Molecular simulation of the effect of epoxy side chains on the microstructure and trap characteristics of the cured system

Epoxy resin is widely used in power equipment as encapsulation insulation material, but its development and application are affected by its thermal stability, charge accumulation, and poor thermal conductivity. In this paper, epoxy resin’s properties are improved by side-linked grafting, and the microstructure and trap properties of epoxy resin that are grafted with Si-O covalent bond, C-F covalent bond, lipid ring structure, and benzene ring are studied by molecular dynamics method. The simulated structure shows that the epoxy side links do not affect the amorphous structure, but the molecular segment mobility, the number, and the free volume of hydrogen bonds will be affected by the system’s chemical structure. Among them, the introduction of bisphenol AF can increase the free volume of the system, improve molecular segments’ mobility, and affect the formation of hydrogen bonds. Molecular segments’ movement can be inhibited by Alicycles’ introduction. The hydrogen bond energy and hydrogen bond quantity of the system will be increased by the new hydroxyl group’s introduction. The system’s thermal conductivity is reduced by epoxy side links. The grafting of specific polar structures in the epoxy resin system can introduce deep hole traps and shallow electron traps.


Introduction
Epoxy resin (EP) is a kind of thermosetting resin.Due to the existence of the chemically active epoxy group in its molecules, it can cross-link the curing reaction with the curing agent, and then generate polymer products with a three-dimensional cross-networking structure.Therefore, epoxy resin (EP) has excellent properties such as low shrinkage rate, excellent mechanical properties, stable chemical properties, and high electrical strength, and has partially replaced traditional glass, ceramic, mica, and oil-paper insulating materials in supporting electrical equipment such as insulators, motors, bushings, transformers, and gas-insulated switchgear (GIS) [1].
At present, the research on epoxy resins in the electrical field usually adopts blending modification or grafting modification to improve the aging resistance and thermodynamic properties of epoxy resins.For example, Zhang et al. [2] used hydroxy-terminated hyperbranched polyester (HBP) to blend and modify the epoxy resin, and the fracture toughness of the epoxy resin was increased by 92%.Tao et al. [3] prepared a new fluorine-containing epoxy resin by technical means.Compared with the unmodified epoxy resin, the fluorine-containing epoxy curing system had better aging resistance.Zhao et al. [4] modified epoxy resin by using hydroxy-terminated polydimethylsiloxane, which not only improved heat resistance and mechanical properties but also facilitated the dispersion of the modified material in the base material.Although there are many researches on the performance modification of epoxy resin at home and abroad, most of them are carried out based on experiments, and it is difficult to analyze and study the mechanism of the microstructure and quantum chemical properties of epoxy resin.In recent years, with the development of computer speed and the improvement of density functional theory, molecular simulation technology has been widely applied in the microstructure and quantum chemical properties of polymers.
In this paper, the microstructure and trap characteristics of epoxy resin side-linked dendritic system are analyzed by molecular dynamics simulation method for different epoxy resin systems, and the effects of grafting materials designed to improve insulation properties on the molecular chain movement capacity, free volume, hydrogen bonding, thermal conductivity, orbital energy level, electrostatic potential distribution, and other aspects are explored.

Establishment of models
In this paper, DDS and DGEBA are selected as curing agents and epoxy resin monomers.The epoxy resin in this paper is E-51 (epoxy equivalent is 196).Forty-one DGEBA molecules with n=0, nine DGEBA molecules with n=1, and twenty-five DDS molecules are therefore selected in the construction system.Nine DGEBA molecules with n=1 are grafted and modified to form new molecules a, b, and c, and monomer models are constructed by using Material Studio (MS) software, and then the monomer models' geometric structure is optimized, as shown in Figure 1.
The EP system is constructed with forty-one DGEBA molecules with n=0, nine DGEBA molecules with twenty-five DDS molecules and n=1, and the DGEBA molecules with n=1 are then replaced by the synthesized new molecules a, b, and c respectively, corresponding to the construction of System A, System B, and System C. The temperature is 600 K, the initial density is 0.6 g/cm 3 , and 10 models are constructed for each system.The molecular model with the lowest energy is selected, and 200 ps NPT molecular dynamics simulation is carried out at 600 K.The pressure is 0.1 MPa, and the step size is 1 fs, so as to obtain a system with density.In the reasonable configuration of the whole simulation process, the force field is COMPASS, the pressure and temperature of the system are controlled by Berendsen methods and Andersen and by Ewald methods and Atom-based, respectively, and the electrostatic action and van der Waals forces are calculated, respectively.

