1. Introduction
The light weight of electric traction systems is a promising trend in the development of high-speed trains, which can effectively reduce the costs in operation and maintenance even track loads. However, the oil-immersed transformer, as the heaviest single device in the electric traction system, greatly limits the realization of light weight [
1]. Dry-type transformers have lighter weight due to the removal of oil tanks and heat sinks, which are expected to replace oil-immersed transformers to achieve the goal of light weight.
Epoxy resin (EP) is widely used in dry-type transformers for its excellent insulation properties and chemical stability [
2,
3]. However, compared with the common dry-type transformers, the vibration phenomenon of dry-type transformers applied in high-speed train is prone to occur when the train is running at high speed, aggravating the fatigue damage of epoxy resin, which has higher requirements on the mechanical properties of epoxy resin for dry-type transformers applied in high-speed train [
4]. In addition, the poor thermal conductivity of the epoxy resin cannot meet the heat-dissipation requirements for the dry-type transformer in a small vehicle body, which further aggravates the degradation of the mechanical properties of the epoxy resin. Therefore, the epoxy resin in the dry-type transformer applied high-speed train needs higher thermomechanical properties to adapt to the actual working conditions while maintaining dielectric properties.
Nanomaterials have some unique properties, such as small size effect, quantum effect, and surface effect, which have been gradually used in dielectric modification [
4,
5,
6,
7]. Researches have shown that the doping of nanoparticles can combine the excellent properties of the filler itself, such as high toughness and thermal conductivity, with epoxy resin to enhance the thermal, dielectric, and mechanical properties of epoxy composites [
8,
9,
10,
11,
12,
13]. However, the compatibility between nanoparticles and epoxy resin matrix is poor due to the high surface energy of filler, which often leads to agglomeration during doping process if there are not any surface treatments, failing to achieve the expected result [
14,
15]. Chemical modification on nanoparticles surface is an effective method to improve the dispersion of fillers in epoxy resin host and interface bonding between the two [
16,
17,
18].
Hyperbranched polyester is a kind of highly branched three-dimensional dendritic polyester which can be used as an effective surface modifier to control the inorganic–organic interface between filler and polymer matrix [
15,
19,
20]. Many active terminal functional groups of hyperbranched polyester grafted on nanoparticles can interact closely with the polymer matrix, acting as a bridge between the two interfaces, which leads to better dispersibility of fillers and interaction bonding to improve the performance of composite [
21,
22,
23,
24]. However, many studies concentrate on the traditional experimental tests, which have difficulty articulating internal mechanisms clearly. Notably, there are still some deficiencies in the research of hyperbranched polyester modification mechanisms of epoxy resin from the microscopic point of view, especially for the research on the relationship between the microstructure and performance of epoxy resins modified by hyperbranched polyester with different terminal groups.
In recent years, with the development of high-performance computing technology, molecular dynamics (MD) simulation has been widely used in the study of the microstructure and macro-properties of composite polymer materials [
25,
26]. MD simulation can build materials on the atomic scale, which greatly reduces the manufacturing cost and development cycle and then simulates the structure and behavior of molecules to calculate the properties of the materials [
27,
28]. At present, many studies have been conducted on the properties of nanocomposite epoxy resins, using MD simulation [
29,
30,
31,
32]. Du et al. studied the effects of different grafting density of amino silane coupling agents on thermomechanical properties of crosslinked epoxy resin. The results showed that, with the increase of the grafting density, the mechanical properties and glass transition temperature of epoxy resin showed a trend of increasing first and then decreasing [
33]. Jeyranpour et al. investigated the effect of the type of curing agent on the thermomechanical properties of epoxy resin, and DGEBA/TETA and DGEBA/DETDA epoxy systems were built, respectively, using MD simulation. The results showed that, under the same crosslinking density, the DGEBA/DETDA had a higher glass transition temperature than that of DGEBA/TETA, while higher mechanical properties were observed in the case of DGEBA/TETA [
34]. Xie et al. studied the effects of size of silica and crosslinking density on the microstructure and thermomechanical properties of silica–epoxy composite. The increase of crosslinking density enhanced the thermomechanical properties of epoxy resin. Meanwhile, the decrease of particle size also contributed to the improvement of thermomechanical properties [
35]. Chang et al. investigated the effect of amino-modified silica on the corrosion resistance of epoxy resin, and better corrosion resistance was found when epoxy resin incorporated with silica modified by amino groups [
36]. The abovementioned research studies proved that MD simulation is an essential instrument in terms of analyzing the relationship between the microstructure and performance of epoxy resin, which is also expected to provide new approaches for the design and preparation of epoxy composites with enhanced performance. Inspired by these research studies, MD simulation was applied to reveal the systematic and detailed interpretation of the relationship between thermomechanical and dielectric properties and structure of epoxy resin brought by hyperbranched polyester with different terminal groups.
