Investigation on the Underlying Mechanisms of the Mechanical and Electrical Enhancement of Nano-SiO₂-Doped Epoxy Resins: A Molecular Simulation Study

Abstract

As a key insulating material in power equipment, epoxy resins (EP) are often limited in practical applications due to space charge accumulation and mechanical degradation. This study systematically investigates the effects of SiO₂ nanoparticle doping on the electrical and mechanical properties of SiO₂/EP composites through molecular dynamics simulations and first-principles calculations. The results demonstrate that SiO₂ doping enhances the mechanical properties of EP, with notable improvements in Young’s modulus, bulk modulus, and shear modulus, while maintaining excellent thermal stability across different temperatures. Further investigations reveal that SiO₂ doping effectively modulates the interfacial charge behavior between EP and metals (Cu/Fe) by introducing shallow defect states and reconstructing interfacial dipoles. Density of states analysis indicates the formation of localized defect states at the interface in doped systems, which dominate the defect-assisted hopping mechanism for charge transport and suppress space charge accumulation. Potential distribution calculations show that doping reduces the average potential of EP (1 eV for Cu layer and 1.09 eV for Fe layer) while simultaneously influencing the potential distribution near the polymer–metal interface, thereby optimizing the interfacial charge injection barrier. Specifically, the hole barrier at the maximum valence band (VBM) after doping significantly increased, rising from the initial values of 0.448 eV (Cu interface) and 0.349 eV (Fe interface) to 104.02% and 209.46%, respectively. These findings provide a theoretical foundation for designing high-performance epoxy-based composites with both enhanced mechanical properties and controllable interfacial charge behavior.

1. Introduction

Epoxy resin (EP), as a core material for insulation systems in electrical power equipment, plays a pivotal role in ensuring long-term operational reliability [1,2,3]. With the continuous increase in voltage levels of power systems, insulation materials are required to withstand more stringent electric field environments, presenting new challenges for the dielectric properties of EP composites [4,5]. Under high electric fields, the migration of electrons can lead to molecular chain damage and the accumulation of space charge, resulting in a significant deterioration of insulation performance [6,7]. Among various modification methods, nanoparticle doping has proven to be particularly effective. Recent studies have shown that interfacial traps introduced by doping at the polymer–metal interface can effectively regulate charge transport behavior across this interface. Research by Yu et al. confirmed that introducing ZnS:O nanoparticles, in which a part of S in ZnS was substituted by O, with specific electronic structures into polymer matrix can effectively confine space charges and improve its insulation properties [8]. Yang’s team found that even without surface modification of diamond nanofillers, optimized interfacial structures between the doping diamond and the EP matrix can suppress charge accumulation and enhance e dielectric strength [9]. These findings highlight the critical role of nanoparticle doping in improving insulation performance of EP. Further studies reveal that the energy level structure and barrier characteristics at polymer–metal interfaces are key factors influencing electron migration behavior across this interface [10,11,12]. Ren et al. theoretically demonstrated that the formation of electric double layers (EDLs) at different polymer–metal (Cu or Al) interfaces significantly affects interface potential barriers [13]. In summary, the modulation of interfacial electronic properties through nanoparticles represents an effective approach for enhancing the electrical characteristics of insulating materials, although the underlying mechanisms require further investigation.

The thermo-mechanical properties of insulation materials are equally crucial in power equipment applications. During long-term operation, materials must endure multiple environmental stresses, including temperature variations, mechanical vibration loads, and thermal aging [14]. It may cause adverse consequences such as EP molecular chain breakage and cross-linking degradation, cyclic load fatigue, and glass transition temperature (Tg) drift. Similarly, doping nanoparticles in EP is also an effective means to optimize the above performance: Wang et al. found that the proper concentration of Ag nanoparticle doping can effectively enhance the thermo-mechanical performance of EP-based composites [15]. Luo’s team achieved synergistic enhancement of thermal conductivity and mechanical properties of EP by doping silver nanoparticles into functionalized boron nitride nanoplates (AgBNs) [16]. Sallal et al. systematically investigated the enhanced mechanical properties of co-doping Al₂O₃ and CaO nanoparticles into EP polymer blends [17]. Additionally, other researchers concluded that the thermos-mechanical performance improvement of polymer nanocomposites primarily stems from three key factors: enhanced interfacial chemical interactions, optimized filler distribution, and improved matrix-nanofiller thermo-mechanical compatibility [18,19,20]. The development of this EP nanocomposite material provides an important technical approach for achieving next-generation insulating materials with pronounced mechanical properties that can adapt to complex working conditions.

