Simulation method and system for temperature dependence of dielectric breakdown field strength

Abstract

The application discloses a dielectric breakdown field strength and temperature dependence simulation method and system, and the simulation method comprises the following steps: establishing a criterion for polymer damage caused by molecular chain slip under the action of heat based on a free volume theory; establishing a breakdown criterion for polymer damage caused by molecular chain slip under the joint action of an electric field and a thermal field; quantifying the serpentine movement of a molecular chain under the action of a strong force; establishing an approximate analytical expression of polymer breakdown strength; and fitting the experimental results of sample breakdown field strength change with temperature according to the analytical expression by using a Curve fitting tool of Matlab. The breakdown model established from the perspective of molecular chain displacement can well explain the change relationship between the polymer nanocomposite dielectric breakdown field strength and temperature, and provides theoretical guidance for the preparation of high-temperature dielectric materials.

Description

Technical Field

[0001] This invention belongs to the research field of computational high voltage engineering, specifically relating to a simulation method and system for the dependence of dielectric breakdown field strength on temperature. Background Technology

[0002] Dielectric energy storage capacitors, with their advantage of releasing energy in a very short time to generate high-power pulses, are widely used in various fields. As actual operating conditions shift towards larger currents and higher temperatures, higher requirements are placed on the high-temperature breakdown strength of dielectric materials. However, a systematic study of high-temperature breakdown strength is currently lacking, a key issue being the contradiction between experimental results and theoretical models. Experimental results show that the breakdown field strength of polymer nanocomposite dielectrics exhibits a convex function relationship with temperature, meaning that the decrease in breakdown field strength increases with increasing temperature. However, traditional breakdown models, such as thermal breakdown models, electrical breakdown models, free volume breakdown models, and electromechanical breakdown models, all show a concave function relationship, meaning that the decrease in breakdown field strength decreases with increasing temperature. Traditional breakdown models cannot elucidate the breakdown mechanism of polymer nanocomposite dielectrics and struggle to clarify the key factors for improving breakdown performance. Therefore, it is urgent to establish new breakdown models to reveal the breakdown mechanism of polymer nanocomposite dielectrics for high-temperature energy storage capacitors, providing theoretical support for the development of advanced energy storage dielectric materials. Summary of the Invention

[0003] The purpose of this invention is to provide a simulation method and system for the dependence of dielectric breakdown field strength on temperature, so as to overcome the problem of contradiction between traditional model theory and experimental results.

[0004] The simulation method for the dependence of dielectric breakdown field strength on temperature includes the following steps:

[0005] S1, Based on the free volume theory, establish a criterion for dielectric failure caused by molecular chain slippage under thermal field.

[0006] S2, Based on the criterion that molecular chain slippage leads to dielectric damage under the action of thermal field, a breakdown criterion that molecular chain slippage leads to dielectric damage under the combined action of electric field and thermal field is established. Based on the breakdown criterion that molecular chain slippage leads to dielectric damage under the combined action of electric field and thermal field, the calculation formula for the local free volume expansion caused by Coulomb force during breakdown under the combined action of electric field and thermal field is obtained.

[0007] S3, quantify the serpentine motion of the molecular chain under the action of Coulomb force, and obtain the distance the molecular chain moves along the channel; based on the distance the molecular chain moves along the channel, and the calculation formula of the local free volume expansion caused by Coulomb force during breakdown under the combined action of electric field and thermal field, obtain the relationship between dielectric breakdown field strength and temperature change.

[0008] S4. Simplify the relationship between the breakdown field strength and temperature, and establish an approximate analytical expression for the dielectric breakdown field strength.

[0009] S5. Through the breakdown-temperature experiment, the experimental values ​​of the breakdown field strength of the dielectric at different temperatures are obtained; based on the experimental values ​​of the breakdown field strength of the dielectric at different temperatures, the parameters in the approximate analytical formula of the dielectric breakdown field strength are determined, and the final approximate analytical formula of the dielectric breakdown field strength is obtained.

[0010] S6, predict the breakdown field strength of the dielectric at the untested temperature based on the approximate analytical formula of the final dielectric breakdown field strength.

[0011] Furthermore, the criterion established in S1 for dielectric failure caused by molecular chain slippage under the influence of a thermal field is as follows:

[0012] λ c =α f(L) N(T c -T g )

[0013] λ c α represents the free volume size at which the dielectric fails. f(L) Where is the linear expansion coefficient of the dielectric, N is the number of chain segments, and T is the linear expansion coefficient of the dielectric. c T is the temperature at which the dielectric is destroyed. g It is the glass transition temperature.

