Calculation method of dielectric constant of epoxy-rubber system based on molecular simulation

Abstract

The present invention discloses a method for calculating the dielectric constant of an epoxy-rubber system based on molecular simulation. The method comprises the following steps: establishing molecular models of an epoxy resin and an anhydride curing agent and performing geometric optimization; placing the optimized molecular models into a cube and mixing them uniformly to form an amorphous unit cell structure; designing a crosslinking script for the epoxy resin and the anhydride curing agent, presetting crosslinking reaction conditions; crosslinking the epoxy resin and the anhydride curing agent molecules according to the crosslinking script and the pre-set crosslinking reaction conditions to form a stable crosslinked epoxy resin model; constructing a rubber molecular model based on the molecular structure of carboxybutylene acrylonitrile (CTBN) and performing geometric optimization; designing a crosslinking script for the crosslinked epoxy resin and CTBN, presetting crosslinking reaction conditions; adding the optimized rubber molecules to the crosslinked epoxy resin model to perform a polymerization reaction to form an epoxy / rubber system; and finally calculating the dielectric constant of the epoxy / rubber system.

Description

Technical Field

[0001] The invention belongs to the technical field of insulating material performance analysis, and relates to a method for calculating the dielectric constant of an epoxy-rubber system based on molecular simulation. Background Art

[0002] Epoxy resins react with curing agents to form thermoset materials with three-dimensional cross-linked networks. These materials exhibit unique properties, including low shrinkage, easy curing, high breakdown strength, and stable chemical properties. They are widely used in aerospace, construction, electronic packaging, and electrical insulation. Epoxy / anhydride curing systems, in particular, exhibit high insulation performance and are currently one of the most commonly used insulating material substrates. With the advancement of high-voltage and ultra-high-voltage power transmission and transformation technologies in power grids, the size of electrical equipment continues to shrink, placing increasingly stringent demands on the insulation, aging resistance, and mechanical properties of epoxy resin insulation materials.

[0003] In order to improve the toughness of epoxy resin, rubber particles are used in the epoxy matrix to form an epoxy-rubber system, which is one of the best toughening solutions currently.

[0004] The dielectric constant is the main parameter that reflects the dielectric properties or polarization properties of the piezoelectric smart material dielectric under the action of an electrostatic field. Piezoelectric elements for different purposes have different requirements for the dielectric constant of piezoelectric smart materials. The polarity of polymer materials can be determined based on the dielectric constant of the material.

[0005] In order to determine the dielectric constant of the epoxy-rubber system, the commonly used method is to determine it through a large number of experiments. However, the experimental preparation is complex, the equipment requirements are high, the required test cycle is long, and the steps are tedious and complicated. This causes a huge waste of human, material and financial resources. In addition, the human error in the experiment is large, which makes the final measurement results deviate greatly. Summary of the Invention

[0006] The purpose of the present invention is to provide a molecular simulation-based method for calculating the dielectric constant of an epoxy-rubber system, which solves the problem that the existing experimental determination method requires a long period of time, has large human errors, and causes large deviations in the final calculation results.

[0007] The technical solution adopted by the present invention is a method for calculating the dielectric constant of an epoxy-rubber system based on molecular simulation, comprising the following steps:

[0008] Step 1: Use Materials Studio software to build a molecular model of a single epoxy resin and anhydride curing agent, and optimize the geometry to obtain the lowest energy configuration;

[0009] Step 2: Place the optimized epoxy resin and anhydride curing agent molecular models into a cube and mix them evenly to form an amorphous unit cell structure;

[0010] Step 3: Design a cross-linking script for the epoxy resin and the anhydride curing agent, and preset the cross-linking reaction conditions;

[0011] Step 4: cross-linking the epoxy resin and the anhydride curing agent molecules in the amorphous unit cell structure according to the cross-linking script and the preset cross-linking reaction conditions to form a stable cross-linked epoxy resin model;

[0012] Step 5: construct a rubber molecular model based on the molecular structure of carboxybutylene acrylonitrile (CTBN), and perform geometry optimization to obtain the lowest energy configuration.

[0013] Step 6: Design a cross-linking script for the cross-linked epoxy resin and CTBN, preset the cross-linking reaction conditions, add the optimized rubber molecule model to the cross-linked epoxy resin model, and polymerize the rubber molecules and the cross-linked epoxy resin according to the cross-linking script and the preset cross-linking reaction conditions to form an epoxy / rubber system. Finally, calculate the dielectric constant of the epoxy / rubber system.

