# A Comparison of Electrical Breakdown Models for Polyethylene Nanocomposites
## 4 Discussion
The general trends of the simulation and experimental results are similar. However, the simulation results of the EBMD model are in best agreement with the experiments. When the nanofiller content is around 0.5 wt%, the simulation results of EBEG and EBEF deviate greatly from the experimental results. According to the experimental results, the maximum electric breakdown strength is 355.8 kVmm\({}^{-1}\), which appears at the nanofiller content of 0.5 wt%, while the simulation results of EBEF, EBEG, and EBMD models are 286.3, 312.2, and 356.1 kVmm\({}^{-1}\), respectively. It is apparent that the simulation results of the EBMD model are more consistent with the experiments. This indicates that the synergistic effect of deep trap centers in interfacial zones and the tight binding of molecular chains enhance the breakdown performance of LDPE nanocomposites. The larger trap energy and density in nanodelectrics doped with small amounts of nanofillers reduce space charge accumulation and electric field concentration, resulting in the increase in the breakdown strength of nanocomposites. However, the changes in trap energy and density have a limited effect on the breakdown electric field. It is necessary to simultaneously consider the space charge accumulation formed by the trapping of deep traps, the free volume expansion caused by the long-range displacement of the molecular chain driven by the electric field force, and the effect of the energy accumulation of electrons in the expanded free volume on the breakdown strength. Comparative studies show that the energy accumulation of electrons in the expanded free volume due to the long-range displacement of the molecular chain dominates the breakdown strength. When the interaction between the molecular chains in the interface region between the nanofiller and the polymer matrix is enhanced, it is difficult for the molecular chains to undergo long-range displacement under the driving of the electric field force. In this case, the free volume expansion is small and it is difficult for electrons to obtain sufficient energy, so the breakdown strength is increased. Therefore, when designing the structure of the interface region, the interaction between the molecular chains in the interface region can be enhanced by the surface modification method, so that the breakdown strength can be greatly improved. LDPE is a key insulating material for power cables and energy storage dielectric capacitors. Revealing the breakdown mechanism of LDPE nanodelectrics can better develop insulating materials with high breakdown strength. This will provide theoretical and simulation model support for the development of high-performance power cables and energy storage dielectric capacitors. Figure 8: Comparison of EBEF, EBEG, and EBMD simulation electrical breakdown fields with experimental results. In addition, the aggregated structure of polymer nanocomposites can be changed to some extent, compared to that of pure polymers. The interface between the crystalline region and the amorphous region, and the interface region between the nanofiller and the polymer matrix, may form different trap distributions. The change in crystallinity and the change in lamellar length may change the interaction strength between molecular chains. Because the molecular chains in the interface region are bound by nanoparticles, the interaction strength between the molecular chains also changes. In future studies, we will correlate aggregated structures with trapping effects and molecular chain interactions through density functional theory [37] and molecular dynamics simulations [38]. Then, the EBMD model will be used to determine the effect of the trapping effect and molecular chain interactions on the breakdown strength. Ultimately, a multiscale model will be established to study the relationship among the aggregated structure, the trapping effect and molecular chain interactions, and the electric breakdown performance.