calculated using equation (14). Figure 9When a small amount of doping is observed, the molecular chains in the interface region are strongly bound by nanoparticles, resulting in a more compact and ordered polymeric condensed structure near the nanoparticles. Stronger intermolecular interactions lead to deeper trap energy levels. However, when the doping concentration reaches 3 wt% and 5 wt%, severe nanoparticle aggregation weakens the binding force on the molecular chains, reducing the order and compactness of the molecular chain arrangement. This results in weaker intermolecular interactions in the interface region, leading to shallower trap energy levels. Furthermore, as the nanoparticle doping concentration increases, the interparticle spacing decreases, and the binding force and aggregation behavior of the molecular chains in the interface region are more significantly influenced by adjacent nanoparticles, causing the interface region to become thinner. Consequently, the spatial distribution range of the trap energy levels decreases with increasing doping concentration. It was also found that the trap energy level changes in the interface region. The trap energy level gradually decreases along the direction away from the nanofiller. This is related to the strength of the interaction between molecular chains. Near the nanofiller, the molecular chains are more tightly bound and thus more tightly arranged, resulting in stronger interactions between molecular chains and deeper trap energy levels. On the other hand, the degree of binding and tightness of the molecular chains decreases as they move away from the nanofiller, and the weakening of interactions between molecular chains makes the trap energy level shallower.

[0110] Example 2

[0111] Interfacial conductivity and trap level distribution characteristics of polypropylene / magnesium oxide nanocomposite dielectrics

[0112] (1) The conductivity test results of polypropylene / magnesium oxide nanocomposite dielectrics with different doping concentrations at different temperatures are shown in the figure. Figure 10 The applied electric field is 50 kV·mm. -1 Temperature dependence analysis of conductivity revealed that the conductivity of polypropylene / magnesium oxide nanocomposite dielectric samples with different doping contents satisfies the condition that the extended lines of the Arrhenius fitting curves intersect at a single point, and the temperature dependence of conductivity follows the Mayer compensation rule. The intersection point is T. MN For 414K, σ 00 3.16×10 -12 S·m -1 The activation energy for electrical conductivity of the polypropylene matrix is ​​0.764 eV.

[0113] (2) X-ray diffraction patterns of polypropylene / magnesium oxide nanocomposite dielectrics with different doping contents, as shown in the figure. Figure 11 The volume crystallinity was calculated and the corrected volume percentages of the nanofillers were 0.24% (PP / 0.5wt%MgO), 0.5% (PP / 1wt%MgO), 1.02% (PP / 2wt%MgO), 1.60% (PP / 3wt%MgO) and 2.72% (PP / 5wt%MgO).

[0114] 3) Establishment of a three-dimensional structural model of polypropylene / magnesium oxide nanocomposite dielectric

[0115] A three-dimensional cubic structure model of polypropylene / magnesium oxide nanocomposite dielectric with different doping contents, comprising a polymer matrix, nanofillers, and an interface region, was constructed using Matlab, as shown below. Figure 12 As shown, the alumina nanoparticles have a particle size of 50 nm. The spatial step size is 2.5 nm, with each dimension divided into 300 parts, resulting in a total length of 750 nm.

[0116] 4) Set the interface area to input the conductivity dataset and solve for the corresponding macroscopic average conductivity.

[0117] The conductivity distribution in the interface region is represented by the Sigmoid function, and the polymer conductivity is 7.875 × 10⁻⁶. -16 S·m -1 The electrical conductivity of the nanoparticles is 1.58 × 10⁻⁶. -12 S·m -1 r nano The value is 25 nm. The Sigmoid function contains the conductivity σ of the interface region near the surface of the nanofiller. interface0 The two independent variables, σ and the interface thickness adjustment parameter r0, can be used to adjust the conductivity distribution characteristics of the interface region. interface0 / σ matrix In 10 -5 Take 40 points between 1 and 0 using the logarithmic division method, r0 / r nano Divide the interval between 0 and 1 into 40 equal parts. σ can be... interface0 The input dataset is set to r0 as 40×40.