[0014] The technical feature of the present invention is that the molecular model is geometrically optimized through the Forcite module to obtain the lowest energy configuration.

[0015] In step 2, the Amorphous cell module is used to place the two optimized molecular models into a three-dimensional cube in a 1:1 ratio, set the initial density and the initial reactive cubic cell size, and impose periodic boundary conditions on the cube to eliminate boundary effects.

[0016] In step 3, based on the cyclic reaction mechanism of hydroxyl groups, epoxy groups and anhydride curing agents in epoxy resin, a cross-linking script of epoxy resin and anhydride curing agent is designed according to the "nearest neighbor similarity" principle.

[0017] Designing a cross-linking script includes reading in a set reaction atom list, initializing, setting the number of iterations and the cutoff radius, and then performing the first-level geometric optimization on the model to determine whether there is a reaction atom pair within the reaction radius. If so, first perform a cross-linking reaction, then perform a second geometric optimization, and then perform annealing. If not, increase the reaction radius, update the reaction atom list, and return to the step of performing the first geometric optimization and repeat. After the annealing is completed, determine whether the number of iterations is less than the set value. If so, increase the number of iterations, update the reaction atom list, and return to the step of performing the first geometric optimization and repeat. If not, determine whether the reaction distance reaches the maximum value. If so, end the process. If not, increase the reaction radius, update the reaction atom list, and return to the step of performing the first geometric optimization and repeat.

[0018] In step 6, based on the reaction mechanism of connecting the C atom at the end of the epoxy resin and the O atom on the carboxyl group at the end of CTBN, the cross-linking script of the epoxy resin and the anhydride curing agent is improved to obtain the cross-linking script of the cross-linked epoxy resin and CTBN;

[0019] Preset cross-linking reaction conditions, including presetting the initial reaction distance, iterative increase distance, number of iterations, final reaction distance and reaction starting temperature.

[0020] In step 4, after the epoxy resin and the anhydride curing agent molecules in the amorphous unit cell structure undergo a cross-linking reaction, a cross-linked epoxy resin model is formed. The Forcite module is used to perform geometric optimization on the model to obtain the lowest energy configuration, and NVT dynamic simulation is performed to balance the configuration, ultimately forming a stable cross-linked epoxy resin model.

[0021] In step 6, before calculating the dielectric constant of the epoxy / rubber system, the geometry is optimized to obtain the lowest energy configuration. Then, the dielectric constant ε of the epoxy / rubber system is calculated using the following formula:

[0022] ε=(ε1+ε2) / 2 (1)

[0023]

[0024]

[0025]

[0026] Where ε1, ε2 and ε ∞ are all intermediate variables. M is the dipole moment of the epoxy / rubber system at one time step, which is directly read from the Castep module. <M 2 >The dipole moment of each sample in the running trajectory of the epoxy / rubber system is squared, summed and averaged; <m> 2 is the average square of all dipole moments sampled in the trajectory of the epoxy / rubber system, V is the volume of the epoxy / rubber system, T is the thermodynamic temperature of the epoxy / rubber system, k B is the Boltzmann constant, ε0 is the vacuum dielectric constant, α is the polarizability, <v>is the average molecular volume of the epoxy / rubber system.

[0027] The beneficial effects of the present invention are that epoxy resin, methylhexahydrophthalic anhydride, and CTBN are modeled using Materials Studio software, and they are formed into an epoxy / rubber system by designing a cross-linking script. Finally, the relative dielectric constant is calculated by statistically averaging the dipole moment. This method requires a short time and has a small human error, greatly improving the accuracy of the calculation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a diagram of the reaction mechanism of the epoxy resin and the acid anhydride curing agent in the present invention;

[0029] Figure 2 This is a flow chart of designing a cross-linking script in the method for calculating the dielectric constant of an epoxy-rubber system based on molecular simulation of the present invention;

[0030] Figure 3 It is a cross-linked epoxy resin model with a cross-linking degree of 95% in the present invention;

[0031] Figure 4 2 is a diagram of the reaction mechanism of epoxy resin and CTBN in the present invention;

[0032] Figure 5 3 is a curve showing the change of relative dielectric constant of the epoxy / rubber system with CTBN content in the embodiment of the present invention. DETAILED DESCRIPTION

[0033] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0034] The present invention provides a method for calculating the dielectric constant of an epoxy-rubber system based on molecular simulation, comprising the following steps:

[0035] Step 1: Based on molecular dynamics simulation, single molecular models of bisphenol A epoxy resin DGEBA and methyl hexahydrophthalic anhydride curing agent were established using Materials Studio software. The geometric optimization of these two molecular models was performed using the Forcite module to obtain the lowest energy configuration. The carbon atom at the end of the epoxy group of the epoxy resin and the oxygen atom in the hydroxyl group were then labeled as R1 and R2, respectively; the carbon atom of the carboxyl group on the methyl hexahydrophthalic anhydride and the oxygen atom at the top were also labeled as R3 and R4, respectively.

