A method for selecting a kind of PMIA insulating film nanofiller based on four-dimensional microscopic parameter collaborative evaluation

Abstract

The application belongs to the technical field of polymer composite insulation material design and molecular dynamics simulation, and discloses a PMIA insulation film nano filler type optimization method based on four-dimensional microcosmic parameter cooperative evaluation. For each candidate nano filler, a nano filler / PMIA molecular dynamics model is constructed under the same doping mass fraction set to obtain the glass transition temperature, the free volume fraction, the interface binding energy and the PMIA molecular chain mean square displacement; a heat resistance ratio, a compactness ratio, a high-temperature interface retention rate and a chain segment confinement ratio are constructed, and a four-parameter cooperative index is obtained by adopting a weightless geometric coupling; and the curve of the cooperative index changing with the doping amount is integrated to form a type optimization index in combination with a low-dose utilization factor. The application simultaneously evaluates macroscopic thermal transition, chain accumulation, interface stability and chain segment motion, and avoids evaluation deviation caused by subjective weight and single doping point.

Description

Technical Field

[0001] This invention belongs to the field of polymer composite insulation material design and molecular dynamics simulation technology. Specifically, it relates to a method for constructing an unweighted four-parameter synergistic index using glass transition temperature, free volume fraction, interfacial binding energy and mean square displacement, and for quantitatively selecting the type of nanofiller for PMIA insulating films based on concentration response area and low-dose utilization factor. Background Technology

[0002] Poly(m-phenylene isophthalamide) (PMIA) possesses excellent heat resistance, mechanical properties, and electrical insulation properties, and is widely used in insulating films and papers for high-temperature electrical equipment such as motors and transformers. As power equipment develops towards higher power density, miniaturization, and long-term high-temperature operation, the thermal stress on insulating materials is continuously increasing. Pure PMIA is prone to phenomena such as enhanced molecular chain motion, relaxed chain stacking structure, and increased free volume under high-temperature conditions, which in turn affects its high-temperature structural stability.

[0003] Introducing nanofillers into PMIA matrices is an important method to improve their thermal stability. Nanofillers can fill the gaps between PMIA molecular chains and restrict molecular chain segment movement and improve chain packing through interfacial interactions. However, the modification effect of nanofillers is affected by factors such as filler type, structural dimensions, surface properties, dispersion state, and doping mass fraction. The modification effect and concentration response of different fillers vary.

[0004] Molecular dynamics simulations can obtain parameters such as glass transition temperature, free volume fraction, interfacial binding energy, and mean square displacement, which respectively reflect the thermal transition characteristics, chain packing state, interfacial interactions, and molecular chain mobility of the composite system. Existing methods typically select nanofillers based on the performance of a single parameter or at a fixed doping mass fraction, making it difficult to comprehensively evaluate the overall modification effect of different fillers; when using linear weighting for multi-index evaluation, it is easily affected by the artificially set weights.

[0005] Furthermore, comparing the performance of each candidate filler only at the locally optimal doping mass fraction is insufficient to reflect the filler's continuous modification ability across the entire candidate doping range, nor can it effectively distinguish the low-dose utilization ability of different fillers. Therefore, it is necessary to establish a method for selecting the best PMIA insulating film nanofiller types that can comprehensively evaluate multiple microscopic parameters, reduce the influence of subjective weights, and take into account both concentration response characteristics and low-dose utilization ability. Summary of the Invention

[0006] The technical problem to be solved by the present invention is that the existing methods for selecting nanofiller types for PMIA insulating films usually rely on single parameters, single doping mass fractions or artificially set index weights, which are difficult to comprehensively reflect the modification effect and low-dose utilization capability of different candidate nanofillers in the entire candidate doping range. As a result, the selection result of filler type is easily affected by evaluation indexes, weight settings and doping point selection.

[0007] To address the aforementioned technical problems, this invention provides a method for optimizing the types of PMIA insulating film nanofillers based on four-dimensional microscopic parameter synergistic evaluation, comprising the following steps:

[0008] S1. Establish a model of the candidate nanofiller / PMIA composite system.

[0009] Determine the set of candidate nanofiller types:

[0010]

[0011] In the formula, This is a collection of candidate nanofiller types. For any candidate nanofiller, This represents the number of candidate nanofiller types.

[0012] A pure poly(m-phenylene isophthalamide) (PMIA) matrix model was established, and models of nanofiller / PMIA composite systems containing different candidate nanofillers were also established. The same set of candidate doping mass fractions was used for each candidate nanofiller.

[0013]

[0014] And satisfy:

[0015]

[0016] In the formula, For the first Each candidate doping mass fraction This represents the number of candidate doping mass fractions.