Although the dielectric and electrical properties of EP nanocomposites have been extensively studied [21,22,23], the influence mechanisms of nanoparticles on its local morphology and electrical performance, particularly at the atomic scale, remain insufficiently understood. To address these fundamental scientific issues, this study focuses on investigating the mechanical properties of nano-SiO₂ doped EP as well as the charge transfer behavior and potential mechanisms at different Metal–EP interfaces. Therefore, we established atomic models of nanoscale EP/SiO₂ composite systems and their Metal–EP interfaces with or without nano-SiO₂ doping, employing a combined approach of molecular dynamics (MD) simulations and density functional theory (DFT) to systematically study the underlying mechanisms of the enhanced mechanical and electrical properties of EP by nano-SiO₂ doping. This dual-scale approach allows us to comprehensively investigate both the mechanical and electronic properties of EP/SiO₂ nanocomposites and metal-EP interfaces. MD simulations effectively capture the mesoscale behavior, such as polymer chain dynamics and bulk mechanical properties, while DFT provides atomic-level insights into electronic structure, charge transfer mechanisms, and defect states at interfaces. By integrating these methods, we bridge the gap between macroscopic material performance and microscopic interactions, offering a more complete understanding of how SiO₂ doping modifies EP’s properties. This work provides theoretical insights for the design of high-performance epoxy-based composites with both enhanced mechanical properties and controllable interfacial charge behavior.

2. Results and Discussion

2.1. Molecular Modeling and Simulation Details

This study investigates the mechanical properties of the EP/SiO₂ nanocomposite and the interfacial electronic behavior of the Metal–EP interface with or without nano-SiO₂ doping. Therefore, two sets of atomic models, EP/SiO₂ nanocomposite models and Metal–EP interfacial models (Cu or Fe for metal layer), were constructed using molecular dynamics approach in the Materials Studio (2020) software from BIOVIA (San Diego, CA, USA). The CIF (Crystal Graphic Information Files) of all models have been placed in the Supplementary Materials. According to previous studies, EP was modeled mainly by crosslinking Bisphenol A diglycidyl ether (DGEBA) as the matrix (polymerization = 1) with phenylenediamine (1,3-phenylenediamine, MPD) as the curing agent [24,25]. Figure 1 shows the molecular structure characteristics of the key components in the system.

2.1.1. EP/SiO₂ Nanocomposite

The EP/SiO₂ nanocomposite atomic model in this study comprise 20 DGEBA polymer chains (degree of polymerization = 1), 10 MPD molecules, and a hydroxyl-functionalized SiO₂ nanosphere (diameter = 4 Å). For the doped system, the weight ratio of SiO₂ is approximately 6.9%. Owing to computational limitations, we used SiO₂ nanoparticles smaller than the standard sizes found in the literature, as nanoparticle size has relatively little effect on the polymer matrix’s electrical properties compared to doping concentration [26].

The three-dimensional amorphous cell model was constructed by using the COMPASS II force field in the Amorphous Cell module of Material Studio (2020) followed by structural optimization via the Forcite module. In this paper, the calculation results obtained using the COMPASS II force field is largely consistent with those derived from the COMPASS III force field. Consequently, the COMPASS II force field is employed in this study [27,28]. Energy minimization was performed sequentially using the steepest descent algorithm and conjugate gradient method, both with a maximum iteration limit of 3000. System equilibration involved sequential NVT (density = 1.0 g/cm³) and NPT (1 atm) ensemble simulations (duration = 100 ps, timestep = 1 fs, temperature = 300 K), employing the COMPASS II force field with Andersen thermostat and Berendsen barostat controls.