[0014] Furthermore, the breakdown criterion established in S2, which involves molecular chain slippage leading to dielectric failure under the combined influence of electric and thermal fields, is: λ E +λ T =λ c , where λ E λ represents the local free volume expansion caused by the Coulomb force. T Let λ be the size of the free volume. c This represents the free volume size when the dielectric fails.

[0015] Furthermore, in S2, the local free volume expansion λ caused by the Coulomb force during breakdown under the combined action of the electric and thermal fields is obtained. E The calculation formula is: λ E =α f(L) N(T c -T); where λ E α represents the local free volume expansion caused by the Coulomb force. f(L) Where is the linear expansion coefficient of the dielectric, N is the number of chain segments, and T is the linear expansion coefficient of the dielectric. c The temperature at which the dielectric is destroyed is T, and the test temperature is T.

[0016] Furthermore, S3 includes the following steps:

[0017] S3.1. Write down the distance λ that the molecular chain travels along the channel. E The expression for (t):

[0018]

[0019] Where, μ tube Let E be the molecular chain channel mobility under the action of Coulomb force, and E be the electric field.

[0020] S3.2 Substituting equation (1) into the formula for calculating the local free volume expansion, the relationship between the dielectric breakdown field strength and temperature change is obtained as follows:

[0021]

[0022] Where, α f(L) Where is the linear expansion coefficient of the dielectric, N is the number of chain segments, and T is the linear expansion coefficient of the dielectric. c The temperature at which the dielectric is destroyed is T, where T is the test temperature.

[0023] Furthermore, after S3.2 is executed, μ will be... tube / N is defined as the flow rate μ' of a single chain segment. tube The relationship between the dielectric breakdown field strength and temperature change is obtained as follows:

[0024]

[0025] Furthermore, S4 includes the following steps:

[0026] S4.1, The distance λ' of a single chain segment moving along the pipe E (t) is represented as:

[0027]

[0028] Where, μ' tube Let E be the pipe flow rate of a single chain segment, and E be the electric field.

[0029] The electric field E is equal to the applied voltage V divided by the sample thickness d, and the voltage rise rate is k. ramp The applied voltage time is t. The voltage on the sample is expressed as the voltage rise rate multiplied by the applied voltage time, i.e., V = k. ramp t; the electric field expression is E = k ramp t / d, and substituting the expression for the electric field into equation (4), we get

[0030]

[0031] S4.2 Integrating both sides of equation (5), and considering that the initial condition of no voltage applied means that the distance a single chain segment moves along the pipe is equal to 0, we get:

[0032]

[0033] Let t = Ed / k ramp Substituting into equation (6), we obtain the relationship between the distance a single chain segment travels along the pipe and the electric field:

[0034]

[0035] S4.3 Substituting the expression (7) for the distance a single chain segment moves along the pipe into the breakdown criterion for dielectric failure caused by molecular chain slippage under the combined action of electric field and heat, we obtain:

[0036]

[0037] Where, α f(L) T is the linear expansion coefficient of the dielectric. c The temperature at which the dielectric is destroyed is T, where T is the test temperature.

[0038] S4.4 According to formula (8), the macroscopic average electric field is expressed as V / d, and considering the breakdown critical condition, the breakdown voltage V is obtained. b The expression is:

[0039]

[0040] Without considering the electric field distortion caused by space charge, the breakdown field strength E is obtained. b The expression is:

[0041]

[0042] Substituting the expression for the mobility of the serpentine flow of the molecular chain into the expression for the breakdown strength (10), we obtain the breakdown strength E. b :

[0043]

[0044] In the formula, ξ t ξ' represents the friction coefficient of a single molecular chain segment or the interaction strength between a single molecular chain segment and surrounding molecular chains. t ′=ξ t / N, where N is the number of segments in the molecular chain;

[0045] S4.5 Assume that the mobility of a single molecular chain segment in a channel has a power function relationship with the electric field.

[0046] μ′ tube =μ′ tube0 E β (12)

[0047] In the formula, μ′ tube0β is the molecular chain channel mobility coefficient, and β is the power function exponent;

[0048] The analytical expression for the breakdown field strength when the mobility of the molecular chain channel exhibits a power function relationship with the electric field is given by equation (10), which is transformed into equation (13), i.e., the breakdown model is:

[0049]

[0050] A simulation system for the dielectric breakdown field strength and its dependence on temperature includes:

[0051] The first criterion establishment module is used to establish a criterion for dielectric failure caused by molecular chain slippage under the action of a thermal field based on the free volume theory.