[0017] Each candidate system uses the same PMIA matrix model with the same degree of polymerization and chain number, and maintains consistency in initial packing density, periodic boundary conditions, and model construction principles to ensure comparability between different nanofillers.

[0018] The doping mass fraction of the nanofiller is determined according to the following formula:

[0019]

[0020] In the formula, For the quality of candidate nanofillers, This refers to the quality of the PMIA matrix.

[0021] S2. Optimize and balance the model.

[0022] Geometric optimization, energy minimization, cyclic annealing, and molecular dynamics equilibrium treatment were performed on the pure PMIA matrix model and the models of various nanofillers / PMIA composite systems to obtain equilibrium configurations in which energy, temperature, and density all reach a stable state.

[0023] Preferably, the interaction between atoms in the system is described by the COMPASS III force field, and the molecular dynamics time step is set to 1 fs; the cyclic annealing temperature range is 300 K to 900 K, and after annealing, the system is subjected to equilibrium treatment in the NVT ensemble and NPT ensemble in sequence.

[0024] For different candidate nanofillers and different candidate doping mass fractions, the same force field, time step, temperature control method, pressure control method, non-bonded interaction calculation method and equilibrium judgment criterion are used to reduce the impact of simulation condition differences on evaluation results.

[0025] S3. Calculate the four basic parameters.

[0026] Based on the equilibrium pure PMIA matrix model, the glass transition temperature of pure PMIA was calculated. and free volume fraction .

[0027] Based on the candidate nanofiller / PMIA composite system models, the candidate nanofillers were calculated respectively. Mass fraction of each candidate dopant glass transition temperature Free volume fraction Interfacial bonding energy at different evaluation temperatures And the mean square displacement of the PMIA molecular chain at the high-temperature evaluation temperature and the unified evaluation time. .

[0028] The glass transition temperature is obtained through a volume-temperature curve. Linear fitting is performed on the low-temperature and high-temperature segments of the curve, and the temperature corresponding to the intersection of the two fitted lines is the glass transition temperature.

[0029] The free volume fraction is calculated according to the following formula:

[0030]

[0031] In the formula, For free volume, To occupy space.

[0032] Interface integration energy can be calculated according to the following formula:

[0033]

[0034] In the formula, The total energy of the nanofiller / PMIA composite system. The energy required to remove the nanofiller from the PMIA portion of the same composite system configuration. The energy required to remove the nanofiller portion from the same composite system configuration.

[0035] The mean square displacement of the PMIA molecular chain is calculated according to the following formula:

[0036]

[0037] In the formula, For the selected number of PMIA atoms, and The first The positions of the atoms at the initial and evaluation times.

[0038] The mean square displacement of each candidate system was evaluated using the same high-temperature evaluation temperature, evaluation time, atom selection range, and trajectory processing parameters.

[0039] S4. Perform dimensionless processing on the four basic parameters.

[0040] The heat resistance ratio was calculated based on the glass transition temperature of the pure PMIA matrix model:

[0041]

[0042] A higher heat resistance ratio indicates that the candidate composite system has a higher glass transition temperature compared to pure PMIA.

[0043] The density ratio was calculated based on the free volume fraction of the pure PMIA matrix model:

[0044]

[0045] Since a smaller free volume fraction usually indicates a more compact packing of PMIA molecular chains, the following approach is adopted. The free volume fraction is converted into a positive index where a larger value indicates a better evaluation result.

[0046] Let the set of temperatures for evaluating interfacial bonding energy be:

[0047]

[0048] The highest evaluation temperature is the high-temperature evaluation temperature. Based on the change in interfacial bonding energy with temperature, the high-temperature interfacial retention rate is calculated:

[0049]

[0050] The high-temperature interface retention rate characterizes the extent to which the interfacial binding energy of a candidate composite system is retained from its peak value within the evaluation temperature range to the highest evaluation temperature. Its value is greater than 0 and not greater than 1. The closer the high-temperature interface retention rate is to 1, the more fully the interfacial interaction of the system is maintained under high-temperature conditions.

[0051] All candidate nanofillers and candidate dopant mass fractions were combined at the high-temperature evaluation temperature. and evaluation time The minimum mean square displacement is determined as the reference mean square displacement:

[0052]

[0053] Calculate the chain segment confinement ratio:

[0054]

[0055] The segment confinement ratio is greater than 0 and not greater than 1. The closer the segment confinement ratio is to 1, the weaker the molecular chain motion of PMIA in the corresponding candidate composite system, and the more obvious the restriction of chain segment motion by the candidate nanofiller.

[0056] S5. Calculate the four-parameter synergy index.