The crosslinking simulation capitalized on the chemical reactivity between epoxy and amine groups: the partially positive terminal carbon atoms of epoxy chains react with electronegative amine nitrogens, inducing nitrogen attack on carbon atoms on DGEBA chains with concomitant hydrogen abstraction, followed by hydroxyl formation via hydrogen–oxygen bonding. Each amine nitrogen can simultaneously react with two carbon atoms on DGEBA chains, enabling three-molecule crosslinking (as shown in Figure 2). Given the higher reactivity of terminal carbons, the DGEBA: MPD molar ratio was fixed at 2:1. Crosslinking simulations were conducted at 300 K and atmospheric pressure using the NPT ensemble and COMPASS II force field, with Perl scripts controlling the reaction process to achieve 90% crosslinking (approaching experimentally values). Post-crosslinking, the system underwent 100 ps NPT equilibration at 500 K until density fluctuations stabilized, followed by stepwise cooling to 300 K in 50 K increments (100 ps per temperature under NPT conditions), concluding with 500 ps NPT equilibration at 300 K. The final equilibrated model (as shown in Figure 2) successfully represents an epoxy composite system with well-defined network structure, providing a reliable atomic-scale foundation for subsequent property investigations.

2.1.2. Interfacial Models Between EP/SiO₂ Nanocomposite Layer and Metal Layer (Cu or Fe)

The Metal/EP (with or without nano-SiO₂ doping) atomic models were constructed as follows: Initially, the cubic unit cells of Cu and Fe were structurally optimized using the Forcite module in the Materials Studio (2020) software, followed by the construction of 4 × 4 × 4 supercells along the (1 0 0) plane with lattice parameters of 11.36 Å × 11.36 Å and 11.45 Å × 11.45 Å, respectively. Secondly, we built an EP layer for the interface model. It contains 10 DGEBA polymer chains (degree of polymerization = 1) and 5 MPD molecules. To ensure lattice matching between the metal and EP layers, the cross-sectional lattice dimensions of the EP structure were adjusted accordingly. By integrating the optimized metal layers with the EP layers, two distinct interfacial structures were successfully established: Cu (1 0 0)/EP and Fe (1 0 0)/EP. To investigate the doping effects, SiO₂ nanospheres were incorporated into the EP layer to form Metal/EP@SiO₂ composite interfacial systems.

All calculations were performed using the VASP 6.1.0 software (Vienna Ab initio Simulation Package, Vienna, Austria), with the PBE-GGA functional [29,30,31,32]. The plane-wave cutoff energy was set to 400 eV, and the self-consistent field convergence criterion was established at 10⁻⁴ eV. A 10 Å vacuum layer was introduced above the metal (1 0 0) surfaces, and a 2 × 2 × 1 k-point mesh was employed for Brillouin zone sampling. The final optimized atomic configurations, as illustrated in Figure 3, provide a reliable atomic modeling foundation for subsequent investigations of interfacial electronic properties between Metal/EP (with or without nano-SiO₂ doping) interfaces.

2.2. Mechanical Properties of EP/SiO₂ Nanocomposite

To further investigate the contribution of molecular thermal motion of EP atoms near SiO₂ nanoparticles to local density fluctuations, we calculated the diffusion characteristics of EP atoms in different regions based on the average of the last 100 ps of NPT ensemble molecular dynamics trajectories, as described above. The diffusion behavior and thermal motion of small molecules or atoms can be characterized by the mean square displacement (MSD) [33,34], which represents the average squared distance deviation of target particles from their initial positions at time 0 to their current positions at time t. By measuring the MSD evolution along particle trajectories during thermal dynamic processes, we can determine whether the particles undergo directional or non-directional diffusion due to molecular thermal motion, expressed as follows [35]:

$$MSD=〈{\left|{\overrightarrow{r}}_i\left(t\right)-{\overrightarrow{r}}_i\left(0\right)\right|}^2〉$$

