Method for calculating the activation energy of an insulating material polymer

Abstract

The application belongs to the field of insulating materials, and relates to a calculation method of polymer activation energy based on an exponential temperature integral algorithm, which comprises the following steps: starting from a traditional integral approximation representation form, an improved exponential integral model is constructed around a unified reaction mechanism function; further combining a reaction rate equation under non-isothermal conditions, an exponential integral approximation expression is introduced, and an improved activation energy calculation method suitable for polymer materials is proposed; finally, an exponential integral change model error calculation equation is constructed to verify the effectiveness of the method. The application can better realize the calculation of the existing polymer activation energy, has good applicability and result accuracy, can represent the aging process of the material through the intermediate change quantity activation energy parameter in the calculation, and provides a basic research method for the activation energy calculation method and evaluation ability of the polymer.

Description

Technical Field

[0001] This invention belongs to the field of insulating materials, and in particular, a method for calculating the activation energy of polymers used in insulating materials. Background Technology

[0002] With the ever-increasing demand for electricity in my country, high-performance SF6 and its mixed gases and alternative gases have become the main insulating and arc-quenching media, leading to the rapid development of gas insulation technology. Gas-sealed transmission lines are now widely used in power generation, transmission, industrial power supply, and urban power transmission systems. In terms of structural insulation materials, polymeric insulating materials have been widely used in power equipment insulation due to their excellent insulation, heat resistance, and ease of processing. However, due to the influence of various factors such as electricity, magnetism, and heat, polymeric insulating materials age and degrade, which can lead to safety accidents in severe cases. Many power equipment in my country have been in use for more than ten years, even decades, urgently requiring a scientific maintenance strategy. Therefore, research on the aging mechanism and lifespan estimation methods of polymeric insulating materials is of great significance in engineering applications.

[0003] Currently, chemical changes inevitably occur during the aging and deterioration of materials, forming or expelling substances that cause internal deformation and internal stress. This transformation is mainly manifested in solid-state reactions, where an active site, or crystal nucleus, appears at the interface of the reaction products. Under various forces, the crystal nucleus continuously grows, develops, and diffuses, ultimately degrading the material's performance. Reaction mechanism functions are often used to study high-temperature cracking of crude oil and coal, as well as reactions such as polymerization and dehydration. They easily reveal the product formation and decomposition characteristics of material cracking processes, thereby determining their stability and service life. In recent years, many scholars have used reaction mechanism functions and thermodynamic parameters such as reaction rates to study the aging of insulating materials and have achieved certain results. However, research on the solution methods and accuracy of activation energy is still relatively lacking.

[0004] Furthermore, traditional methods for calculating polymer activation energy parameters rely on prior solutions to reaction mechanism functions. While many reaction mechanisms for complex processes in solid-state materials have been derived, their inherent complexity, the irregularities in the geometry and stacking of actual samples, and the diversity of their physical and chemical properties mean that the obtained reaction mechanism functions often fail to effectively characterize processes such as nucleation. Therefore, there is an urgent need to supplement and revise current methods for calculating activation energy parameters to establish a method for calculating polymer activation energy based on an exponential temperature integral algorithm. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for calculating the activation energy of polymer insulating materials. This method has good applicability and accuracy, and can characterize the aging process of materials by calculating intermediate changes in activation energy parameters. It also provides a fundamental research method for calculating and evaluating the activation energy of polymers.

[0006] The technical solution for achieving the objective of this invention is as follows:

[0007] A method for calculating the activation energy of an insulating polymer includes the following steps:

[0008] (1) Construct the improved exponential integral model, the specific expression of which is as follows:

[0009]

[0010] In equation (1-1), P(u) represents the integral form of the Arrhenius equation, u = E / RT; E represents the activation energy of the current reactant; R is the gas molar constant; and T is the Kelvin temperature.

[0011] (2) Combining the reaction rate equation under non-isothermal conditions, an exponential integral approximation expression is introduced, and an improved activation energy calculation model suitable for polymer materials is proposed. The specific expression is as follows:

[0012]

[0013] In equation (1-2), A represents the frequency factor; β represents the heating rate parameter used in the experiment; and G(α) is the reaction mechanism function.