[0057] By geometrically coupling the heat resistance ratio, density ratio, high-temperature interface retention rate, and segment confinement ratio, candidate nanofillers were obtained. In candidate doping mass fraction The following four-parameter synergy index:

[0058]

[0059] Right now:

[0060]

[0061] The four parameters correspond to the overall thermal transition, chain packing density, interfacial high-temperature retention capability, and PMIA molecular chain mobility. A fourth-order geometric coupling method is employed, ensuring that each parameter participates in the evaluation in the same way, eliminating the need for manually setting index weights, and ensuring that any significantly low parameter will constrain the synergistic index of the four parameters.

[0062] S6. Calculate the concentration response area.

[0063] Candidate nanofillers were formed by plotting the mass fraction of candidate doping on the x-axis and the synergistic index of the four parameters on the y-axis. The corresponding four-parameter synergistic exponent discrete curve.

[0064] The concentration response area of ​​the candidate nanofiller across the entire candidate doping range was calculated using the trapezoidal integral method.

[0065]

[0066] In the formula, and These are the minimum and maximum values ​​in the set of candidate doping mass fractions, respectively.

[0067] By dividing by the candidate doping region width The trapezoidal integral result is converted into the average synergistic level within the candidate doping range. The larger the concentration response area, the higher and more stable the overall modification ability of the corresponding candidate nanofiller throughout the entire candidate doping range.

[0068] S7. Calculate the low-dose utilization factor

[0069] The low-dose utilization factor of candidate nanofillers was calculated based on the four-parameter synergistic index under different candidate doping mass fractions:

[0070]

[0071] Wherein, the coefficients are:

[0072]

[0073] The four-parameter synergistic index decreases linearly with increasing candidate doping mass fraction, resulting in a larger contribution of the four-parameter synergistic index to the low-dose utilization factor at low doping mass fractions and a smaller contribution at high doping mass fractions.

[0074] The larger the low-dose utilization factor, the more the synergistic modification benefits of the candidate nanofiller are distributed in the lower doping mass fraction region, that is, the stronger the ability of the candidate nanofiller to obtain the comprehensive modification effect with less doping.

[0075] S8. Calculate the type selection index and determine the target filler.

[0076] Multiplying the concentration response area by the low-dose utilization factor yields the preference index for candidate nanofillers:

[0077]

[0078] Calculate the set of candidate nanofiller types respectively The selection index of each candidate nanofiller was determined and sorted from largest to smallest.

[0079] The candidate nanofiller with the highest selection index was identified as the target nanofiller type.

[0080]

[0081] In the formula, To select the optimal type of target nanofiller.

[0082] The type selection index simultaneously incorporates the average four-parameter synergy level and low-dose utilization capability of candidate fillers across the entire doping range, thus avoiding the need to determine filler type solely based on the local maximum value of a single doping point.

[0083] Compared with existing nanofiller screening methods, the present invention has the following advantages.

[0084] 1. This invention uses glass transition temperature, free volume fraction, interfacial binding energy and mean square displacement for evaluation, which respectively reflect the overall thermal transition, molecular chain stacking, interfacial high-temperature stability and molecular chain segment motion of the composite system, thereby reducing the evaluation bias caused by using a single parameter for screening.

[0085] 2. This invention converts fundamental parameters with different dimensions and different directions of change into dimensionless indices by using heat resistance ratio, density ratio, high-temperature interface retention rate, and chain segment confinement ratio. The larger the value, the better the evaluation result, which facilitates a unified comparison between different types of nanofillers.

[0086] 3. This invention uses fourth-order geometric coupling to construct a four-parameter synergistic index, which does not require manual weighting through expert scoring or experience-based judgment, and can constrain any obviously low parameter to the comprehensive evaluation result, reducing the situation where a single advantage masks other performance weaknesses.

[0087] 4. This invention uses concentration response area to evaluate the average modification level of candidate nanofillers throughout the entire candidate doping range, avoiding the determination of filler type based solely on a fixed doping mass fraction or local maximum value, so that the optimization results can reflect the overall performance of the filler at multiple candidate doping points.

[0088] 5. This invention improves the evaluation contribution of synergistic benefits at low doping mass fractions by using a low-dose utilization factor, which can distinguish candidate fillers with similar overall modification effects but different required doping amounts, and reflects the low-dose utilization capability of candidate nanofillers.

[0089] 6. This invention requires different candidate fillers to use the same PMIA matrix model, candidate doping mass fraction set, and molecular dynamics simulation conditions, which improves the comparability between different candidate systems and the repeatability of evaluation results.

[0090] 7. This invention is not limited to Along with fluorinated graphene, it can be used to compare the types of inorganic nanoparticles, two-dimensional nanosheets and other nanofillers. It can also be applied to the design of PMIA composite insulation materials under different operating temperature requirements by adjusting the set of candidate doping mass fractions and the set of evaluation temperatures.