(1)

where ${\overrightarrow{r}}_{i }\left(t\right)$ and ${\overrightarrow{r}}_i \left(0\right)$ represent the position vectors of the i-th atom at time t and initial time 0 in each timestep, respectively. The diffusion coefficient (D) [30] can be obtained by fitting the MSD curve according to Equation (2) during MD simulations.

$$D={\displaystyle \frac{1}{6N}}\underset{t\to \infty }{{\displaystyle \lim }}{\displaystyle \frac{d}{dt}}{\displaystyle {\sum }_{i=1}^n{\left|{\overrightarrow{r}}_i\left(t\right)-{\overrightarrow{r}}_i\left(0\right)\right|}^2=}{\displaystyle \frac{1}{6}}a$$

(2)

Here, N denotes the number of target molecules in the model, n represents the number of timesteps, and a is the slope obtained from linear fitting of the MSD curve. The free volume ratio refers to the ratio of the volume not occupied by molecules in a material to the total occupied volume. It affects the movement of molecules and the glass transition of materials. When the free volume decreases to a certain extent, the movement of molecular chains is restricted, thereby causing changes in the properties of the material. The MSD of EP atoms at different temperatures was calculated and plotted in Figure 4a.

Figure 4a presents the calculation results of the mean squared displacement (MSD). Specifically, the colored solid lines in the main plot denote the MSD calculation results, whereas the stars marked in various colors in the subplot indicate the diffusion coefficients corresponding to different systems or temperatures. Comparative analysis reveals that, at identical temperatures, the MSD values of the undoped system are significantly higher than those of the doped system. This observation mainly stems from mechanisms such as the physical interaction between the functional groups grafted on the surface of nanoparticles and the polymer chains, which restricts the movement of molecular chains and strengthens the cross-linked network [36,37,38], unequivocally confirming that the incorporation of SiO₂ nanoparticles effectively suppresses the thermal motion of epoxy resin molecular chains. As temperature increases, the diffusion coefficient of EP molecules gradually rises. However, across all calculated temperatures, the diffusion coefficient of EP molecules in the SiO₂ nanoparticle-doped system remains lower than that in the pure EP system.

Concurrently, as the temperature rises, both the MSD values and free volume fractions for all systems show an increasing trend, reflecting the enhanced molecular chain mobility promoted by elevated temperatures. Notably, the free volume analysis results, as shown in Figure 4b, corroborate the diffusion coefficient findings, verifying a direct relationship between molecular chain mobility and the internal free volume ratio of the material. This phenomenon could be attributed to the increase in the local density of molecular chains in the interface region of the doped system, which leads to a decrease in the free volume of the system [39,40].

As shown in Figure 5, the results of Young’s modulus, bulk modulus, and shear modulus obtained through molecular dynamics simulations indicate that the incorporation of SiO₂ nanoparticles significantly enhances the mechanical properties of EP-based composites [41]. Compared to pure EP systems, the doped systems exhibit superior mechanical performance under all tested temperature conditions. The increase in elastic modulus suggests an enhanced ability of the material to resist deformation. Furthermore, the improvement in bulk modulus reflects an optimization in the material’s resistance to volumetric compression. Lastly, the rise in shear modulus confirms a heightened capacity of the material to withstand shear deformation. Notably, this enhancement is maintained across various temperature conditions, indicating that SiO₂ doping not only improves the mechanical properties at room temperature but also imparts good thermal stability to the composite materials. This enhancement effect may be attributed to several mechanisms: (1) the interfacial interactions between nanoparticles and EP matrix restrict molecular chain mobility; (2) the rigid characteristics of nanoparticles help distribute external stress more effectively.

After confirming that the incorporation of SiO₂ nanoparticles significantly enhances the mechanical properties of EP-based composites, we further investigated the electronic properties at the interface between this composite system and the metals. Firstly, the practical application of polymer composites often involves contact with metal electrodes; moreover, interfacial charge behavior directly influences the electrical insulation performance and long-term reliability of high-voltage power equipment. Secondly, the introduction of nanoparticles may modulate charge injection and transport processes by altering the electronic structure at the interface. To this end, this study systematically examines the interfacial electronic properties between the composite system and typical metals layers (Cu and Fe), focusing on analyzing changes in energy level alignment, potential distribution, and interfacial potential barrier before and after nano-SiO₂ doping.