Molecular dynamics simulation
The cross-linking curing reaction of the four systems is realized by using Perl language programming.The cross-linking temperature is 600 K, the preset cross-linking degree is 85%, and the initial reaction truncation radius is set at 0.35 nm, which is increased to 0.85 nm gradually, with a rise of 0.05 nm each time.Under each radius, the four systems' cross-linking process is repeated five times.The newly formed chemical bond's structure is optimized and 25 ps NPT's molecular dynamic balance is performed.After the cross-linking is completed, molecular dynamics simulations of 200 ps NPT and 200 ps NVT are performed on the four cross-linked systems.The pressure is 0.1 MPa, the step size is 1 fs, and the temperature is 600 K.In order to eliminate the systems' local internal stress and make the systems' configuration reasonable, the four systems are annealed from 600 K to 300 K.The temperature interval is 20 K, and MD simulations of 200 ps and 100 ps are performed for each temperature in the NPT ensemble and NVT, respectively.The cooling rate is 20 K/300 ps, and the pressure is 0.1 MPa.

Computational methods of quantum chemistry
Through the DMol3 module of Materials Studio 2020 software, the structure of the molecules in the EP system, A system, B system, and C system is optimized and their trap characteristics are analyzed.
The Perdue-Burke-Nzehoff (PBE) function is selected by the generalized gradient approximation (GGA) to analyze the electrostatic potential, electron density, and orbital energy level, and the calculation is completed by the double numerical polarization (DNP) and the global orbital cutoff set of 4 Å [5].Meanwhile, the dispersion correction method is adopted by Grimme DFT-D. the weak interaction between different fragments is considered.When using the DMol3 module for geometric optimization, the convergence tolerances for energy, maximum force, and maximum displacement are 0.005 Ha, 0.04 Ha/Å.

Radial Distribution Function
The relative likelihood of discovering another atom or set of atoms at a distance from the reference particle r is reflected in the value of the radial distribution function (RDF), which may be written as follows: where n B represents the number of B atoms at the distance r around A atom, N B represents the total number of B atoms, and V represents the volume of the whole system.All four solidified systems' atoms at room temperature (300 K) are depicted in Figure 2's RDF pictures.It is possible to determine whether the grafting of various side chains by epoxy resin has any appreciable impact on the all-atomic RDF of epoxy resin systems by comparing the RDF curves of the various side chain systems that have been grafted by epoxy resin.These curves exhibit similar characteristics and do not obviously differ from one another.These four systems all have the features of distant disordered structure, as shown by the fact that g(r) approaches 1 and has no peaks in the range larger than 0.4 nm.
The covalent bonds between hydroxyl (-OH), carbon (C), and hydrogen (H), π bonds between carbon atoms (C) in the benzene ring, and C-C covalent bonds created between carbon atoms (C) are the four systems' clearly visible peaks, which are located at 9.5 Å, 1.105 Å, 1.40 Å, 1.53 Å, and 2.15 Å, respectively.The two bonds are separated by the distance of atoms.
It is important to note that there are notable changes in each system's data at around 1.3 Å, 1.53 Å, and 1.64 Å.This is because Systems A and C have introduced C-F covalent bonds between carbon (C) and fluorine (F).More π bonds between carbon atoms (C) in the benzene ring are introduced in Systems A and B, while Si-O covalent connections between silicon atoms (Si) and oxygen atoms (O) are introduced in Systems B and C.

Free Volume Properties
Because the size of different resin systems is different, it needs to be normalized.Consequently, the relative magnitude of the free volume across various systems is stated by using the Fractional Free Volume (FFV) [6], which may be written as follows: where 0 V represents the occupied volume, f V represents the free volume.In this paper, MS software is used to create a Connolly surface, a spherical probe with a radius of 1 Å is used to probe the model [7], and the free volume fractions of the four systems are calculated.As shown in Figure 3, it can be seen that the FFV of the four systems is B<EP<C<D.Compared with the EP system, the FFV of System B is slightly decreased, which is because the alicyclic ring is a rigid group, which reduces the flexibility of molecular chain segments and impedes the movement of molecular chain segments.So FFV reduction is small.Compared with the EP system, the FFV of System A and System D both increases and the amplitude is larger, mainly because the side chain structure of epoxy resin in System A and System D affects the accumulation of surrounding molecular chain segments and increases the distance between molecular chains.However, due to the rigid groups in System D, the FFV of System D is lower than that of System A.