[0014] For equation (1-2), after obtaining the polymer thermogravimetric change curve at the heating rate, based on the principle of constant reaction mechanism function G(α) at ​​constant conversion, ln(β / T) is established. 1.868479 The linear fitting curve of 1 / T is obtained, and the activation energy parameter is solved based on the slope of the curve.

[0015] Furthermore, it also includes constructing the error calculation equation for the exponential integral change model, the specific expression of which is as follows:

[0016]

[0017] In equation (1-3), m and a represent the parameters to be determined, and δ represents the relative error of the activation energy.

[0018] Furthermore, the general representation model approximated by the exponential form is expressed as:

[0019]

[0020] In equation (1-4), b represents the undetermined solution parameter, used to describe different approximate integrals;

[0021] The fundamental function of the integral approximation is expressed as:

[0022]

[0023] Furthermore, solving the improved exponential integral model includes the following steps:

[0024] (1) From equation (1-5), we can obtain

[0025]

[0026] (2) In equation (1-6), H(u) can be rearranged to obtain:

[0027]

[0028] In equation (1-7), H(u) represents the equivalent term of the integral by parts in the temperature integral approximation, and L is the remainder term in the expansion.

[0029] (3) Substituting equation (1-4) into equation (1-7) yields:

[0030]

[0031] (4) Take the logarithm of both sides of equation (1-8):

[0032] ln[H(u)]=(2-m)lnu+(1+a)u+b (1-9)

[0033] (5) Differentiating equation (1-9) and then taking the quotient, we get:

[0034]

[0035] (6) Taking the derivative of equation (1-10):

[0036]

[0037] (7) Taking the differential of both sides of equation (1-6):

[0038] P′(u)=-e -u / u 2 (1-12)

[0039] (8) Substituting equation (1-11) into equation (1-12) yields:

[0040]

[0041] (9) Combining equations (1-10) and (1-13), we get:

[0042]

[0043] (10) In equation (1-14), the independent variable u is used as the independent variable, and u / H(u) in equation (1-14) is used as the dependent variable. By using the least squares fitting method, the undetermined parameters m and a are solved. Substituting the parameters into equation (1-9) and combining them with equation (1-8), the improved exponential integral model can be obtained, as shown in equation (1-1):

[0044]

[0045] Furthermore, the establishment of the improved activation energy calculation method model includes the following steps:

[0046] (1) The general form of the Arrhenius rate equation is:

[0047] k is the reaction rate.

[0048] (2) Taking the logarithm of both sides of equation (1-16) and rearranging, we get equation (1-17).

[0049]

[0050] (3) Substituting (1-1) into (1-17) and rearranging, we obtain the improved activation energy calculation model, as shown in equation (1-2):

[0051]

[0052] Furthermore, the establishment of the error calculation equation for the exponential integral change model includes the following steps:

[0053] (1) Substituting equation (1-6) into equation (1-17) and rearranging, we get (1-18), where E2 represents the activation energy under the exponential integral solution model, u2=E2 / (RT):

[0054]

[0055] (2) Taking the derivative of (1-18) and rearranging the terms, we get equation (1-19):

[0056]

[0057] (3) Taking the derivative of (1-17) and rearranging the terms, we get equation (1-20):

[0058]

[0059] (4) In equation (1-20), the activation energy characterizes the equivalent of the model without using the integral approximation. The activation energy obtained by this equation is the true value, and thus the relative error of the activation energy is:

[0060]

[0061] (5) Further, by combining equations (1-19) and (1-21), we obtain the expression for the error calculation equation of the exponential integral change model as shown in equation (1-3):

[0062]

[0063] Advantages and beneficial effects of the present invention:

[0064] This invention provides a method for calculating the activation energy of insulating polymers based on an exponential temperature integral algorithm. This method can solve for the activation energy parameters of existing polymers by bypassing the reaction mechanism function, and has good practicality and universality. It can improve the calculation accuracy and reliability based on existing known solution functions. It can characterize the aging process of materials by calculating intermediate change activation energy parameters, and provides a basic research method for calculating and evaluating the activation energy of polymers. Attached Figure Description