[0052] The second criterion establishment module is used to establish a breakdown criterion for dielectric breakdown caused by molecular chain slippage under the action of a thermal field, based on the criterion for dielectric breakdown caused by molecular chain slippage under the action of a thermal field, and to obtain the calculation formula for the local free volume expansion caused by Coulomb force during breakdown under the combined action of an electric field and a thermal field based on the breakdown criterion for dielectric breakdown caused by molecular chain slippage under the combined action of an electric field and a thermal field.

[0053] The module for establishing the relationship between breakdown field strength and temperature is used to quantify the serpentine motion of molecular chains under the action of Coulomb force, and obtain the distance the molecular chains move along the pipe; based on the distance the molecular chains move along the pipe, and the calculation formula for the local free volume expansion caused by Coulomb force during breakdown under the combined action of electric field and thermal field, the relationship between dielectric breakdown field strength and temperature change is obtained.

[0054] The simplification module is used to simplify the relationship between the breakdown field strength and temperature, and to establish an approximate analytical expression for the dielectric breakdown strength.

[0055] The simulation module is used to collect experimental values ​​of the breakdown field strength of the dielectric at different temperatures, determine the parameters in the approximate analytical formula of the dielectric breakdown field strength, and obtain the final approximate analytical formula of the dielectric breakdown field strength.

[0056] Compared with the prior art, the present invention has the following beneficial technical effects:

[0057] This invention discloses a simulation method for the temperature dependence of dielectric breakdown field strength, comprising the following steps: establishing a criterion for polymer destruction caused by molecular chain slippage under thermal action based on free volume theory; establishing a breakdown criterion for polymer destruction caused by molecular chain slippage under the combined action of electric and thermal fields; quantifying the serpentine motion of molecular chains under strong forces; establishing an approximate analytical formula for polymer breakdown strength; and, based on the analytical formula, using Matlab's Curve fitting tool to fit the experimental results of the sample breakdown field strength changing with temperature, obtaining the molecular chain channel mobility of the polymer dielectric, thereby analyzing molecular chain interactions, explaining the reasons for the performance improvement of polymer dielectric materials, and thus providing targeted improvements to performance enhancement methods, providing theoretical guidance for the development of advanced energy storage dielectric materials.

[0058] Using the simulation method described in this invention, only 5 sets of breakdown experiments at temperature points between 25℃ and 150℃ are needed to obtain the temperature-breakdown characteristics of the dielectric over the entire temperature range, which greatly saves experimental time and can also obtain the breakdown field strength at temperature points that cannot be achieved under current experimental conditions.

[0059] This invention reveals for the first time the failure mechanism of polymer thermal breakdown from the perspective of free volume expansion caused by molecular chain displacement. The simulation analytical solution can well explain the convex function relationship of the breakdown field strength of polymer dielectric with temperature in the experiment, and solves the problem that traditional breakdown theoretical models cannot explain experimental results.

[0060] The simulation model obtained by this invention has stronger universality and can uniformly explain the influence mechanism of factors such as sample thickness, temperature, pressure boosting rate, doping content, and pressure on the breakdown characteristics of polymer nanocomposite dielectrics. Attached Figure Description

[0061] Figure 1 This is a logic block diagram for simulating the dependence of polymer dielectric breakdown field strength on temperature in an embodiment of the present invention.

[0062] Figure 2 This is a comparison diagram of the breakdown analytical solution and experimental results of the polypropylene / alumina nanocomposite dielectric of the present invention;

[0063] Figure 3 This is a comparison diagram of the breakdown analytical solution and experimental results of the polyimide / alumina nanocomposite dielectric of the present invention;

[0064] Figure 4 This is a comparison diagram of the breakdown analytical solution and experimental results of the polyetherimide / alumina nanocomposite dielectric of the present invention;

[0065] Figure 5 This is a schematic diagram of the simulation system provided by the present invention. Detailed Implementation

[0066] 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.

[0067] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the implementation of the present invention is not limited thereto.

[0068] The breakdown model established in this invention from the perspective of molecular chain displacement can well explain the relationship between the breakdown field strength of polymer nanocomposite dielectrics and temperature, providing theoretical guidance for the preparation of high-temperature dielectric materials.

[0069] Example 1

[0070] This invention discloses a method for establishing a breakdown model based on charge trapping and molecular chain displacement in polymer dielectrics. Figure 1 The following is a logic block diagram of the simulation method based on the breakdown field strength and temperature dependence of polymer dielectrics in this embodiment of the invention. Each process will be described in detail below:

[0071] Step 1: Establish a criterion for polymer destruction caused by molecular chain slippage under thermal action based on the free volume theory;