[0091] 8. The data processing of this invention is completed by explicit formulas, which facilitates batch calculation of multiple candidate fillers using the program, and can maintain a uniform evaluation standard and processing flow even when the number of candidate fillers increases. Attached Figure Description

[0092] Figure 1 This is a flowchart of the PMIA insulating film nanofiller type selection method based on four-dimensional microscopic parameter synergistic evaluation, according to the present invention. Detailed Implementation

[0093] like Figure 1 As shown, the PMIA insulating film nanofiller selection method of the present invention sequentially includes: establishing a composite system model, optimizing and balancing the model, obtaining four basic parameters, calculating the high-temperature interface retention rate and chain segment confinement ratio, calculating the synergistic index of the four parameters, calculating the concentration response area, calculating the low-dose utilization factor, and calculating the selection index and determining the target nanofiller. The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be noted that the following specific embodiments are only used to explain the present invention and are not intended to limit the scope of protection of the present invention.

[0094] Example 1

[0095] This embodiment uses nano-zirconium dioxide (… Using fluorinated graphene (FG) and fluorinated graphene (FG) as candidate nanofillers, under the same PMIA matrix structure, candidate doping mass fraction set, and molecular dynamics simulation conditions, the glass transition temperature, free volume fraction, interfacial binding energy, and mean square displacement of PMIA molecular chains of each candidate composite system were calculated. Based on these, the four-parameter synergy index, concentration response area, low dose utilization factor, and species selection index were calculated, and the target nanofiller species for improving the high-temperature structural stability of PMIA insulating films were finally determined.

[0096] S1. Determination of candidate fillers and doping mass fraction

[0097] The candidate nanofiller types in this embodiment are as follows:

[0098]

[0099] The same set of candidate doping mass fractions was used for both candidate nanofillers:

[0100]

[0101] The doping mass fraction of candidate nanofillers is calculated according to the following formula:

[0102]

[0103] In the formula, For the quality of nanofillers, The mass of the PMIA matrix is ​​determined by adjusting the amount of nanofiller and PMIA molecular chains in the composite system. Both the / PMIA system and the FG / PMIA system achieved doping mass fractions of 1 wt%, 3 wt%, and 5 wt%, respectively.

[0104] All candidate systems were subjected to the same PMIA degree of polymerization, PMIA chain number, initial packing density, and periodic boundary conditions, thereby reducing the impact of matrix structure differences on the comparison results of filler types.

[0105] S2. Construction of the molecular model

[0106] PMIA repeating units were constructed using Materials Studio software. After determining the head and tail atoms of the repeating units, a PMIA molecular chain with a degree of polymerization of 10 was generated using polymer build tools. Preliminary geometric optimization of the PMIA molecular chain was performed to eliminate unreasonable bond lengths, bond angles, and interatomic contacts.

[0107] An amorphous periodic model of pure PMIA was constructed using the Amorphous Cell module. The initial packing density of both the pure PMIA model and each nanofiller / PMIA composite system model was set to 0.6 g / L. Setting a lower initial packing density can provide appropriate initial spacing for PMIA molecular chains during the model building stage, reducing severe overlap and interpenetration of chain segments, which is beneficial for subsequent geometry optimization and annealing process convergence.

[0108] Building nano Cluster models were used, and their geometry was independently optimized before being placed into PMIA amorphous unit cells. The model used in this embodiment... The feature size of the cluster is approximately 7.695 in both principal directions. The optimized Clusters were placed within periodic unit cells, and PMIA molecular chains were filled around the clusters to obtain 1 wt%, 3 wt%, and 5 wt% PMIA, respectively. / PMIA composite system model.

[0109] An FG nanosheet model was constructed, and independent geometric optimization was performed on the FG nanosheets. The in-plane dimensions of the FG nanosheets used in this embodiment are approximately 14.103. ×13.354 The optimized FG nanosheets were placed into periodic unit cells, and the area around the sheets was filled with [materials related to FG nanosheets]. The FG / PMIA system has PMIA molecular chains with the same degree of polymerization and chain number setting principle, and FG / PMIA composite system models with 1 wt%, 3 wt%, and 5 wt% were obtained respectively.

[0110] Using the above methods, a pure PMIA matrix model and three models with different doping mass fractions were established. / PMIA model and FG / PMIA models with three different doping mass fractions.

[0111] S3. Model Optimization and Molecular Dynamics Equilibrium

[0112] The same optimization and balancing process was used for both the pure PMIA model and the six nanofiller / PMIA composite system models.