2.3. Electronic Properties Across Different Metal/EP Interfaces with/Without Nano-SiO₂ Doping

To elucidate the electronic characteristics at Metal/EP interfaces, this study systematically investigated the electronic density of states (DoS) of both nano-SiO₂-doped and undoped EP interfaces with Cu and Fe using first-principles calculations. To systematically evaluate the distinct contributions of the metal, nanocomposite, and epoxy (EP) bulk to defect states near the interface, we computed the local density of states (LDOS) across three key interfacial regions: (1) the metallic zone, (2) the interfacial “EP surface” region containing the nanocomposite, and (3) the sub-surface “EP bulk” region, as illustrated in Figure 6.

Figure 7 clearly reveals that in SiO₂-doped systems, the LDoS of the interfacial “EP surface” region exhibits pronounced defect states within the bandgap, which are completely absent in un-doped systems. This phenomenon primarily results from SiO₂ nanoparticle doping, which reconstructs the interfacial electronic structure through the introduction of deep defect states. Additionally, the hydrogen-bond network formed between surface hydroxyl groups (-OH) of SiO₂ nanoparticles and epoxy molecular chains may serve as a complementary mechanism for defect state formation. It is notable that multiple defect states have emerged near the mid-gap of the doped interface structure, which can serve as “springboards” to increase the carrier mobility in the polymer, thereby reducing the accumulation of space charges at this interface [42,43].

Regarding charge transfer mechanisms, theoretical predictions suggest two dominant pathways: (1) direct tunneling, where electrons traverse the barrier from the insulator valence band to the metal conduction band [44], and (2) defect-assisted hopping via gap states. This study finds that the Fermi levels of all interface systems reside stably within the bandgap, unequivocally confirming that interfacial charge transfer primarily occurs through defect-assisted hopping [45,46]. Furthermore, comparative analysis shows that the DoS values near the Fermi level for both metals exceed those of epoxy resin by orders of magnitude, directly reflecting the superior electron exchange capability of metal electrodes that dominates interfacial charge transfer processes.

To systematically investigate the influence of SiO2 doping on interfacial potential distribution, this study calculated the electrostatic potential profiles of four representative interface structures based on first-principles calculations. The Cu-1s and Fe-1s core level was selected as the reference energy level for potential alignment for different models due to its stable electron binding energy that remains unaffected by interfacial charge transfer processes [47].

The calculated potential distributions are presented in Figure 8, showing potential variation ranges of [0, 15.59] Å for Cu layers and [0, 13.88] Å for Fe layers. Notably, the EP layers behind both metal interfaces exhibit significant potential oscillations. To quantify this characteristic, we specifically calculated the average potential values in the bulk region along the Z-axis direction with stable oscillations (within the range of [18–60] Å), as summarized in

Table 1. The potential shift in Metal in the bulk region.

	Average Potential (eV)	Potential Shift (eV)
Cu-EP	−5.132	0
Cu-EP/SiO2	−5.566	−0.434
Fe-EP	−4.122	0
Fe-EP/SiO2	−4.381	−0.259

and

Table 2. The potential shift in Epoxy resin in the bulk region.

	Average Potential (eV)	Potential Shift (eV)
Cu-EP	2.025	0
Cu-EP/SiO2	1.025	−1.0
Fe-EP	1.482	0
Fe-EP/SiO2	0.393	−1.089

. These results clearly demonstrate that SiO₂ doping effectively reduces the average potential of the EP matrix while significantly altering the potential distribution near the Metal/EP interfaces.