[0072] Polymer molecular chains are bound together by enthalpy (H) (or cohesive energy). Entropy (S) causes conformational relaxation or Brownian motion within the polymer chains. Higher temperatures result in greater TS, more vigorous chain motion, and a greater ease with which the chains transition from one equilibrium conformation to another, as well as Brownian motion. When the free energy of the molecular chain, G = H - TS, approaches zero, the entropy completely counteracts the enthalpy, causing the chains to diffuse in a serpentine pattern. At this point, the polymer structure is completely altered, and the polymer is destroyed. Entropy also leads to the expansion of the polymer's free volume; when this expansion reaches a certain threshold, it can cause polymer destruction. According to the Fox-Flory free volume theory, the movement of molecular chains requires free volume. Glass transition temperature (T) g In summary, the amplitude of molecular chain motion increases under thermal influence, and this amplitude is directly proportional to the free volume size. Fox-Flory's free volume theory posits that the glass transition temperature T... g Hereinafter, the polymer can be considered as having an isofree volume state; glass transition temperature T gAs shown above, the free volume begins to expand, and the expansion coefficient is constant. Therefore, the size λ of the free volume can be obtained. T Proportional to the linear expansion coefficient α f(L) Number of chain segments N in the molecular chain, temperature difference (TT) g ),Right now

[0073] λ T =α f(L) N(TT g (1)

[0074] Where T is the test temperature.

[0075] For non-crosslinked polymers, when the temperature exceeds the melting temperature and reaches a characteristic temperature, the polymer may be destroyed. For crosslinked polymers, when the temperature approaches or exceeds the softening temperature, the polymer may be destroyed. The temperature at which the polymer is destroyed is T. c The free volume size λ at the time of failure c Proportional to the difference between the characteristic temperature and the glass transition temperature (T c -T g The criterion for polymer destruction is:

[0076] λ c =α f(L) N(T c -T g (2).

[0077] Step 2: Establish a breakdown criterion for polymer destruction caused by molecular chain slippage under the combined action of electric and thermal fields.

[0078] Molecular chains trap electric charges, and under the influence of Coulomb forces, the molecular chains undergo serpentine motion, leading to an increase in the free volume in localized regions. From a microscopic perspective, under the combined influence of electric and thermal fields, the amount of localized free volume expansion λ caused by the Coulomb force can be... E Free volume expansion λ under thermal action T If we consider the superposition, then we can assume that when the free volume reaches the characteristic temperature T... c The size of the free volume is the breakdown criterion for polymer destruction caused by molecular chain slippage under the combined action of electric and thermal fields, i.e.

[0079] λ E +λ T =λ c (3)

[0080] Or, to put it another way, if a very strong Coulomb force causes the molecular chains to move to a degree that occurs when the temperature rises to T... c The polymer will break down if the test temperature is close to the glass transition temperature T. gThe expansion of free volume caused by heat (or entropy force) is very small and can be ignored. Therefore, at slightly above T... g At the test temperature, the expansion of molecular chains caused by Coulomb forces is mainly considered. In this case, the free volume λ of the molecular chain expanding due to serpentine motion under the action of Coulomb forces is... E Reaching characteristic temperature T c When the dielectric reaches a certain size, it will break down.

[0081] If the test temperature is much greater than the glass transition temperature T >> T g The expansion of free volume due to heat (or entropy force) is relatively large. In this case, the combined effect of heat (or entropy force) and Coulomb force needs to be considered. At temperature T, the free volume size is proportional to (TT). g The free volume expansion caused by temperature rise is calculated using equation (1). At this point, the free volume expansion caused by the combined effects of Coulomb force and heat (or entropy force) is λ. E +λ T Considering both Coulomb force and thermal (or entropy force) effects, the breakdown criterion is given by equation (3). Substituting equations (1) and (2) into equation (3), we can obtain the local free volume expansion λ caused by the Coulomb force during breakdown under the combined action of electric and thermal fields. E The expression is

[0082] λ E =α f(L) N(T c -T) (4)

[0083] Step 3: Quantify the serpentine motion of molecular chains under strong forces, and use the breakdown criterion obtained in Step 2 to obtain the relationship between the breakdown field strength and temperature.

[0084] When a deep trap on a molecular chain captures a charge, the chain undergoes directional migration under the influence of a Coulomb force applied by an external electric field. Assuming that the molecular chains in the polymer exhibit serpentine motion under the Coulomb force acting on the functional groups of the deep-trapped molecular chains, the diffusion coefficient D of this serpentine motion is... tube Proportional to temperature T and inversely proportional to the coefficient of friction ξ between molecular chains t ,Right now

[0085]

[0086] Where, k B Boltzmann's constant;

[0087] The coefficient of friction between molecular chains ξ t This reflects the strength of the interactions between molecular chains in the polymer. The stronger the interactions between molecular chains, the greater the coefficient of friction between them, and the greater the energy required for relative displacement or slippage of the molecular chains.