[0118] Applying 50 kV·mm along the x-direction to a nanocomposite dielectric -1 The electric field was determined by solving the steady-state charge conservation equation for the conductivity gradient using the finite volume formula Jacobi iteration method to calculate the internal potential and electric field distribution of the nanocomposite dielectric. Then, the macroscopic effective conductivity was calculated using effective dielectric theory. Figure 13 The simulation results show the macroscopic effective conductivity of polypropylene / magnesium oxide nanocomposite dielectrics with different doping contents under 1600 different interface region conductivity distributions.

[0119] 5) Mesoscopic distribution characteristics of conductivity in the interfacial region of polymer nanocomposite dielectrics

[0120] The calculated macroscopic effective conductivity of 1600 types was compared with experimental results. Figure 14 (a) When the simulated and experimental results of the effective conductivity of polypropylene / magnesium oxide nanocomposite dielectrics with different doping contents are equal, the effective conductivity at σ interface0 / σ matrix and r0 / rnano A contour map of a plane, taking the σ value at the point of maximum curvature in the contour map. interface0 r0 is used as a parameter in the Sigmoid function for the conductivity distribution in the interface region. The Sigmoid curves for the conductivity distribution in the interface region of polypropylene / magnesium oxide nanocomposite dielectrics with different doping contents and the variation in interface region thickness are shown below. Figure 14 As shown in (b) and (c), the three-dimensional distribution of conductivity in the interface region is as follows: Figure 15 As shown.

[0121] 6) Mesoscopic distribution characteristics of traps in the interface region of polymer nanocomposite dielectrics

[0122] The mesoscopic distribution characteristics of trap energy levels in the polypropylene / magnesium oxide interface region with different doping contents were calculated using equation (14). Figure 16 When the doping concentration is no higher than 3 wt%, the nanoparticles exert a strong binding effect on the nearby molecular chains, forming a tightly ordered polymeric condensed structure in the interface region. The interactions between molecular chains are strong, resulting in deep trap energy levels. However, when the doping concentration reaches a high level of 5 wt%, the tightness and order of the molecular chains weakens, leading to weaker interactions between molecular chains in the interface region and shallower trap energy levels. Furthermore, as the nanoparticle content increases, the interface region becomes thinner, and the spatial distribution range of the trap energy levels decreases with increasing doping content. Moreover, along the direction away from the nanofiller, the strength of interactions between molecular chains decreases, and the trap energy levels in the interface region become shallower.

[0123] This invention discloses a method for characterizing mesoscopic traps in the interface region by inverting the steady-state charge conservation equation in polymer nanocomposite dielectrics. This method characterizes the trap distribution within the tiny interface region at the tens to hundreds of nanometer scale of nanocomposite dielectrics. It overcomes the limitation of experimentally measuring the conductivity and mesoscopic trap distribution characteristics within the interface region, providing an effective method for quantitatively studying mesoscopic conductivity and trap distribution characteristics. Furthermore, it can provide methodological support for establishing the relationship between the condensed-state structure and molecular motion of the interface region and macroscopic electrical properties.

