# A Comparison of Electrical Breakdown Models for Polyethylene Nanocomposites
## 3 Results  
Both the trap energies and the breakdown strengths of LDPE nanodielectrics doped with various fillers first increased and then decreased with the increase in doping content [5; 6; 11; 12]. It is generally believed that the interfacial region is responsible for the excellent electrical properties of polymer nanocomposites. The trap levels in the interfacial region and the interaction between molecular chains are two key factors to improving the breakdown strength of polymer nanocomposites. However, which factor is more influential remains unclear. The main influencing factors of the breakdown strength are determined by comparing the above-mentioned breakdown simulation models with the experimental results. The quantitative relationship between the influencing factors and  
Figure 2: Electrical breakdown criteria of EBEG (**a**) and EBMD (**b**) models under a ramp voltage.  
the breakdown strength was obtained. We took the LDPE/Al\({}_{2}\)O\({}_{3}\) nanocomposite as an example to compare the three breakdown models. In order to easily compare the simulation results with the experimental results, the parameters in the simulation model were derived from the experimental results [13]. The thickness of the LDPE/Al\({}_{2}\)O\({}_{3}\) nanocomposite was 200 \(\upmu\)m and the temperature of the sample was 300 K. We investigated the breakdown properties of pure LDPE and LDPE/Al\({}_{2}\)O\({}_{3}\) nanodielectrics with nanofiller contents of 0.1, 0.5, 2, and 5 wt%. Since the numerical simulation of the charge drift equation should obey the Courant-Friedrich-Levy (CFL) law, the films were discretized into 300 elements and the computational time interval \(\Delta t\) was set as 1 ms [34]. Figure 3 shows the trap density, trap energy level, and attempt-to-escape frequency of pure LDPE and LDPE/Al\({}_{2}\)O\({}_{3}\) nanodielectrics as a function of nanofiller content [13]. \(N_{T}\), \(u_{T}\), and \(v_{0}\) were obtained from the experimental results of thermally stimulated depolarization currents, and they all first increased and then decreased with the increase in nanofiller content. Charges in the electrodes may first be transferred to the surface traps in the nanocomposite and then injected into the bulk of the material. In this case, the charge injection barriers can be set to the deep trap levels. The mobilities of mobile electrons and mobile holes in the extended states of the nanocomposite were both set to be 1 \(\times\) 10\({}^{-13}\) m\({}^{2}\)V\({}^{-1}\)s\({}^{-1}\). The trapping probabilities of the deep traps were calculated from the trap densities and the carrier mobilities of the mobile charges. The detrapping probabilities of trapped charges were calculated from the trap levels and the attempt-to-escape frequencies. The recombination coefficients of positive and negative charges were calculated from the mobilities of mobile electrons and mobile holes.  
It can be seen that the trap energy and density are positively correlated with the breakdown strength of the polymer nanocomposites. However, quantitative studies are still lacking about how much the trap energy and density can change the breakdown strength by affecting the space charge accumulation and electric field concentration. In addition, quantitative studies are also lacking about the extent to which the trap energy and density change the breakdown strength by affecting the electric field distortion and the energy accumulation of electrons in a fixed free volume. Moreover, whether the increase in breakdown strength is caused by the binding effect of nanofillers on molecular chains should also be considered. In order to obtain these quantitative relationships, it is necessary to carry out simulation studies of different breakdown models and compare them with the experimental results to determine the primary and secondary influencing factors. Finally, the quantitative relationship between each influencing factor and the variation range in the breakdown strength can be obtained.