[0088] Furthermore, the molecular chain channel mobility μ under the action of Coulomb force can be obtained from Einstein's formula. tube With diffusion coefficient D tube Relationship,

[0089]

[0090] e is the elementary charge;

[0091] Substituting equation (5) into equation (6), we can obtain the expression for the mobility of the serpentine flow channel of the molecular chain:

[0092]

[0093] Equation (7) shows that the molecular chain channel mobility is independent of temperature. The molecular chain channel mobility is mainly related to the friction coefficient between molecular chains or the interaction between molecular chains. The stronger the interaction between molecular chains, the greater the friction coefficient between molecular chains, and the smaller the molecular chain channel mobility.

[0094] Under the influence of Coulomb force, the product of the molecular chain mobility and the electric field represents the speed of molecular chain motion. Integrating this speed over time yields the distance λ the molecular chain travels along the channel. E (t), that is

[0095]

[0096] Where E is the electric field;

[0097] Substituting equation (8) into the breakdown criterion equation (4), the breakdown criterion can be expressed as follows:

[0098]

[0099] To reduce the number of independent variables in the breakdown model, μ tube / N defines a new variable μ' tube This refers to the flow rate of a single chain segment. This allows the breakdown criterion to be transformed into:

[0100]

[0101] According to the Williams-Landel-Ferry equation, the linear expansion coefficient of the free volume of a polymer is a constant, which is 1 / 3 of the bulk expansion coefficient, i.e., α. f(L) =1.6×10 -4 K -1 Therefore, according to formula (10), only two parameters μ' are needed. tube and T c This allows us to analyze the relationship between the breakdown of polymer nanocomposite dielectrics and temperature changes.

[0102] Step 4: Establish an approximate analytical expression for the polymer breakdown strength, i.e., a breakdown model.

[0103] The electric field E is equal to the applied voltage V divided by the sample thickness d. Since it is a ramp voltage with a constant rate of increase, the rate of increase is k. ramp The applied voltage time is t. The voltage on the sample can be expressed as the voltage rise rate multiplied by the applied voltage time, i.e., V = k. ramp t. The distance λ' that a single chain segment travels along the pipe. E (t) is represented as

[0104]

[0105] The electric field is represented as E = k ramp t / d, and substituting the expression for the electric field into equation (11), we can obtain

[0106]

[0107] Integrating both sides of equation (12), and considering that the initial condition of zero distance traveled by a single chain segment along the pipe when no voltage is applied, we can obtain:

[0108]

[0109] Then t = Ed / k ramp Substituting into equation (13), we can obtain the relationship between the distance a single chain segment travels along the pipe and the electric field.

[0110]

[0111] Substituting the expression for the distance traveled by a single chain segment along the pipe (14) into the breakdown criterion (10) under the combined action of electric field and heat, we can obtain

[0112]

[0113] The macroscopic average electric field is expressed as E = V / d, and the breakdown voltage is V. b It can be represented as: E b =V b / d, and considering the breakdown criterion, the breakdown voltage V can be obtained. b The expression is

[0114]

[0115] Without considering the electric field distortion caused by space charge, the breakdown field strength E can be obtained. b The expression,

[0116]

[0117] Substituting the expression for the mobility of the serpentine molecular chain channel (7) into the expression for the breakdown strength (17), we can obtain the breakdown strength:

[0118]

[0119] In the formula, ξ t ξ' represents the friction coefficient of a single molecular chain segment or the interaction strength between a single molecular chain segment and surrounding molecular chains. t ′=ξ t / N. The greater the friction factor between molecular chains, the less easily the molecular chains move, and the lower the breakdown strength E. b The higher the molecular weight, the greater the friction factor between molecular chains. The main factors leading to an increase in the friction factor between molecular chains are molecular weight and the intermolecular interaction forces. Clearly, the larger the molecular weight, the more difficult it is for the molecular chains to move, and the higher the breakdown strength of the polymer. The stronger the intermolecular interaction, the greater the friction factor between the molecular chains, and the higher the breakdown strength of the polymer is likely to be.

[0120] Assuming that the mobility of a molecular chain channel or the mobility of a single molecular chain segment follows a power function relationship with the electric field.

[0121] μ′ tube =μ′ tube0 E β (19)

[0122] In the formula, μ′ tube0 β is the molecular chain channel mobility coefficient, and β is the power function exponent.

[0123] From the above derivation process, an approximate analytical expression for the dielectric breakdown field strength when the molecular chain channel mobility has a power function relationship with the electric field can be obtained. Equation (17) becomes formula (20), that is, the breakdown model:

[0124]

[0125] The above process is derived from the breakdown field strength expression (20) obtained by the scenario of molecular chain slippage under the action of Coulomb force. It can uniformly explain the influence mechanism of factors such as sample thickness, temperature, pressure increase rate, doping content, and pressure on the breakdown characteristics of polymer nanocomposite dielectrics.