Mean Square Displacement
Mean square displacement (MSD) is used to describe molecular segments' mobility in a polymer system and can be expressed as: where N is the total number of atoms in the system, ( ) i R  respectively denote the displacement vectors of an atom i in the system at time t and the initial time.
In order to characterize side chain modification's effect on EP systems' kinetic properties, the MSD values of different systems at room temperature (300 K) are calculated by means of the forcite module.The calculated results are shown in Figure 4.It can be seen that the four systems' MSD is B<EP<C<D, which is consistent with FFV's law in the previous section, indicating that the movement ability of the polymer system's molecular chain segments is related to the same system's free volume fraction.

Hydrogen Bonds
Hydrogen bond refers to the bond formed by the interaction of two highly electronegative atoms with hydrogen atoms as the medium, which is a weak interaction force widely existing in the intramolecular and intermolecular except for Van der Waals force.The annealing system is simulated by NVT molecular dynamics at 200 ps at 300 K, the trajectory file is processed by Perl programming language, and the average number of hydrogen bonds of the four systems is obtained.
The number of the four systems' hydrogen bonds is shown in Figure 5, and the four systems' hydrogen bond energy is shown in Figure 6.As is visible from the figure, the hydrogen bond energy and hydrogen bond quantity of these four systems are positively correlated, the hydrogen bond energy and hydrogen bond quantity of System B are the largest, the hydrogen bond energy and hydrogen bond quantity of System A are the smallest, and the hydrogen bond energy and hydrogen bond quantity of System C and the EP system are similar and located between System B and System A. This is because the side chain structure in System A increases molecular chains' spacing and reduces the packing density of molecular chains, which is not conducive to hydrogen bonds' formation.A new hydroxyl group is introduced by the side chain structure of System B, increasing the number of hydrogen bonds in the system.The side chain structure in System C not only introduces a new hydroxyl group but also increases the distance between molecular chains, so the energy and number of hydrogen bonds in System C are similar to those in System A.

Thermal Conductivity
Thermal conductivity determines the heat dissipation capacity of the system and is a key parameter to characterize the thermal performance of the system.Therefore, the original system is expanded to build a 1×1×3 model, and the NEMD method [8] is adopted to generate constant heat flow and temperature gradient by applying heat sources and cold sources on both sides of the model.The thermal conductivity of the material is calculated based on Fourier's law and can be expressed as: where J is the energy flux and T is the temperature gradient.Figure 7 shows the thermal conductivity values of the four systems.It can be seen from the figure that the heat inside the epoxy resin is transferred to adjacent particles mainly through the thermal vibration of atoms at the equilibrium position while grafting increases the regular winding degree of molecular chain segments, resulting in lower crystallinity of the system and a large number of scattering of phonons as heat transfer carriers during the transfer process.Therefore, in Systems A, B, and C, the free path of phonon propagation is reduced, so that it is difficult to form a continuous thermal conductivity region, and thus the thermal conductivity of the system is reduced.