[0113] First, the COMPASS III force field was used for energy minimization and geometry optimization, which reduced the total energy of the system and eliminated unreasonable atomic contacts in the initial configuration. Then, five cycles of annealing were performed in the temperature range of 300 K to 900 K, which allowed the PMIA molecular chain to overcome local potential barriers during heating and cooling, reducing the model's dependence on the initial configuration.

[0114] After annealing, molecular dynamics equilibrium was performed sequentially in the NVT and NPT ensembles. The molecular dynamics time step was set to 1 fs, and the temperature and pressure were controlled using the Andersen method and the Berendsen method, respectively. Van der Waals interactions were calculated using the Atom-based method, and electrostatic interactions were calculated using the Ewald method. The equilibrium time for each candidate system was set to 500 ps, ​​and the temperature, pressure, cutoff parameters, and trajectory output frequencies were kept consistent.

[0115] The system temperature was stabilized using the NVT ensemble, and then the volume and density of the periodic unit cells were adjusted using the NPT ensemble. After equilibrium, the temperature, total energy, and density of each system fluctuated around their respective average values, with the model density approaching 1.3. This yields a stable configuration for subsequent parameter calculations.

[0116] To ensure the comparability of basic data for each candidate system, this embodiment employs the same equilibrium determination principle. The changes in model temperature, total energy, potential energy, and density over simulation time are examined. When these parameters, after the initial adjustment phase, all fluctuate slightly around their respective average values ​​without showing a sustained upward or downward trend, the system is considered to have reached equilibrium. Subsequent calculations of glass transition temperature, free volume fraction, interfacial binding energy, and mean square displacement are based on the equilibrium configuration or trajectory, avoiding evaluation errors caused by using an initial configuration that has not yet fully relaxed.

[0117] S4. Calculation of the four basic parameters

[0118] S41 Glass transition temperature

[0119] Staged NPT cooling simulations were performed within a temperature range covering the glassy and elastic states of each system, with a temperature interval of 50 K between adjacent temperature points. The final configuration after equilibrium at the previous temperature point was used as the initial configuration for each temperature point, and the system density was read after equilibrium was reached.

[0120] Calculate the specific volume based on the system density:

[0121]

[0122] In the formula, For specific volume, The equilibrium density of the system is given. Linear fitting is performed on the data for the low-temperature and high-temperature ranges, with temperature as the x-axis and specific volume as the y-axis. The temperature corresponding to the intersection of the two fitted lines is the glass transition temperature. .

[0123] The pure PMIA model and all candidate composite systems used the same temperature intervals, equilibrium conditions, and piecewise fitting principles.

[0124] S42 Free volume fraction

[0125] The free volume and occupied volume of each equilibrium model were calculated using the Atom Volumes & Surfaces tool. The free volume fraction was calculated using the following formula:

[0126]

[0127] In the formula, For free volume, To determine volume, all systems were calculated using the same probe and grid conditions. A smaller free volume fraction generally indicates less space within the system for the movement of PMIA molecular chain segments, resulting in a more compact chain packing structure.

[0128] S43 interface bonding energy

[0129] The total energy, PMIA matrix energy, and nanofiller energy of the composite system were extracted at 340 K, 360 K, 380 K, 400 K, and 420 K, respectively. The interfacial binding energy was calculated according to the following formula:

[0130]

[0131] In the formula, The total energy of the nanofiller / PMIA composite system. The energy required to remove the nanofiller portion from the same equilibrium configuration in the PMIA section. The energy required to remove the nanofiller portion from the same equilibrium configuration after removing PMIA.

[0132] The larger the absolute value of the interfacial binding energy, the stronger the interfacial interactions that need to be overcome to separate the nanofiller from the PMIA matrix. This invention further uses high-temperature interfacial retention rate to characterize the extent to which interfacial interactions are maintained from their peak state to the highest evaluation temperature.

[0133] S44 Mean Square Displacement

[0134] Trajectory analysis was performed on each composite system at 420 K, with PMIA molecular chain atoms selected as the statistical objects. The mean square displacement was calculated according to the following formula:

[0135]

[0136] In the formula, The number of PMIA atoms selected. and The first The positions of the atoms at the initial and evaluation times.

[0137] All candidate systems were evaluated using the same evaluation temperature, evaluation time, trajectory length, and atom selection range. The smaller the MSD, the more significant the restriction on the molecular chain motion of PMIA.

[0138] S5. Basic Data and Dimensionless Parameter Calculation

[0139] The glass transition temperature of the pure PMIA model is 554 K, and the free volume fraction is 19.51%. These are used as the baseline values ​​for the heat resistance ratio and density ratio, respectively.

[0140]

[0141]

[0142] At 420 K and the uniform evaluation time, the minimum MSD among all candidate composite systems is 6.35. Therefore, we take:

[0143]

[0144] The basic data for each candidate system are shown in Table 1.