[0126] 1) Equation (20) shows that the breakdown strength E b The relationship between the breakdown field strength and the sample thickness d is an inverse power function, with the power exponent being -1 / (β+1). This is consistent with experimental results showing that the breakdown field strength also exhibits an inverse power function relationship with the sample thickness.

[0127] 2) Breakdown strength E b With boost rate k ramp 1 / (β+1) There is a positive correlation: the faster the voltage rises, the greater the breakdown strength.

[0128] 3) The higher the temperature T, the higher the breakdown strength E. b The breakdown strength E will gradually decrease, and the higher the temperature, the greater the breakdown strength E. b The faster the rate of descent, the more consistent this is with the experimental results we are seeing now.

[0129] 4) Assuming the friction factor of a single molecular chain segment is inversely power-law related to the electric field, ξ t ′=ξ t0 ′E -β ξ t0 ′ is the friction factor coefficient of the molecular chain segment. Then we can obtain μ. tube0 =e / ξ t0 ′。 Put μ tube0 =e / ξ t0 Substituting into the breakdown strength expression (20), we can obtain

[0130]

[0131] In appropriately doped nanocomposite dielectrics, the molecular chains are bound, the intermolecular interactions are enhanced, or the intermolecular friction coefficient ξ is reduced. t As the threshold increases, according to equation (21), the breakdown field strength increases, and the temperature stability of the breakdown field strength improves. The enhanced interaction between molecular chains in the interface region also reduces the number of weakly bound molecular chain segments, lowers the probability of breakdown caused by molecular chain segment slippage, and increases the shape parameter of the Weibull distribution.

[0132] Step 5: Conduct a breakdown-temperature experiment and analyze the experimental results of the breakdown field strength changing with temperature using equation (20).

[0133] In this embodiment, the experimental data on the breakdown of polypropylene / alumina nanocomposite dielectrics with different doping concentrations as a function of temperature are summarized in Table 1.

[0134] Table 1

[0135]

[0136] Input the experimental data into Matlab's Curve fitting tool and set the fitting formula to y = a(bT). c , where a, b, and c are undetermined coefficients. That is...

[0137]

[0138] The fitted curve is as follows Figure 2 As shown, once the undetermined coefficients are determined, the molecular chain channel mobility can be obtained.

[0139]

[0140] The undetermined coefficients are determined by fitting, and the power exponent β and characteristic temperature T are obtained by equations (22) and (23). c Molecular chain channel mobility coefficient μ' tube0 The results are summarized in Table 2.

[0141] Table 2

[0142]

[0143] Example 2

[0144] Steps 1 to 4 are the same as in Example 1. Example 2 is the experimental data on the breakdown of polyimide / alumina nanocomposite dielectrics with different doping concentrations as a function of temperature. The experimental data are summarized in Table 3.

[0145] Table 3

[0146]

[0147] The fitting curves obtained from the experimental data and breakdown model in Table 3 are as follows: Figure 3 As shown, the undetermined coefficients are determined by fitting, and the power exponent β and characteristic temperature T are obtained from equations (22) and (23). c Molecular chain channel mobility coefficient μ' tube0 The results are summarized in Table 4.

[0148] from Figure 3 It is understood that the breakdown model proposed in this invention is also applicable to polyimide / alumina nanocomposite dielectrics with different doping concentrations.

[0149] Table 4

[0150]

[0151]

[0152] Example 3

[0153] Steps 1 to 4 are the same as in Example 1. This example presents experimental data on the breakdown of polyetherimide / alumina nanocomposite dielectrics with temperature at different doping concentrations. The experimental data are summarized in Table 5.

[0154] Table 5

[0155]

[0156] The fitted curves obtained from the experimental data and breakdown model in Table 5 are as follows: Figure 4 As shown, the undetermined coefficients are determined by fitting, and the power exponent β and characteristic temperature T are obtained from equations (22) and (23). c Molecular chain channel mobility coefficient μ' tube0 The results are summarized in Table 6.

[0157] Table 6

[0158]

[0159] from Figure 4 It is understood that the breakdown model proposed in this invention is also applicable to polyetherimide / alumina nanocomposite dielectrics with different doping concentrations.

[0160] Example 4

[0161] Reference Figure 5 A simulation system for the dependence of dielectric breakdown field strength on temperature, comprising:

[0162] The first criterion establishment module is used to establish a criterion for dielectric failure caused by molecular chain slippage under the action of a thermal field based on the free volume theory.