[0065] Figure 1 This is a flowchart of the method of the present invention;

[0066] Figure 2 This is an error curve diagram of the present invention;

[0067] Figure 3 Thermogravimetric curve of epoxy resin material for basin insulator;

[0068] Figure 4 The conversion rate curve of epoxy resin material for basin insulators;

[0069] Figure 5 The fitted line is the improved activation energy calculation model of this invention. Detailed Implementation

[0070] The present invention will be further elaborated and explained below with reference to specific implementation examples and accompanying drawings. It should be understood that the specific implementation examples described herein are only used to explain the present invention and are not limited to these examples.

[0071] like Figure 1 As shown, a method for calculating the activation energy of polymers based on the exponential temperature integral algorithm, taking epoxy resin for basin insulators as an example, mainly includes the following steps.

[0072] (1) Construct the improved exponential integral model, the specific steps of which are as follows:

[0073] The fundamental function of the traditional integral approximation form is expressed as follows:

[0074] The general representation model approximated by the exponential form is expressed as:

[0075]

[0076] In equation (1-4), b represents the undetermined solution parameter, used to describe different approximate integrals;

[0077] The fundamental function of the integral approximation is expressed as:

[0078]

[0079] Solving the improved exponential integral model involves the following steps:

[0080] 1) From equation (1-5), we can obtain

[0081]

[0082] 2) In equation (1-6), H(u) can be rearranged to obtain:

[0083]

[0084] In equation (1-7), H(u) represents the equivalent term of the integral by parts in the temperature integral approximation, and L is the remainder term in the expansion.

[0085] 3) Substituting equation (1-4) into equation (1-7) yields:

[0086]

[0087] 4) Take the logarithm of both sides of equation (1-8):

[0088] ln[H(u)]=(2-m)lnu+(1+a)u+b (1-9)

[0089] 5) Differentiating equation (1-9) and then taking the quotient, we get:

[0090]

[0091] 6) Take the derivative of equation (1-10):

[0092]

[0093] 7) Take the differential of both sides of equation (1-6):

[0094] P′(u)=-e -u / u 2 (1-12)

[0095] 8) Substituting equation (1-11) into equation (1-12) yields:

[0096]

[0097] 9) Combining equations (1-10) and (1-13), we can obtain:

[0098]

[0099] 10) In equation (1-14), the independent variable u is used as the independent variable, and u / H(u) in equation (1-14) is used as the dependent variable. By using the least squares fitting method, the undetermined parameters m and a are solved. Substituting the parameters into equation (1-9) and combining them with equation (1-8), the improved exponential integral model can be obtained, as shown in equation (1-1):

[0100]

[0101] In equation (1-1), P(u) represents the integral form of the Arrhenius equation, u = E / RT; E represents the activation energy of the current reactant; R is the gas molar constant; and T is the Kelvin temperature.

[0102] (2) Combining the reaction rate equation under non-isothermal conditions, an exponential integral approximation expression is introduced, and an improved activation energy calculation model suitable for polymer materials is proposed. The solution steps are as follows:

[0103] 1) The general form of the Arrhenius rate equation is expressed as:

[0104] k is the reaction rate.

[0105] 2) Taking the logarithm of both sides of equation (1-16) and rearranging, we get equation (1-17).

[0106]

[0107] 3) Substituting (1-1) into (1-17) and rearranging, we obtain the improved activation energy calculation model, as shown in equation (1-2):

[0108]

[0109] In equation (1-2), A represents the frequency factor; β represents the heating rate parameter used in the experiment; and G(α) is the reaction mechanism function.

[0110] For equation (1-2), after obtaining the polymer thermogravimetric change curve at the heating rate, based on the principle of constant reaction mechanism function G(α) at ​​constant conversion, ln(β / T) is established. 1.868479 The linear fitting curve of 1 / T is obtained, and the activation energy parameter is solved based on the slope of the curve.