[0145] Table 1. Basic data for different filler and doping mass fractions.

[0146] Candidate packing Doping mass fraction / K FFV / % MSD / Peak binding energy / ( ) 420 K binding energy / ( ) 1 wt% 593 9.22 6.35 470 450 3 wt% 578 10.15 7.70 490 435 5 wt% 560 11.56 9.80 535 425 FG 1 wt% 579 20.11 27.20 117 67 FG 3 wt% 591 10.00 6.40 164 103 FG 5 wt% 585 13.63 19.60 74 36

[0147] Based on the data in Table 1, calculate the heat resistance ratio, density ratio, high-temperature interface retention rate, and segment confinement ratio respectively:

[0148]

[0149] in, , For a unified MSD evaluation time.

[0150] At 1 wt% Taking the PMIA system as an example, its four dimensionless parameters are:

[0151]

[0152] S6. Calculation of the Synergistic Index of Four Parameters

[0153] The four-parameter synergy index is calculated according to the following formula:

[0154]

[0155] 1 wt% Substituting the four dimensionless parameters of the PMIA system into the above equation, we get:

[0156]

[0157] The four-parameter synergy index is a dimensionless comprehensive evaluation quantity. Its value is used for lateral comparisons within the same set of candidate fillers, the same set of candidate dopant mass fractions, and under the same simulation conditions. It is not used as an absolute measurement of any single physical property of the material. When all four dimensionless parameters are kept at a high level, the four-parameter synergy index increases accordingly; when any parameter decreases significantly, the geometric coupling result decreases accordingly. Therefore, this index can preserve the common constraint relationship between different parameters on the overall performance and prevent a higher parameter from completely compensating for a significantly lower parameter.

[0158] The remaining candidate systems were calculated using the same method, and the results are shown in Table 2. Data in the table is displayed with four decimal places; subsequent calculations use unrounded values.

[0159] Table 2. Synergistic Indices of Four Parameters for Each Candidate System

[0160] Candidate packing Doping mass fraction Heat resistance ratio Density Interface retention rate Link segment limit ratio Four-parameter synergistic index 1 wt% 1.0704 2.1161 0.9574 1.0000 1.2135 3 wt% 1.0433 1.9222 0.8878 0.8247 1.1008 5 wt% 1.0108 1.6877 0.7944 0.6480 0.9680 FG 1 wt% 1.0451 0.9702 0.5726 0.2335 0.6068 FG 3 wt% 1.0668 1.9510 0.6280 0.9922 1.0672 FG 5 wt% 1.0560 1.4314 0.4865 0.3240 0.6986

[0161] As can be seen from Table 2, High levels of four-parameter synergy were maintained at the 1 wt%, 3 wt%, and 5 wt% doping sites, with the 1 wt% system exhibiting the highest synergy index. With... As the doping concentration increases, the free volume fraction and MSD gradually increase, while the high-temperature interface retention rate gradually decreases, indicating that excessive particles may weaken the effective interface constraint effect.

[0162] The FG system exhibits a significant non-monotonic concentration response. At 1 wt%, the number of flakes is relatively small, resulting in insufficient effective interface constraints; at 3 wt%, the FG flakes form sufficient interfacial contact with PMIA, and FFV and MSD decrease significantly; at 5 wt%, flake stacking may reduce the effective interface area, leading to a further decrease in the synergistic exponent.

[0163] S7. Concentration Response Area Calculation

[0164] To evaluate the overall performance of candidate fillers across the entire doping range of 1 wt% to 5 wt%, trapezoidal integrals were performed on the discrete curves of the four-parameter synergy index as a function of doping mass fraction:

[0165]

[0166] In this embodiment, ,therefore:

[0167]

[0168] The calculation yielded:

[0169]

[0170] The concentration response area is greater than that of FG, indicating that within the entire candidate doping range of 1 wt% to 5 wt%, It has a higher average level of synergy among the four parameters.

[0171] S8. Calculation of Low-Dose Utilization Factor

[0172] The ability of candidate fillers to achieve synergistic benefits at low doping levels is evaluated using a coefficient that decreases linearly with increasing doping mass fraction.

[0173]

[0174] In this embodiment:

[0175]

[0176] The calculation yielded:

[0177]

[0178]

[0179] The low-dose utilization factor is greater than that of FG, indicating that The synergistic modification benefits are more distributed at lower doping mass fractions; the main modification benefits of FG are concentrated around 3 wt%.

[0180] S9. Category Optimization Index and Optimization Results

[0181] Multiplying the concentration response area and the low-dose utilization factor yields the species preference index:

[0182]

[0183] for :

[0184]

[0185] Regarding FG:

[0186]

[0187] The calculation results are shown in Table 3.