[0163] The second criterion establishment module is used to establish a breakdown criterion for dielectric breakdown caused by molecular chain slippage under the action of a thermal field, based on the criterion for dielectric breakdown caused by molecular chain slippage under the action of a thermal field, and to obtain the calculation formula for the local free volume expansion caused by Coulomb force during breakdown under the combined action of an electric field and a thermal field based on the breakdown criterion for dielectric breakdown caused by molecular chain slippage under the combined action of an electric field and a thermal field.

[0164] The module for establishing the relationship between breakdown field strength and temperature is used to quantify the serpentine motion of molecular chains under the action of Coulomb force, and obtain the distance the molecular chains move along the pipe; based on the distance the molecular chains move along the pipe, and the calculation formula for the local free volume expansion caused by Coulomb force during breakdown under the combined action of electric field and thermal field, the relationship between dielectric breakdown field strength and temperature change is obtained.

[0165] The simplification module is used to simplify the relationship between the breakdown field strength and temperature, and to establish an approximate analytical expression for the dielectric breakdown strength.

[0166] The simulation module is used to collect experimental values ​​of the breakdown field strength of the dielectric at different temperatures, determine the parameters in the approximate analytical formula of the dielectric breakdown field strength, and obtain the final approximate analytical formula of the dielectric breakdown field strength.

[0167] 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 simulation method for the dependence of dielectric breakdown field strength on temperature, characterized in that, Includes the following steps: S1, Based on the free volume theory, establish a criterion for dielectric failure caused by molecular chain slippage under thermal field. S2, Based on the criterion that molecular chain slippage leads to dielectric damage under the action of thermal field, a breakdown criterion that molecular chain slippage leads to dielectric damage under the combined action of electric field and thermal field is established. Based on the breakdown criterion that molecular chain slippage leads to dielectric damage under the combined action of electric field and thermal field, the calculation formula for the local free volume expansion caused by Coulomb force during breakdown under the combined action of electric field and thermal field is obtained. S3, quantify the serpentine motion of the molecular chain under the action of Coulomb force, and obtain the distance the molecular chain moves along the channel; based on the distance the molecular chain moves along the channel, and the calculation formula of the local free volume expansion caused by Coulomb force during breakdown under the combined action of electric field and thermal field, obtain the relationship between dielectric breakdown field strength and temperature change. Specifically, the following steps are included: S3.

1. Write down the distance the molecular chain traveled along the channel. The expression: （1）； in, μ tube This refers to the mobility of the molecular chain channel under the influence of Coulomb forces. E For electric field; S3.2 Substituting equation (1) into the formula for calculating the local free volume expansion, the relationship between the dielectric breakdown field strength and temperature change is obtained as follows: (2)； in, is the linear expansion coefficient of the dielectric. N The number of segments in the molecular chain. T c The temperature at which the dielectric is destroyed. T For testing temperature; S4. Simplify the relationship between the breakdown field strength and temperature, and establish an approximate analytical expression for the dielectric breakdown field strength. S5. The breakdown field strength of the dielectric at different temperatures is obtained through a breakdown-temperature experiment. Based on the breakdown field strength of the dielectric at different temperatures, the parameters in the approximate analytical formula of the dielectric breakdown field strength are determined, and the final approximate analytical formula of the dielectric breakdown field strength is obtained. S6, based on the approximate analytical formula of the final dielectric breakdown field strength, predict the dielectric breakdown field strength at different temperatures.

2. The simulation method for dielectric breakdown field strength and temperature dependence according to claim 1, characterized in that, The criterion established in S1 for dielectric damage caused by molecular chain slippage under the influence of a thermal field is as follows: λ c This refers to the free volume size when the dielectric fails. is the linear expansion coefficient of the dielectric. N The number of segments in the molecular chain. T c The temperature at which the dielectric is destroyed. T g It is the glass transition temperature.

3. The simulation method for the dependence of dielectric breakdown field strength on temperature according to claim 1, characterized in that, The breakdown criterion for dielectric damage caused by molecular chain slippage under the combined action of the electric and thermal fields established in S2 is as follows: ,in, λ E This represents the local free volume expansion caused by the Coulomb force. λ T Let be the size of the free volume, and be λ c This represents the free volume size when the dielectric fails.

4. The simulation method for the dependence of dielectric breakdown field strength on temperature according to claim 1, characterized in that, In S2, the local free volume expansion caused by the Coulomb force during breakdown under the combined action of the electric and thermal fields is obtained. λ E The calculation formula is: ;in, λ E This represents the local free volume expansion caused by the Coulomb force. is the linear expansion coefficient of the dielectric. N The number of segments in the molecular chain. T c The temperature at which the dielectric is destroyed. T For testing temperature.

