## 1 Introduction
### Physical Properties
#### 2.1.3 Scanning Electron Microscopy Test  
Using scanning electron microscopy (SEM) to analyze the surface condition of silicone rubber has been widely adopted in evaluating the aging degree of composite insulators aged for different aging times [11]. In this paper, the surface topography of samples after each aging process was assessed with SEM. The test methods of SEM are as follow.  
The surfaces of the samples were inspected using a FEI Quanta 200 SEM from Philips. To enhance the electrical conductivity of silicone rubber, samples were sprayed with gold for 60 s before testing.  
The differences in the micro-structures of samples tested by SEM at a magnification of 5000\(\times\) are shown in Figure 2.  
In Figure 2a, there are few cracks and voids detected on the surface of sample A\({}_{1}\) aged for 1 year. When aging time increases, the number of cracks and voids appearing on samples increases compared with A\({}_{1}\), as shown in Figure 2b,c. However, in this case, the surface material of silicone rubber remained flat and the silicone rubber was still in good condition. When the aging time reaches 8 years, it can be found that some rough bumps along with cracks and voids appear (sample A\({}_{4}\)). With an increase of aging time, there are more rough bumps, exposed fillers and organic residues, as shown on the surface of sample A\({}_{6}\) aged for 12 years, leading to more loose space in the surface material of sample A\({}_{6}\). Based on images captured by SEM, it can be inferred that samples manufactured by Factory A still have a good anti-aging ability under an environment of strong UV radiation and high humidity for a period of up to 6 years. When the aging time exceeds 8 years, the anti-aging ability of samples gradually weakens and their aging rate gradually accelerates.  
In Reference [22], it was found that the hydrophobicity of the surface material was related to the micro-structure of the surface material, and roughness and porosity were the main factors affecting the micro-structure of silicone rubber. This paper adopts the Wenzel model to explain the contact between a water drop and the surface material of silicone rubber. In the Wenzel model, the relationship between  
Figure 2: Morphology of samples using scanning electron microscopy (SEM), 5000\(\times\): (**a**) A\({}_{1}\); (**b**) A\({}_{2}\); (**c**) A\({}_{3}\); (**d**) A\({}_{4}\); (**e**) A\({}_{5}\); (**f**) A\({}_{6}\).  
the static contact angle \(\theta\) and [PERSON]'s contact angle \(\theta_{1}\) (contact angle of new composite insulators) is as follows:  
\[\cos\theta=r\cos\theta_{1} \tag{1}\]  
where, \(r\) is the rate of roughness in the Wenzel model, which can be obtained by the ratio of the real contact area of a water drop on the surface of silicone rubber to the contact area of a water drop on the surface of silicone rubber.  
In Figure 2a-c, the roughness of the surface material of silicone rubber gradually increases with time, which leads to a slow increase of \(r\). As shown in Figure 3a-c, with an increase of \(r\), the contact area of a water drop on the surface material expands, but with no sign of collapsing. This means the hydrophobicity of silicone rubber is good at this stage. When aging time exceeds 8 years, the rate of surface roughness increases faster, which leads to a faster increase of \(r\). As is shown in Figure 3d-f, the water drop on silicone rubber collapses gradually, leading to a decrease of hydrophobicity in the surface material of silicone rubber.  
In this paper, a method where aging levels (denoted \(S_{em}\)) of composite insulators are classified by the roughness of silicone rubber was proposed, and aging levels \(S_{em}\) of composite insulators sampled in this paper based on standards are listed in Table 3.