[0188] Table 3 Optimization Results of Candidate Nanofiller Types

[0189] Candidate packing Concentration response area Low-dose utilization factor Variety Preferred Index 1.0958 0.4299 0.4711 FG 0.8599 0.3845 0.3307

[0190] because:

[0191]

[0192] Therefore, nano The target nanofiller species for improving the high-temperature structural stability of PMIA insulating films was identified in the candidate filler set of this embodiment.

[0193] S10. Validation of Optimization Results

[0194] From the perspective of individual parameters, 1 wt% The glass transition temperature of the / PMIA system is 593 K, which is 39 K higher than that of pure PMIA; its free volume fraction is 9.22%, significantly lower than the 19.51% of pure PMIA; and its MSD is 6.35 at 420 K and the unified evaluation time. It is the minimum value among all candidate systems; its high-temperature interface retention rate is 0.9574, indicating that the interface effect is maintained from the peak state to 420 K with small attenuation.

[0195] The 3 wt% FG / PMIA system also exhibited good single-point modification effects, with a glass transition temperature of 591 K, a free volume fraction of 10.00%, and an MSD of 6.40. However, the interface retention rate and segment confinement ratio of FG decreased significantly at 1 wt% and 5 wt%, indicating that its modification effect was mainly concentrated near the medium doping mass fraction.

[0196] In comparison, The three candidate doping sites all exhibited relatively continuous four-parameter synergistic levels, and good overall modification effects were achieved even at relatively low doping mass fractions. Therefore, It also exhibits a large concentration response area and a high low-dose utilization factor. These results demonstrate that the method of this invention can not only compare the single-point performance of different fillers, but also reflect the comprehensive performance and low-dose utilization capability of candidate fillers across the entire doping range.

[0197] To improve the repeatability of the optimization results, in practical applications of this method, all candidate systems should use the same number of decimal places and calculation order. Heat resistance ratio, density ratio, high-temperature interface retention rate, and segment confinement ratio can be displayed with at least four decimal places. Concentration response area, low-dose utilization factor, and species selection index should be calculated using unrounded intermediate results, and the final results should be retained with a uniform number of decimal places. For amorphous systems with random initial configurations, multiple independent initial models can be established and repeatedly calculated using the same optimization and balancing process, with the average value of each parameter used as evaluation data, thereby reducing the influence of a single initial configuration on the packing material ranking results.

[0198] The candidate fillers in this embodiment are not limited to... For FG, the candidate doping mass fractions are not limited to 1 wt%, 3 wt%, and 5 wt%. For other inorganic nanoparticles, nanosheets, or surface-modified nanofillers, as long as the same PMIA matrix model, candidate doping mass fraction set, molecular dynamics simulation conditions, and parameter extraction method are used, the type preference index can be calculated and the filler type selection can be completed according to the steps described in this invention.

[0199] As shown in Table 4, the specific physical meaning of each symbol in the formula is as follows.

[0200] Table 4: Symbols and Meanings

[0201] symbol meaning Collection of candidate nanofillers Any candidate nanofiller No. Candidate nanofillers The preferred type of target nanofiller Number of candidate nanofillers Candidate doping mass fraction set Doping mass fraction of nanofillers No. Candidate doping mass fraction 、 Minimum and maximum values ​​in the candidate doping mass fraction set Number of candidate doping mass fractions quality of candidate nanofillers PMIA matrix quality Glass transition temperature of pure PMIA matrix model filler In doping mass fraction glass transition temperature Free volume fraction of pure PMIA matrix model filler In doping mass fraction Free volume fraction Free volume Occupied volume Specific volume System equilibrium density filler In doping mass fraction and temperature The interface integration energy Total energy of the nanofiller / PMIA composite system Energy of the PMIA component after removing nanofillers from the composite system configuration Energy of the nanofiller portion after removing PMIA from the composite system configuration filler In doping mass fraction High temperature evaluation temperature and evaluation time Mean square displacement of the lower PMIA molecular chain The minimum mean square displacement among all candidate systems, i.e., the reference mean square displacement Number of PMIA atoms involved in mean square displacement calculation Atom numbers involved in mean square displacement calculation 、 No. The atoms at the initial time and at time... position vector Interface bonding energy evaluation temperature set The bonding energy of any interface is used to evaluate temperature. 1 to 1 The interface binding energy can be used to evaluate temperature. The number of temperatures that can be evaluated by interfacial bonding energy The highest evaluation temperature in the set of interface bonding energy evaluation temperatures. Unified evaluation time of mean square displacement Heat resistance ratio Density High temperature interface retention rate Link segment limit ratio Four-parameter synergistic index Concentration response area Low-dose utilization factor Variety Preferred Index