5. The simulation method for the dependence of dielectric breakdown field strength on temperature according to claim 1, characterized in that, After S3.2 is executed, μ tube / N Defined as the flow rate of a single chain segment pipe μ ' tube The relationship between the dielectric breakdown field strength and temperature change is obtained as follows: (3)。 6. The simulation method for the dependence of dielectric breakdown field strength on temperature according to claim 1, characterized in that, S4 includes the following steps: S4.1, The distance a single chain segment travels along the pipe Represented as: （4） in, μ ' tube For the pipe flow rate of a single chain segment, E For electric field; electric field E Equal to applied voltage V Divide by the sample thickness d The boost rate is k ramp The applied voltage time is t The voltage on the sample is expressed as the voltage ramp rate multiplied by the applied voltage time, i.e. V = k ramp t The electric field expression is: E = k ramp t / d Substituting the expression for the electric field into equation (4), we obtain... (5)； S4.2 Integrating both sides of equation (5), and considering that the initial condition of no voltage applied means that the distance a single chain segment moves along the pipe is equal to 0, we get: (6) Will t = Ed / k ramp Substituting into equation (6), we obtain the relationship between the distance a single chain segment travels along the pipe and the electric field: (7)； S4.3 Substituting the expression (7) for the distance a single chain segment moves along the pipe into the breakdown criterion for dielectric failure caused by molecular chain slippage under the combined action of electric field and heat, we obtain: (8)； in, is the linear expansion coefficient of the dielectric. T c The temperature at which the dielectric is destroyed. T For testing temperature; S4.4 According to formula (8), the macroscopic average electric field can be expressed as: V / d Considering the breakdown critical condition, the breakdown voltage is obtained. V b The expression is: (9) Without considering the electric field distortion caused by space charge, the breakdown field strength is obtained. E b The expression is: (10) Substituting the expression for the mobility of the serpentine molecular chain channel into the expression for the breakdown strength (10), we obtain the breakdown strength. E b : (11) In the formula, ξ t This refers to the coefficient of friction of a single molecular chain segment or the strength of the interaction between a single molecular chain segment and the surrounding molecular chains. ξ t = ξ t / N , ξ t The coefficient of friction between molecular chains. N This represents the number of segments in the molecular chain. S4.5 Assume that the mobility of a single molecular chain segment in a channel has a power function relationship with the electric field. (12) In the formula, This is the molecular chain channel mobility coefficient. β The exponent of the power function; The analytical expression for the breakdown field strength when the mobility of the molecular chain channel exhibits a power function relationship with the electric field is given by equation (10), which is transformed into equation (13), i.e., the breakdown model is: (13)。 7. A system for establishing a dielectric charge trapping and molecular chain displacement breakdown model, characterized in that, include: The first criterion establishment module is used to establish a criterion for dielectric failure caused by molecular chain slippage under the action of a thermal field based on the free volume theory. The second criterion establishment module is used to establish a breakdown criterion for dielectric breakdown caused by molecular chain slippage under the action of a thermal field, based on the criterion for dielectric breakdown caused by molecular chain slippage under the action of a thermal field, and to obtain the calculation formula for the local free volume expansion caused by Coulomb force during breakdown under the combined action of an electric field and a thermal field based on the breakdown criterion for dielectric breakdown caused by molecular chain slippage under the combined action of an electric field and a thermal field. The module for establishing the relationship between breakdown field strength and temperature is used to quantify the serpentine motion of molecular chains under the action of Coulomb force, and obtain the distance the molecular chains move along the pipe; based on the distance the molecular chains move along the pipe, and the calculation formula for the local free volume expansion caused by Coulomb force during breakdown under the combined action of electric field and thermal field, the relationship between dielectric breakdown field strength and temperature change is obtained. Specifically, the following steps are included: Write down the distance the molecular chain travels along the tube. The expression: （1）； in, μ tube This refers to the mobility of the molecular chain channel under the influence of Coulomb forces. E For electric field; Substituting equation (1) into the formula for calculating the local free volume expansion, we obtain the relationship between the dielectric breakdown field strength and temperature change as follows: (2)； in, is the linear expansion coefficient of the dielectric. N The number of segments in the molecular chain. T c The temperature at which the dielectric is destroyed. T For testing temperature; The simplification module is used to simplify the relationship between the breakdown field strength and temperature, and to establish an approximate analytical expression for the dielectric breakdown strength. The simulation module is used to collect experimental values ​​of the breakdown field strength of the dielectric at different temperatures, determine the parameters in the approximate analytical formula of the dielectric breakdown field strength, and obtain the final approximate analytical formula of the dielectric breakdown field strength.

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