To further elucidate the interfacial electronic characteristics between SiO₂-doped EP and metals, we determined the interface potential barriers according to the following formulation:

$$E_{sVBM}^i=E_{VBM}^i-E_{Cu/Fe-1s}^i$$

(3)

$$E_{sCBM}^i=E_{CBM}^i-E_{Cu/Fe-1s}^i$$

(4)

$$\mathrm{\Delta }{E}_{sVBM}^i=E_{sVBM}^i-E_{sVBM}^1$$

(5)

$$\mathrm{\Delta }{E}_{sCBM}^i=E_{sCBM}^i-E_{sCBM}^1$$

(6)

where VBM and CBM denote the valence band maximum and conduction band minimum of bulk EP, respectively, while Cu/Fe-1s represents the 1s core-level energies of the respective metals. The core-level-corrected VBM and CBM are designated as sVBM and sCBM. Four representative interface configurations (i = 1–4) were investigated: Cu/EP, Cu/EP@SiO₂, Fe/EP, and Fe/EP@SiO₂. To address the bandgap underestimation issue of PBE functional, we employed the PBE0 hybrid functional (with a 2 × 2 × 2 k-point mesh and 400 eV cutoff energy) for calculating average potentials and band edge positions [48]. Considering the computational limitations for large-scale interface models, we adopted the band alignment method to determine the Metal/EP interface barriers. Structural optimization was performed using the following lattice parameters: Cu (2.84 Å cubic unit cell), Fe (2.86 Å cubic unit cell), and EP systems (15 Å cubic supercell). Based on the PBE0-calculated Fermi levels of metals and band positions of EP, combined with the reference potential values from Table 1 and Table 2, we ultimately obtained the interface barrier distribution results shown in Figure 9, which provides important insights into the charge transport mechanisms.

The analysis of interface barrier indicates that the incorporation of SiO₂ significantly alters the electronic structure characteristics at the Metal/EP interface after an average potential correction. For the Cu/EP@SiO₂ and Fe/EP@SiO₂ systems, the reduction in metal interface potential energy aligns with previous findings on potential distribution. Notably, in both metallic interface structures, there is a pronounced decrease in electron barriers at the conduction band minimum (CBM) following doping; Specifically, for Cu/EP@SiO₂ and Fe/EP@SiO₂ systems, the metal interface potential barriers decreased by approximately 30.43% and 41.74%, respectively. These changes may promote electron injection and exacerbate the risk of space charge accumulation and local electric field distortion, thereby leading to dielectric failure [49,50,51,52]. However, there is a significant increase in hole barriers at the valence band maximum (VBM) post-doping, rising from initial values of 0.448 eV (Cu interface) and 0.349 eV (Fe interface) to increases of 104.02% and 209.46%, respectively, which is much larger than the decrease in electron barriers at the CBM. Overall, in these Metal/EP interfacial systems, the enhancement of electronic properties due to the increased hole barriers near VBM after doping is more significant than the detrimental effects caused by electron barriers at CBM. This study provides important theoretical guidance for designing high-performance nanocomposite insulating materials through quantitative calculations of SiO₂-doped interfacial barriers. By enhancing electronic coupling between metals and epoxy resins, this interfacial engineering strategy holds promise for significantly improving the overall insulation performance of composite materials.

3. Conclusions

This study systematically investigates the regulation mechanism of SiO₂ nanoparticle doping on EP composite properties through various computational simulations, combining molecular dynamics and first-principles calculations. The results demonstrate that SiO₂ doping simultaneously enhances both mechanical properties and interfacial electrical properties. Mechanically, the nanoparticles significantly improve material strength by reinforcing interfacial interactions between the nanoparticle and the EP matrix, leading to the enhancement of its shear modulus, Young’s modulus, and bulk modulus. Electrically, nano-SiO₂ doping improves the electrical performance of EP via dual mechanisms: (a) raise the hole injection barrier to suppress charge accumulation. At the interface between EP and Cu, SiO₂ doping increased the barrier by approximately 0.54 eV. For Fe, the hole injection barrier increased by 0.73 eV, and (b) introduced multiple defect states in EP that promote charge dissipation while mitigating space charge accumulation. This unique synergistic compensation mechanism effectively ensures the insulation reliability of the material. The proposed interface engineering strategy provides a fundamental theoretical basis for designing high-performance epoxy insulating materials, with the multifunctional optimization approach being extendable to other nanocomposite dielectric systems.