## 4 Results and Discussion  
The TPB length of the EE was firstly calculated using our proposed theoretical model by Office Excel. Subsequently, a study was conducted to determine the effects of the impregnation loading, particle radius, and fiber radius on the TPB length. Baseline conditions were set for the parametrical study: the volume fraction of the ion-conducting fibers \(V_{\rm io}\) is 0.45, the fiber radius is 150 nm, the particle radius is 30 nm, and \(p_{\rm el}=1\). Unless otherwise stated, the baseline conditions were adopted.  
Figure 6 shows the dependence of the percolation ratio \(p_{\rm el}\) on the impregnation loading with different radii of the electron conducting particles \(r_{\rm el}\). Note that for an impregnation loading below the threshold, \(p_{\rm el}=0\) due to no percolating particles existing. Furthermore, the threshold of the impregnation loading \(\eta\) increases with the increase of the \(r_{\rm el}\). This is because the smaller \(r_{\rm el}\), the more particles around the fiber, which will provide more options from the top to bottom of the fiber and form the percolated cluster. However, for an impregnation loading higher than the threshold, the percolation ratio \(p_{\rm el}\) steeply increases. When the impregnation loading is larger than 0.66, all particles are connected for different \(r_{\rm el}\), that is, \(p_{\rm el}=1\).  
Figure 7 shows the dependence of the TPB length on the impregnation loading. At a fixed \(V_{io}\), particles do not percolate when the impregnation loading is too low. Thus, the effective TPB length is 0. However, when the impregnation loading reaches the threshold value of 0.48, an effective TPB begins to form and reaches for \(\eta\) in the range from 0.48 to 0.6, which can be attributed to the increase in the percolation ratio \(p_{\rm el}\) and coordination number. Compared with \(0.48<\eta<0.6\), the effective TPB length enhances relatively slowly for \(\eta>0.6\). This is due to the fact that the percolation ratio \(p_{\rm el}\) reaches its maximum (1) at \(\eta>0.6\) and remains constant.  
Figure 7 shows that the effective TPB length increases with increasing \(V_{io}\) when the impregnation loading is larger than the threshold value of 0.48. Moreover, the difference in the effective TPB length due to the change of \(V_{io}\) increases with increasing \(\eta\). For example, when \(\eta\) is 0.5, the effective TPB length for \(V_{io}\) of 0.5 is \(2.1\times 10^{12}\) m-1 higher than that for \(V_{io}\) of 0.4. However, when \(\eta\) is 0.6, the effective TPB length for \(V_{io}\) of 0.5 is 13.8\(\times 10^{12}\) m-1 higher than that for \(V_{io}\) of 0.4.  
Figure 6: The dependence of the percolation ratio \(p_{\rm el}\) on the impregnation loading.  
Figure 8 shows the TPB length as a function of the electron-conducting particle radius \(r_{\rm el}\) and ion-conducting fiber radius \(r_{i0}\) with the \(\eta=1\). The TPB length of EE is high on the order of \(1\times 10^{14}\), which is close to the value of IE [30]. Note that the TPB increases with decreasing \(r_{\rm el}\) or \(r_{io}\). The TPB length at a \(r_{\rm el}\) value of 30 nm only accounts for 37% of that at a \(r_{\rm el}\) value of 10 nm for \(r_{io}=150\,nm\). However, the influence of \(r_{\rm el}\) on the TPB length varies. For instance, at a smaller \(r_{\rm el}\), the TPB length drops more rapidly; at a larger \(r_{\rm el}\), the influence is weakened. Although finer impregnation particles are favorable for the TPB length, they can also increase the aggregation risk and directly lead to a decrease of the TPB length and bad electrode performance. In practice, the size of the impregnation particles must be carefully controlled to maximize the electrode performance.