Band Distribution
The four systems' band distribution is shown in Table 1.In the table, HOMO is the highest occupied molecular orbital energy level, corresponding to the valence band top energy level; LUMO is the lowest unoccupied molecular orbital energy level, corresponding to the conduction band bottom energy level; Band gap is the difference between HOMO energy level and LUMO energy level, indicating the band gap width; The inverse number of the lowest unoccupied molecular orbital energy is used to measure the molecule's ability to attract electrons, that is, the electron affinity.It can be seen from Table 1 that the LUMO energy level of Systems A, B, and C is lower than that of the EP system, and the HOMO energy level of Systems B and C is higher than that of the EP system.Referring to the traditional definition of polymer trap depth, the trap energy below 1.1 eV is a shallow trap, and the trap energy above 1.1 eV is deep hydrazide.Therefore, shallow electron traps are introduced in Systems A, B, and C, and deep hole traps are introduced in Systems B and C.
A deep hole trap and a shallow electron trap are introduced into Systems C and B with a higher HOMO level and lower LUMO level, and the system's Fermi level is raised.The interface between the medium and the electrode changes from ohmic contact to blocking contact.When the depletion zone width of the interface between the medium and the electrode is less than the distance of the electron tunneling effect, the probability of electrons passing through the barrier from the electrode to the medium is equal to the probability of electrons passing through the barrier from the medium to the electrode, so that the interface between the medium and the electrode forms neutral contact, and there is neither electron space charge nor hole space charge in the medium under DC voltage's action.Space charge's accumulation therefore is inhibited by the introduction of deep hole trap and shallow electron trap in epoxy resin in the medium.
The band structure diagram's energy is relative.The vacuum level (VL) is taken at the reference's zero level.Koopman's theory states that the electron affinity is approximately equal to the gap distance between the LUMO and the VL, that is, the energy released when the material captures the electron.It is visible from Table 1 that compared with the EP system, the electron affinity of the three systems A, B, and C is greater, so the electron attraction of the three systems A, B, and C is greater.
System B and System C have relatively narrow band gaps, and the narrower the band gap is, the more localized states exist, which is conducive to the dissipation of high-energy electron energy, reduces the probability of direct collision and ionization of electrons with molecular chains, reduces the bombardment of molecular chains, weakens the direct destruction of molecular chains, makes it difficult to form discharge channels, and improves the electrical strength of the system.

Electrostatic Potential Distribution
The four systems' electrostatic potential distribution is shown in Figure 8, and the electrostatic potential's unit is Ⅴ.The negative electrostatic potential is represented by the red position, and the positive electrostatic potential is represented by the blue position.In the EP system, the negative electrostatic potential near N and O in the DDS structure is larger, the positive electrostatic potential near C is larger, the negative electrostatic potential near O in the DGEBA structure is larger, and the positive electrostatic potential at benzene ring's edge is larger.Besides, the positive electrostatic potential of the hydrogen atoms in the phenol hydroxyl group of System A is large, which can form an electrostatic attraction with the negative charge, which is manifested as an electron trap.The oxygen atoms in Si-OH and C-O-Si in Systems C and B have large negative electrostatic potential, which can trap positive charges with each other, resulting in coulomb repulsion of negative charges, which is manifested as a hole trap.Systems A, B, and C introduce shallow electron traps, which depend on the introduction of benzene or alicyclic structures, and Systems B and C introduce deep hole traps, which depend on the introduction of more hydroxyl groups or Si-O structures.These structures provide more chargetrapping centers for the epoxy resin system, which affects the charge transport characteristics.
Therefore, by adding polar groups with high electrostatic potential [9] to the epoxy resin system, local states can be generated within the band gap of the epoxy resin, traps are introduced, charge migration is inhibited, the contact property with the electrode is changed, the accumulation of space charge in the epoxy resin system under DC voltage is inhibited, and the insulation performance of the material is improved.

Conclusions
It is possible that the van der Waals forces of bisphenol AF and epoxy resin molecular chains are lower, so FFV in System A is increased by 2.57%, and the number and energy of hydrogen bonds are decreased by 13.41% and 15.55%, respectively.Compared with the EP system, FFV and MSD of System B decrease slightly, and the number of hydrogen bonds and hydrogen bond energy increase by 9.76% and 14.78%, respectively, due to the greater rigidity of alicyclic ring and the increase of hydroxyl group.The microscopic properties of System C lie between System A and System B. The side links of epoxy resin make the scattering phenomenon more obvious, so the thermal conductivity of Systems A, B, and C decreases by 11.11%, 2.99%, and 5.56%, respectively.The addition of silyl and phenolic hydroxyl groups to the epoxy resin system can introduce traps and improve the electron affinity of the system.

Figure 3 .
Figure 3. FFV of different systems.Figure 4. MSD of different systems.

Figure 4 .
Figure 3. FFV of different systems.Figure 4. MSD of different systems.

Figure 5 .
Figure 5.The number of hydrogen bonds of different systems.

Figure 6 .
Figure 6.Hydrogen bond energy of different systems.

Figure 7 .
Figure 7. Thermal conductivity of different systems.

Figure 8 .
Figure 8. Electrostatic potential distribution of different systems.

Table 1 .
Band Distribution of Different EP Systems.