[0111] 4) Thermogravimetric analysis (TGA) was conducted on the epoxy resin material for pot insulators using a Mettler TGA instrument. 10 mg samples were taken each time, and the upper temperature limit was set at 600℃. The experiment was conducted under a nitrogen atmosphere, with heating rates ranging from 5-25℃ in 5℃ intervals. The TGA curves of the epoxy resin material for pot insulators at five different heating rates are shown below. Figure 3 As shown:

[0112] For equation (1-2), after obtaining the thermogravimetric change curves at the heating rate, based on the principle of constant reaction mechanism function G(α) at ​​the constant conversion rate, ln(β / T) is established. 1.868479 The linear fitting curve of 1 / T is obtained, and the activation energy parameter is solved based on the slope of the curve.

[0113] Further establish the conversion rate curve of epoxy resin material for basin insulators, as follows: Figure 4 As shown in Table 1, the temperature points corresponding to different conversion rates at different heating rates are as follows:

[0114] Table 1 Temperature points at heating rates corresponding to different conversion rates

[0115] α 5℃ / min 10℃ / min 15℃ / min 20℃ / min 25℃ / min 0.20 334.959 346.306 353.780 359.668 363.476 0.30 347.148 358.654 366.531 372.639 375.956 0.40 357.407 369.157 377.263 383.614 386.754 0.50 365.252 377.155 384.498 391.904 395.453 0.60 372.503 384.309 392.725 399.198 402.500 0.70 380.849 392.301 400.695 407.497 409.959 0.80 390.022 403.122 411.658 418.749 420.306

[0116] 5) Substitute the temperature point T at the constant conversion rate and its corresponding heating rate β into equation (1-2) to construct a construction curve. Figure 5 To fit the improved activation energy calculation model to the curve, the average activation energy can be calculated to be 169.021 kJ / mol based on the slope of the function curve.

[0117] (3) Construct the error calculation equation for the exponential integral change model and verify the effectiveness of the method. The specific steps are as follows:

[0118] 1) Substituting equation (1-6) into equation (1-17) and rearranging, we get (1-18), where E2 represents the activation energy under the exponential integral solution model, u2=E2 / (RT):

[0119]

[0120] 2) Taking the derivative of (1-18) and rearranging the terms, we get equation (1-19):

[0121]

[0122] (3) Taking the derivative of (1-17) and rearranging the terms, we get equation (1-20):

[0123]

[0124] 4) In equation (1-20), the activation energy characterizes the equivalent of the model without using the integral approximation. The activation energy obtained by this equation is the true value, and thus the relative error of the activation energy is:

[0125]

[0126] 5) Furthermore, by combining equations (1-19) and (1-21), the expression for the error calculation equation of the exponential integral change model can be obtained as shown in equation (1-3):

[0127]

[0128] In equation (1-3), m and a represent the parameters to be determined, and δ represents the relative error of the activation energy.

[0129] Based on the current typical error analysis methods and the corresponding u-value range, the commonly used exponential activation energy integral calculation method is adopted. Generally, the obtained percentage deviation δ is less than 0.03%, and the corresponding u-value shows a positive correlation. Therefore, when the general u-value range is selected as [5, 65], the u-value range of the exponential activation energy integral calculation method under the typical percentage deviation is shown in Table 2.

[0130] Table 2. Calculation method of exponential activation energy integral under typical percentage deviation. Range of u values.

[0131]

[0132]

[0133] 6) The error curves established based on Table 2 and Equation (1-3) are shown in the figure. Figure 2 As shown.

[0134] In summary, this invention provides a method for calculating the activation energy of polymers based on an exponential temperature integral algorithm. This method can solve for the activation energy parameters of existing polymers by bypassing the reaction mechanism function, and it has good practicality and universality. It can improve the calculation accuracy and reliability based on existing known solution functions. It can characterize the aging process of materials by calculating intermediate changes in activation energy parameters, and provides a basic research method for calculating and evaluating the activation energy of polymers.

[0135] The above-described embodiments are examples used to explain this invention. However, the implementation methods and steps of this invention are not limited to the above-described embodiments. Any changes, modifications, combinations, etc., made by others that violate the spirit and principle of this invention are equivalent substitution methods and should be within the protection scope of this invention.

