# Effect of Environmental Temperature on the Insulating Performance of Epoxy/MgO Nanocomposites
## 3 Results and Discussion
### Breakdown Performance  
The process of breakdown is complex, and the measurement of breakdown data is affected by many factors. After years of experimental research, Swedish physicists finally discovered the law of the Weibull distribution [33]. This law is widely used to study the breakdown distribution and product service life prediction. The Weibull distribution expression of two parameters is:  
\[P_{\mathbf{e}}=1-e^{-(\frac{\kappa}{2}/\varepsilon_{0})^{\delta}} \tag{2}\]  
Figure 5: Dielectric loss of MgO/epoxy composites as a function of frequency at (**a**) 20 \({}^{\circ}\)C; (**b**) 80 \({}^{\circ}\)C; (**c**) 150 \({}^{\circ}\)C.  
where \(P_{e}\) is the breakdown probability of the sample, \(E\) is the field strength when the sample is broken down, \(\beta\) is the shape parameter, and \(E_{0}\) is the breakdown strength when the probability of occurrence is 63.2%. The logarithmic change of Equation (2) is:  
\[In(-In(1-P_{e}))=\beta(InE-InE_{0}) \tag{3}\]  
If \(E\) is certain, then it can be calculated by:  
\[P_{e}=\frac{i-0.5}{n+0.25}\oplus \tag{4}\]  
where \(i\) is the number of times the sample breakdown field strength is arranged in ascending order, and \(n\) represents the total number of tests for each sample. The experimental results reveal that the breakdown strength of the composites at 20 and 80 \({}^{\circ}\)C was very small. When the temperature reached 150 \({}^{\circ}\)C, the breakdown strength of the composites decreased significantly. Compared with the strength at 20 \({}^{\circ}\)C, the maximum breakdown strength decreased by 51.3%. As shown in Table 1, the parameters of the Weibull distribution of the composites decreased with an increasing temperature. For example, the dispersion of breakdown strength increased and the stability of the composites at high temperatures decreased. This may be due to the fact that, at low temperatures, the composites are in a glassy state. At this time, the internal molecular structure of the composites is stable, the movement of the molecular structure is very low and the breakdown performance of the material does not change significantly, thus resulting in a low breakdown strength. When the temperature was higher than the glass transition temperature of the composites, the molecular chains inside the material began to move violently, showing the characteristics of a rubbery state, and as the temperature further increased, the binding of the molecular structure inside the material weakened. Consequently, the material exhibited viscous flow characteristics, and the molecular movement was violent. Under the action of an external electric field, the molecular structure changed greatly, and the performance was affected by the temperature. The dielectric loss greatly increased, and the breakdown strength of the material rapidly decreased. On the other hand, the interaction zone formed between the added MgO nanoparticles and the epoxy-matrix makes the structure of the composites closer. When the mass fraction of MgO nanoparticles increased, the interaction zone in the epoxy-matrix formed a pathway, which was conducive to the formation of a breakdown pathway, and the breakdown strength of the composites decreased. The increase in temperature led to intensified molecular motion and the inhibition of the interaction zone. This weakened as the temperature increased, decreasing the breakdown strength of the composites [34]. As shown in Figure 6, the breakdown strength first increased and then decreased with the increase in MgO nanoparticle content. At a concentration of 1%, the breakdown strength of the composite dielectric reached the maximum value of 35.15 kV/mm, which was 11.1% higher than the breakdown strength of the pure epoxy resin (31.63 kV/mm). When the content of MgO nanoparticles was 7%, the electrical strength of the composite dielectric was close to that of the pure epoxy resin. It was hypothesized that the introduction of a large number of heterogeneous crystal nuclei into the composites