[0036] Step 2: Use the Amorphouscell module to place the two optimized molecular models into a three-dimensional cube at a ratio of 1:1 and mix them evenly. In this example, 50 epoxy resin molecules and 50 methylhexahydrophthalic anhydride curing agent molecules are added respectively, and the density is set to 1g / cm 3 The initial density of the cube is set, and periodic boundary conditions are applied to the cube to eliminate the boundary effect and make the model closer to reality. The model system established is an initial physical melt mixture of epoxy resin and curing agent with a reactive functional group ratio of 1:1. The initial cubic cell size that can react is set to Finally, an amorphous unit cell structure is formed;

[0037] The Forcite module is used again to geometrically optimize the amorphous unit cell structure to obtain its lowest energy molecular structure model. The optimized model is subjected to 2000 steps of NVT dynamics simulation to relax the molecular system model. The equilibrium temperature is set to a high temperature of 300K to ensure that the cross-linking process can be more easily achieved at high temperature. In the molecular dynamics simulation, in order to simplify the reaction conditions, the absence of a promoter is usually adopted. First, the hydroxyl group of the epoxy resin reacts with the acid anhydride to generate a carboxylic acid containing an ester chain. The carboxylic acid and the epoxy group of the epoxy resin undergo a ring-opening addition reaction to generate a secondary hydroxyl group. The generated hydroxyl group reacts with another acid anhydride. Simultaneously with the above reaction, the generated secondary hydroxyl group reacts with another epoxy group.

[0038] Step 3, see Figure 1 Based on the cyclic reaction mechanism of hydroxyl groups, epoxy groups and anhydride curing agents in epoxy resin, a crosslinking script for epoxy resin and anhydride curing agents was designed according to the "nearest neighbor similarity" principle, namely a Perl language script, and the crosslinking reaction conditions were preset, including the preset initial reaction distance of The iterative increase distance is The number of iterations is 3 and the final reaction distance is The reaction starting temperature is 400K and the cross-linking degree is 95%.

[0039] Design cross-linking script, refer to the specific process Figure 2 , including reading in the set reaction atom list, then initializing, setting the number of iterations and the cutoff radius, and then performing the first-level geometric optimization on the model, judging whether there are reaction atom pairs within the reaction radius. If so, first perform a cross-linking reaction, then perform a second geometric optimization, and then perform annealing. If not, increase the reaction radius, update the reaction atom list, and return to the first geometric optimization step to repeat. After the annealing is completed, judge whether the number of iterations is less than the set value. If so, increase the number of iterations, update the reaction atom list, and return to the first geometric optimization step to repeat. If not, judge whether the reaction distance reaches the maximum value. If so, end the process. If not, increase the reaction radius, update the reaction atom list, and return to the first geometric optimization step to repeat.

[0040] Step 4: According to the cross-linking script and the preset cross-linking reaction conditions, the epoxy resin and the anhydride curing agent molecules in the amorphous unit cell structure are cross-linked, with the terminal C atom R1 on the epoxy group of the DGEBA molecule as the sphere center and the distance set in the cross-linking script as the radius search. If there is a single bond O atom R4 on the anhydride curing agent, cross-linking treatment is performed; then, the O atom R2 of the hydroxyl group on the DGEBA is used as the sphere center and the distance set in the cross-linking script is used as the radius search. If there is a C atom R3 of the carboxyl group on the anhydride curing agent, cross-linking treatment is performed. Finally, a cross-linked epoxy resin model is formed, and the model is geometrically optimized using the Forcite module to obtain the lowest energy configuration, and 50,000 steps of NVT dynamic simulation are performed to balance the configuration, and finally a stable cross-linked epoxy resin model is formed;

[0041] During the cross-linking reaction, care should be taken to avoid the occurrence of bond-penetrating rings. When cross-linking the active groups in the configuration, the number of bonds formed at one time should not be too large, ensuring that it is within 10 to avoid excessive local stress. Repeat the above cross-linking structure establishment process and perform alternating geometry optimization and annealing treatments for balance. When the cross-linking degree of the system reaches the required value, the final configuration is balanced through geometry optimization and annealing treatment. Select Fine for Quality, and finally a cross-linked epoxy resin model with a cross-linking degree of up to 95% is obtained. See Figure 3 .