[0124] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for characterizing mesoscopic traps in the interfacial region of polymer nanocomposite dielectrics, characterized in that, Includes the following steps: S1, a three-dimensional structural model of the nanocomposite dielectric was constructed using the Monte Carlo method; S2, taking the interface region size and mesoscopic conductivity of the nanocomposite dielectric as input, uses high-throughput simulation to solve the steady-state charge conservation equation to calculate the electric field distribution of the nanocomposite dielectric under different interface region conductivity distributions, and then calculates the effective conductivity of the nanocomposite dielectric based on the effective dielectric theory; S3. By comparing the obtained effective conductivity with the conductivity experimental results, the mesoscopic conductivity distribution characteristics of the interface region of the nanocomposite dielectric are obtained by inversion. S4. The relationship between the mesoscale trap energy level and conductivity in the interface region is derived from the Mayer compensation behavior of conductivity temperature dependence. Then, the mesoscale distribution characteristics of the trap energy level in the interface region are obtained based on the mesoscale conductivity distribution characteristics of the nanocomposite dielectric interface region. Specifically, based on the unchanged shape distribution parameters of the trap density-energy level distribution in the interface region, and combining the mesoscopic distribution characteristics of conductivity in the interface region of the polymer nanocomposite dielectric with the Mayer compensation behavior of conductivity, the analytical expression for the mesoscopic distribution of trap energy levels in the interface region is derived as follows: (13) In the formula, u T(ir) For the trap energy levels at different locations in the interface area, u T(matrix) denoted as the trap energy level of the polymer matrix; r represents the three-dimensional spatial coordinates in the polymer nanocomposite dielectric. T To test the temperature, T MN To compensate for temperature for Meyer, This represents the conductivity distribution in the interface region; k B Boltzmann's constant; Substituting the sigmoid equation for conductivity into the analytical expression for the trap energy level as a function of conductivity, the mesoscopic distribution of trap energy levels in the interface region can be quantitatively calculated: (14) r The length extending outward from the center of the nanoparticle; the shape parameters of the trap density-energy level distribution in the polymer nanocomposite dielectric are the same in the interface region and in the polymer matrix. r nano Where is the radius of the nanoparticle. r 0 represents the interface area thickness adjustment parameter. σ matrix The electrical conductivity of the polymer matrix. σ interface0 The conductivity of the interface region near the surface of the nanofiller is given.

2. The method for characterizing mesoscopic traps in the interface region of polymer nanocomposite dielectrics according to claim 1, characterized in that, The quantity of nanofillers per unit volume can be calculated by using the doping ratio and the shape parameters of the nanoparticles. Then, the Monte Carlo method can be used to construct a three-dimensional structural model of an amorphous polymer-based nanocomposite dielectric containing three phases: polymer matrix, nanofillers, and interface region.

3. The method for characterizing mesoscopic traps at the interface region of polymer nanocomposite dielectrics according to claim 1, characterized in that, The volume crystallinity of the semi-crystalline polymer was calculated based on the X-ray diffraction test results. Then, the volume occupied by the amorphous region was calculated. The corrected volume percentage of the nanofiller was obtained by dividing the doping volume fraction of the nanofiller by the volume percentage of the amorphous region. Then, the Monte Carlo method was used to construct a three-dimensional structural model of the semi-crystalline polymer-based nanocomposite dielectric containing the three phases of amorphous region, nanofiller, and interface region.

4. The method for characterizing mesoscopic traps at the interface region of polymer nanocomposite dielectrics according to claim 1, characterized in that, When creating a 3D structural model, set the spatial step size to 1. 2nm, in the three-dimensional structural model, each dimension is divided into 300 500 copies, corresponding to a total length of 300nm 1μm.

5. The method for characterizing mesoscopic traps at the interface region of polymer nanocomposite dielectrics according to claim 1, characterized in that, The conductivity of the interface region of the nanocomposite dielectric is set to a radial distribution of the Sigmoid function space to achieve a smooth transition in conductivity between the interface region and the polymer matrix.

6. The method for characterizing mesoscopic traps at the interface region of polymer nanocomposite dielectrics according to claim 5, characterized in that, Will σ interface0 / σ matrix Within the set interval, divide according to the logarithmic method. n One point, r 0 / r nano Divide into linear equal parts within a certain interval. n One point.

7. The method for characterizing mesoscopic traps at the interface region of polymer nanocomposite dielectrics according to claim 1, characterized in that, An external electric field is applied to the polymer nanocomposite dielectric, and the steady-state charge conservation equation is solved using the finite volume formula Jacobi iteration method to obtain the internal potential and electric field distribution of the polymer nanocomposite dielectric in steady state.

8. The method for characterizing mesoscopic traps at the interface region of polymer nanocomposite dielectrics according to claim 7, characterized in that, Macroscopic effective conductivity is calculated using effective dielectric theory, and the conductivity distribution parameters at the interface region of polymer nanocomposite dielectrics are analyzed. r 0 and σ interface0 of n × n Input dataset, calculate n 2 Group macroscopic effective conductivity.

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