Claims

1. A method for calculating the activation energy of polymer insulating materials, characterized in that, Includes the following steps: (1) Construct the improved exponential integral model, the specific expression of which is as follows: In equation (1-1), P(u) represents the integral form of the Arrhenius equation, u = E / RT; E represents the activation energy of the current reactant; R is the gas molar constant; and T is the Kelvin temperature. (2) Combining the reaction rate equation under non-isothermal conditions, an exponential integral approximation expression is introduced, and an improved activation energy calculation model suitable for polymer materials is proposed. The specific expression is as follows: In equation (1-2), A represents the frequency factor; β represents the heating rate parameter used in the experiment; and G(α) is the reaction mechanism function. For equation (1-2), after obtaining the polymer thermogravimetric change curve at the heating rate, based on the principle of constant reaction mechanism function G(α) at ​​constant conversion, ln(β / T) is established. 1.868479 The linear fitting curve of 1 / T is obtained, and the activation energy parameter is solved based on the slope of the curve.

2. The method for calculating the activation energy of the insulating material polymer according to claim 1, characterized in that, It also includes constructing an error calculation equation for an exponential integral change model, the specific expression of which is as follows: In equation (1-3), m and a represent the parameters to be determined, and δ represents the relative error of the activation energy.

3. The method for calculating the activation energy of the insulating material polymer according to claim 2, characterized in that, The general representation model approximated by the exponential form is expressed as: In equation (1-4), b represents the undetermined solution parameter, used to describe different approximate integrals; The fundamental function of the integral approximation is expressed as:

4. The method for calculating the activation energy of the insulating material polymer according to claim 3, characterized in that, Solving the improved exponential integral model involves the following steps: (1) From equation (1-5), we can obtain (2) In equation (1-6), H(u) can be rearranged to obtain: In equation (1-7), H(u) represents the equivalent term of the integral by parts in the temperature integral approximation, and L is the remainder term in the expansion. (3) Substituting equation (1-4) into equation (1-7) yields: (4) Take the logarithm of both sides of equation (1-8): ln[H(u)]=(2-m)ln u+(1+a)u+b (1-9) (5) Differentiating equation (1-9) and then taking the quotient, we get: (6) Taking the derivative of equation (1-10): (7) Taking the differential of both sides of equation (1-6): P′(u)=-e -u / in 2 (1-12) (8) Substituting equation (1-11) into equation (1-12) yields: (9) Combining equations (1-10) and (1-13), we get: (10) In equation (1-14), the independent variable u is used as the independent variable, and u / H(u) in equation (1-14) is used as the dependent variable. By using the least squares fitting method, the undetermined parameters m and a are solved. Substituting the parameters into equation (1-9) and combining them with equation (1-8), the improved exponential integral model can be obtained, as shown in equation (1-1):

5. The method for calculating the activation energy of the insulating material polymer according to claim 4, characterized in that, The establishment of the improved activation energy calculation method model includes the following steps: (1) The general form of the Arrhenius rate equation is: k is the reaction rate. (2) Taking the logarithm of both sides of equation (1-16) and rearranging, we get equation (1-17). (3) Substituting (1-1) into (1-17) and rearranging, we obtain the improved activation energy calculation model, as shown in equation (1-2):

6. The method for calculating the activation energy of the insulating material polymer according to claim 5, characterized in that, The establishment of the error calculation equation for the exponential integral change model includes the following steps: (1) Substituting equation (1-6) into equation (1-17) and rearranging, we get (1-18), where E2 represents the activation energy under the exponential integral solution model, u2=E2 / (RT): (2) Taking the derivative of (1-18) and rearranging the terms, we get equation (1-19): (3) Taking the derivative of (1-17) and rearranging the terms, we get equation (1-20): (4) In equation (1-20), the activation energy characterizes the equivalent of the model without using the integral approximation. The activation energy obtained by this equation is the true value, and thus the relative error of the activation energy is: (5) Further, by combining equations (1-19) and (1-21), we obtain the expression for the error calculation equation of the exponential integral change model as shown in equation (1-3):

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