Claims

1. A method for optimizing the types of PMIA insulating film nanofillers based on four-dimensional microscopic parameter synergistic evaluation, characterized in that, Includes the following steps: S1. Establish a pure poly(m-phenylene isophthalamide) matrix model, i.e., a pure PMIA matrix model, and establish nanofiller / PMIA composite system models containing different candidate nanofillers; for each candidate nanofiller, use the same set of candidate doping mass fractions. ; S2. Perform geometric optimization, cyclic annealing and molecular dynamics equilibrium treatment on the pure PMIA matrix model and each nanofiller / PMIA composite system model to obtain a stable configuration; S3. Calculate the glass transition temperature and free volume fraction of the pure PMIA matrix model, and calculate the glass transition temperature, free volume fraction, interfacial binding energy at different evaluation temperatures, and mean square displacement of PMIA molecular chains at high evaluation temperature and evaluation time for each candidate nanofiller with different doping mass fractions. S4. Based on the curves of interfacial bonding energy versus temperature and the mean square displacement curve, calculate the high-temperature interface retention rate and the segment confinement ratio: S5. Calculate the four-parameter synergistic index of candidate nanofillers at each candidate doping mass fraction: S6. Based on the discrete curve of the four-parameter synergistic index as a function of the candidate doping mass fraction, calculate the concentration response area of ​​the candidate nanofiller: S7. Calculate the low-dose utilization factor of candidate nanofillers: S8. Calculate the type preference index of candidate nanofillers, and determine the candidate nanofiller with the highest type preference index as the target nanofiller type: The set of candidate nanofiller types is denoted as The target nanofiller type is denoted as .

2. The method for selecting the type of PMIA insulating film nanofiller based on four-dimensional microscopic parameter synergistic evaluation according to claim 1, characterized in that, In step S1, each candidate nanofiller uses the same set of candidate doping mass fractions, the same PMIA matrix model with the same degree of polymerization and chain number, the same initial packing density, and the same periodic boundary conditions.

3. The method for selecting the type of PMIA insulating film nanofiller based on four-dimensional microscopic parameter synergistic evaluation according to claim 1, characterized in that, In step S2, the third-generation force field, namely COMPASS III force field, is used to study the molecular potential energy of condensed phase optimization atomic simulation to describe the interatomic interaction. The molecular dynamics time step is 1 fs, the cyclic annealing temperature range is 300 K to 900 K, and after annealing, equilibrium treatment is carried out in a canonical ensemble and an isothermal and isobaric ensemble in sequence.

4. The method according to claim 1, characterized in that, In step S3, the glass transition temperature is obtained by the intersection of piecewise linear fitting of the volume-temperature curve; the mean square displacement of each candidate system is read at the same high-temperature evaluation temperature, the same evaluation time, and the same atomic selection range.

5. The method for selecting the type of PMIA insulating film nanofiller based on four-dimensional microscopic parameter synergistic evaluation according to claim 1, characterized in that, In step S3, the free volume fraction is the ratio of the free volume to the sum of the free volume and the occupied volume; interfacial binding energy. It is equal to the negative of the difference between the total energy of the composite system and the energy of the PMIA matrix and the energy of the nanofiller; in, For free volume, To occupy space.

6. The method for selecting the type of PMIA insulating film nanofiller based on four-dimensional microscopic parameter synergistic evaluation according to claim 1, characterized in that, In step S4, the set of temperatures for evaluating interfacial binding energy is denoted as... The highest evaluation temperature is the high-temperature evaluation temperature; the reference mean square displacement is the minimum mean square displacement of all candidate fillers and candidate dopant mass fractions at the high-temperature evaluation temperature and evaluation time. The high-temperature interface retention rate and the segment confinement ratio are both greater than 0 and not greater than 1.

7. The method for selecting the type of PMIA insulating film nanofiller based on four-dimensional microscopic parameter synergistic evaluation according to claim 1, characterized in that, In step S5, the four-parameter synergistic index adopts fourth-order root geometric coupling, so that any weak term among glass transition temperature, free volume fraction, high-temperature interface retention rate and mean square displacement constrains the four-parameter synergistic index, and no subjective weight is set.

8. The method for selecting the type of PMIA insulating film nanofiller based on four-dimensional microscopic parameter synergistic evaluation according to claim 1, characterized in that, In step S6, the concentration response area is calculated by summing the trapezoidal areas between adjacent candidate doping mass fractions and dividing by the candidate doping interval width; in step S7, a coefficient that decreases linearly with increasing doping mass fraction is used to reduce the contribution of high doping points.

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