In this paper, the effects of terminal groups on the thermomechanical and dielectric properties of epoxy resin composite incorporated with silica grafting with hyperbranched polyester were studied based on MD simulation. A group of pure epoxy resin and four groups of silica–epoxy resin composite were established, where the silica surface was hydrogenated, grafted with silane coupling agent (KH560 was selected), hyperbranched polyester with terminal carboxyl (CHBP), and hyperbranched polyester with terminal hydroxyl (HHBP), respectively. Moreover, the thermomechanical and dielectric properties were calculated quantitatively including thermal conductivity, glass transition temperature, elastic modulus, and dielectric constant. The four microscopic indexes such as mean square displacement, hydrogen bonds, fractional free volume and binding energy were computed to explain the internal modification mechanism from a microscopic view. This research laid a theoretical foundation for the preparation of high-performance epoxy resin.
2. Materials and Methods
The models in this paper were built using Material Studio software (Accelrys Co., Ltd., San Diego, CA, USA). Five group of models were established to investigate the influence of terminal groups on the performance of silica–epoxy resin modified by hyperbranched polyester. The models were defined as follows: pure epoxy resin (EP), epoxy resin composite model doped into silica (SiO2-EP), epoxy resin composite model doped into silica grafted silane coupling agent KH560 (SiO2-KH560/EP), epoxy resin composite model doped into silica grafted with hyperbranched polyester with carboxyl terminal group (SiO2-CHBP/EP) and the epoxy resin composite model doped into silica grafted with hyperbranched polyester with hydroxyl terminal group (SiO2-HHBP/EP). The specific steps of model construction were as follows.
2.1. Epoxy Resin Models
Bisphenol A epoxy resin (DGEBA) and 4,4′-diaminodiphenyl sulfones were built to act as polymer host and the curing agent, respectively, as shown in
Figure 1a,b. In the experimental study, the average degree of polymerization of DGEBA is usually between 0.1 and 0.2, so the polymerization of DGEBA molecules was set to zero in this simulation [
37]. Reference [
32] indicates that the cell size had no large effect on the calculated properties. Considering the actual reaction situation that two DGEBA molecules react with one 44DDS to form a three-dimensional crosslinked epoxy resin, we constructed a 50 × 50 × 50 Å
3 amorphous model containing DGEBA and 44DDS molecules by a 2:1 ratio, using the Amorphous Cell Tools, as shown in
Figure 1d [
38]. The initial density of the amorphous model was set to 0.6 g/cm
3, and periodic boundary conditions were applied to the unit cell to avoid the size effect of the material.
An energy optimization calculation with energy convergence of 1 × 10−4 kcal/mol and displacement of 5 × 10−4 Å for 10,000 steps iterations was performed in the established amorphous model. Subsequently, the model was annealed in the constant volume and temperature (NVT) ensemble from 300 to 900 K to obtain the lowest energy conformation. Molecular dynamics simulations were conducted based on the lowest energy conformation. To reduce the stress generated in the modeling and reach the actual density of epoxy resin, MD simulations were first performed in the NVT ensemble for 500 ps at 300 K; and in the constant pressure and temperature (NPT) ensemble, the model was equilibrated for 1000 ps at 1 atm. In the abovementioned simulations, the force field COMPASS was applied, and the electrostatic and Vander Waals were calculated, using the Ewald and Atom Based, respectively. The Andersen and Berendsen were used to control temperature and pressure.