[0042] Step 5: Based on the molecular structure of carboxybutylene acrylonitrile (CTBN), rubber molecules with different polymerization degrees were constructed, and the geometry of the molecular model was optimized using the Forcite module to obtain the lowest energy configuration.

[0043] Step 6, see Figure 4 The cross-linking script of epoxy resin and anhydride curing agent was improved based on the reaction mechanism of connecting the C atom at the end of epoxy resin and the O atom at the carboxyl group at the end of CTBN. In the cross-linked epoxy resin system, all C atoms at the end of epoxy resin were marked as R1, and the O atom at the carboxyl group at the end of CTBN was marked as R2, thus obtaining the cross-linking script of cross-linked epoxy resin and CTBN.

[0044] Preset cross-linking reaction conditions, including the preset initial reaction distance The iterative increase distance is The number of iterations is 3 and the final reaction distance is The reaction starting temperature is 423.15K.

[0045] According to the cross-linking script and the preset cross-linking reaction conditions, the rubber molecules and the cross-linked epoxy resin undergo a polymerization reaction. Since different rubber contents in the cross-linked epoxy resin system will exhibit different mechanical, thermal, and electrical properties, the specific ratio is determined according to actual needs. In this example, four epoxy / rubber systems with different CTBN contents were prepared, where the number of CTBN molecules was 5, 10, 15, and 20, respectively. Finally, these five epoxy / rubber systems were geometrically optimized to obtain the lowest energy configuration.

[0046] Step 7, calculate the dielectric constant ε of the five epoxy / rubber systems using the following formula:

[0047] ε =(ε1+ε2) / 2 (1)

[0048]

[0049]

[0050]

[0051] Where ε1, ε2 and ε ∞ are all intermediate variables. M is the dipole moment of the epoxy / rubber system at one time step, which is directly read from the Castep module. <M 2 >The dipole moment of each sample in the running trajectory of the epoxy / rubber system is squared, summed and averaged. <m> 2 is the average square of all dipole moments sampled in the trajectory of the epoxy / rubber system, V is the volume of the epoxy / rubber system, T is the thermodynamic temperature of the epoxy / rubber system, M, <M 2 >、 <m> 2 , V and T can be read directly from the output text after the Castep module is run. B is the Boltzmann constant, ε0 is the vacuum dielectric constant, and α is the polarizability, which is usually taken as <v>is the average molecular volume of the epoxy / rubber system and can be read directly from the output text after geometry optimization.

[0052] The dipole moment is the product of the distance between the centers of positive and negative charges and the charge carried by the charge centers. It is a vector. The connections between different atoms have different dipole moment values. In the cross-linked epoxy resin system, different rubber contents will change the number of chemical bonds in the total system and the distance between atoms. The changes in the number of chemical bonds and the distance between atoms will affect the changes in the dipole moment of the total system.

[0053] The Castep module can perform first-principles quantum mechanics calculations and can calculate the surface properties of materials such as semiconductors, metals, and crystals. This module performs calculations based on the establishment of a periodic 3D model file. After the model is dynamically relaxed, a statistical analysis of the dipole moment is performed. Each fixed charge model is run at a temperature of 298K for 100ps in a constant temperature and constant volume ensemble. Each group of models is calculated 10 times to obtain the average dipole moment, and their average value is taken to reduce the error. For specific results, see Figure 5 .< / v> < / m> < / m> < / v> < / m>

Claims

1. A method for calculating the dielectric constant of an epoxy-rubber system based on molecular simulation, characterized in that: The following steps are involved: Step 1: Use Materials Studio software to build a single epoxy resin and anhydride curing agent molecular model, and optimize the geometry to obtain the lowest energy configuration; Step 2: Place the optimized epoxy resin and anhydride curing agent molecular models into a cube and mix them evenly to form an amorphous unit cell structure; Step 3: Design a cross-linking script for the epoxy resin and the anhydride curing agent, and preset the cross-linking reaction conditions; In step 3, based on the cyclic reaction mechanism between the hydroxyl group and epoxy group in the epoxy resin and the anhydride curing agent, a crosslinking script of the epoxy resin and the anhydride curing agent is designed according to the "nearest neighbor similarity" principle; Designing a cross-linking script includes reading in a set reaction atom list, then initializing, setting the number of iterations and the cutoff radius, and then performing a first-level geometry optimization on the model, judging whether there is a reaction atom pair within the reaction radius. If so, first perform a cross-linking reaction, then perform a second geometry optimization, and then perform annealing. If not, increase the reaction radius, update the reaction atom list, and return to the step of performing the first geometry optimization and repeat. After the annealing is completed, judge whether the number of iterations is less than the set value. If so, increase the number of iterations, update the reaction atom list, and return to the step of performing the first geometry optimization and repeat. If not, judge whether the reaction distance reaches the maximum value. If so, end the process. If not, increase the reaction radius, update the reaction atom list, and return to the step of performing the first geometry optimization and repeat. Step 4: cross-linking the epoxy resin and the anhydride curing agent molecules in the amorphous unit cell structure according to the cross-linking script and the preset cross-linking reaction conditions to form a stable cross-linked epoxy resin model; Step 5: construct a rubber molecular model based on the molecular structure of carboxybutylene acrylonitrile (CTBN), and perform geometry optimization to obtain the lowest energy configuration. Step 6: Design a cross-linking script for the cross-linked epoxy resin and CTBN, preset cross-linking reaction conditions, add the optimized rubber molecules to the cross-linked epoxy resin model, and polymerize the rubber molecules and the cross-linked epoxy resin according to the cross-linking script and the preset cross-linking reaction conditions to form an epoxy / rubber system. Finally, calculate the dielectric constant of the epoxy / rubber system. In step 6, before calculating the dielectric constant of the epoxy / rubber system, the geometry is optimized to obtain the lowest energy configuration. Then, the dielectric constant ɛ of the epoxy / rubber system is calculated using the following formula: （1） （2） （3） （4） Where ɛ1, ɛ2 and are all intermediate variables, M is the dipole moment of the epoxy / rubber system at one time step, <M 2 >The dipole moment of each sample in the running trajectory of the epoxy / rubber system is squared, summed and averaged. <m> 2 It is the average of all dipole moments sampled in the running trajectory of the epoxy / rubber system and then squared. V is the volume of the epoxy / rubber system, T is the thermodynamic temperature of the epoxy / rubber system, k B is the Boltzmann constant, ɛ0 is the vacuum dielectric constant, α is the polarizability, is the average molecular volume of the epoxy / rubber system.< / m> 2. The method for calculating the dielectric constant of an epoxy-rubber system based on molecular simulation according to claim 1, wherein: The molecular model was geometrically optimized using the Forcite module to obtain the lowest energy configuration.

3. The method for calculating the dielectric constant of an epoxy-rubber system based on molecular simulation according to claim 1, wherein: In step 2, the Amorphous cell module is used to place the two optimized molecular models into a three-dimensional cube at a ratio of 1:1, the initial density and the initial responsive cubic cell size are set, and periodic boundary conditions are applied to the cube to eliminate boundary effects.

4. The method for calculating the dielectric constant of an epoxy-rubber system based on molecular simulation according to claim 1, wherein: In step 6, based on the reaction mechanism of connecting the C atom at the end of the epoxy resin and the O atom on the carboxyl group at the end of CTBN, the crosslinking script of the epoxy resin and the anhydride curing agent is improved to obtain the crosslinking script of the crosslinked epoxy resin and CTBN.

5. The method for calculating the dielectric constant of epoxy-rubber system based on molecular simulation according to claim 1, characterized in that: Preset cross-linking reaction conditions, including presetting the initial reaction distance, iterative increase distance, number of iterations, final reaction distance and reaction starting temperature.

6. The method for calculating the dielectric constant of epoxy-rubber system based on molecular simulation according to claim 1, characterized in that: In step 4, after the epoxy resin and the anhydride curing agent molecules in the amorphous unit cell structure undergo a cross-linking reaction, a cross-linked epoxy resin model is formed. The Forcite module is used to perform geometric optimization on the model to obtain the lowest energy configuration, and NVT dynamic simulation is performed to balance the configuration, ultimately forming a stable cross-linked epoxy resin model.

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