The crosslinking process between the epoxy resin monomer and curing agent monomer was simulated by running the PERL language in the next steps, and the involved chemical reactions are shown in
Figure 1f. The carbon atom of epoxy group in DGEBA and the nitrogen atom of amino group in 44DDS were marked as R1 and R2, respectively. When the distance between the atom R1 and the atom R2 met the preset distance, a crosslinking reaction occurred to form a C-N bond. The target conversion degree (TCD) was set to 80%, the initial cutoff distance R
0 was 3 Å, the maximum cutoff distance R
max was 8 Å and the crosslink temperature was set to 350 K.
Figure 2 shows the changes of molecular weight of the first three largest fragments in the model as the crosslinking density increase. The molecular weight of the largest fragment gradually increased, indicating that the epoxy resin monomer and curing agent molecules were continuously reacting to form a whole crosslinked network. The second largest and the third largest fragment molecular weight first increased and then decreased, which was mainly attributed to fact that the original segments were also crosslinked with the largest segment as the crosslinking density approached its maximum.
Finally, the same energy optimization and molecular dynamics simulations were performed as before to obtain the crosslinked model.
2.2. Silica–Epoxy Resin Models
In this study, epoxy resin composites containing silica were treated with four different surface treatments: the silica surfaces were hydrogenated, grafted with silane coupling agent, hyperbranched polyester with terminal carboxyl, and hyperbranched polyester with terminal hydroxyl, respectively.
First, a spherical silica particle with a radius of 10 Å was constructed, and the unsaturated oxygen atoms and unsaturated silicon atoms on the silica surface were bonded with hydrogen atoms and hydroxyl to perform surface hydrogenation, respectively. Based on grafting mechanism shown in
Figure 3, eight hydroxyl groups at different positions among eighty-two hydroxyl groups on the surface of established silica were randomly selected to manually graft the silane coupling agent and two kinds of hyperbranched polyesters with different terminal groups on the silica surface, with a target grafting rate of 10%.
The four constructed silica above were placed in the center of cells, and the crosslinking process and MD simulations were performed according to the methods in
Section 2.1, where the TCD was also maintained at 90%. In addition, the volume fraction of silica in the four composites’ models was kept at about 7.2% by adjusting the molecular numbers of DGEBA and 44DDS.
2.3. Simulation Details
The temperature rise can exacerbate the deterioration of epoxy resin performance. To determine the temperature range in the simulation, the temperature field of dry-type on-board traction transformer was simulated, and the hot-spot temperature and average temperature of the winding were obtained under different thermal conductivities of the epoxy resin, as shown in
Figure 4.
The hot-spot temperature of the winding of could reach 441 K when the ambient temperature and thermal conductivity was set as 300 K and 0.25 W/(m·K), respectively, so the maximum temperature in the MD simulation should be higher than 441 K, considering the rise in ambient temperature and the low thermal conductivity of epoxy resin (usually below 0.2 W/(m·K)). In addition, the glass transition temperature was calculated by fitting the density–temperature curve in the temperature interval above and below the glass transition temperature, which is generally from 400 to 500 K, so the maximum temperature was chosen to be 600 K. Considering the heat generated by the transformer during actual operation, the epoxy is usually exposed to a minimum temperature higher than room temperature, so the minimum temperature of 300 K was chosen. Therefore, in this paper, the variation in the performance of the epoxy resin was studied from 300 to 600 K.
Based on the crosslinked models established in
Section 2.1 and
Section 2.2, the quasi-static cooling process was performed. First, MD simulations were conducted successively for 500 ps in NVT and NPT ensemble in 600 K, and the simulation parameters were consistent with
Section 2.1. Then, the crosslinked models were cooled from 600 to 300 K, at a cooling rate of 25 K/1000 ps [
31]. Based on this process, the structure parameters of epoxy resin at different temperatures were obtained which lay the foundation for the subsequent analysis of performance.