## 3 Results
The intersection value of plot and real axis reflects the intrinsic resistance and interface resistance of electrolyte and active material (denoted as \(R_{8}\)) [35]. The \(R_{8}\) of Co\({}_{3}\)O\({}_{4}\)-1, Co\({}_{3}\)O\({}_{4}\)-2 and Co\({}_{3}\)O\({}_{4}\)-3 are 0.55, 0.52 and 0.53 \(\Omega\), respectively (tiny difference). The semicircle acquired in high frequency range represents the double-layer capacitance (\(C_{\rm dl}\)) and the charge-transfer resistance (\(R_{\rm ct}\), corresponds to the semicircle diameter). The semicircle also expresses that the Cd\({}_{\rm dl}\) and \(R_{\rm ct}\) are connected in parallel [36]. Apparently, the \(R_{\rm ct}\) value of Co\({}_{3}\)O\({}_{4}\)-2 is much smaller than Co\({}_{3}\)O\({}_{4}\)-1 and Co\({}_{3}\)O\({}_{4}\)-3 (Figure 6b). In low frequency region, the approximate line in Nyquist plot is related to the interfacial diffusive process and determined by pseudocapacitance (\(C_{\rm ps}\)) and Warburg element (\(W\)). The equivalent circuit is shown in Figure 6c. Benefited from the hollow structure constructed by numerous nanoparticles, the slops for all electrodes are larger than 45\({}^{\circ}\), which presents an efficient electrolyte diffusion. Furthermore, a quasi-vertical line displayed by the plot of Co\({}_{3}\)O\({}_{4}\)-2 electrode implies a scarcely limited ions diffusion and the behavior tends to an ideal capacitor [23; 36]. The  
Figure 5: Specific capacitances of Co\({}_{3}\)O\({}_{4}\)-1, Co\({}_{3}\)O\({}_{4}\)-2 and Co\({}_{3}\)O\({}_{4}\)-3 electrodes as a function of current densities. merits of Co\({}_{3}\)O\({}_{4}\)-2 electrode proposed in EIS results well coincide with the superior electrochemical performance of Co\({}_{3}\)O\({}_{4}\)-2 electrode in CV and GCD assessments. The Co\({}_{3}\)O\({}_{4}\)-2 was employed as the optimized electrode through CV, GCD and EIS results for long term cycling investigation, as recorded in Figure 7. The evaluation was carried out by using a repetitive GCD process at 20 A/g. The Co\({}_{3}\)O\({}_{4}\)-2 electrode retains 85.9% of its initial specific capacitance even after undergoing 5000 cycles. The insets display the GCD curves of the Co\({}_{3}\)O\({}_{4}\)-2 electrode at first and last for 10 cycles. The coulombic efficiency (\(\eta\)) is also an important criterion for evaluating the durability and can be calculated based on Equation (2) [37]:  
\[\eta=\frac{t_{\text{d}}}{t_{\text{c}}}, \tag{2}\]  
where \(t_{\text{d}}\) (s) is the discharge time and \(t_{\text{c}}\) (s) is the charge time. All deduced coulombic efficiency values reach over 95%. The excellent electrochemical stability of Co\({}_{3}\)O\({}_{4}\)-2 electrode is significant for possible commercial application. Figure 6: (**a**) Electrochemical impedance spectroscopy (EIS) plots of Co\({}_{3}\)O\({}_{4}\)-1, Co\({}_{3}\)O\({}_{4}\)-2 and Co\({}_{3}\)O\({}_{4}\)-3 electrodes; (**b**) enlarged view of high frequency region; (**c**) equivalent circuit involves intrinsic resistance and interface resistance (\(R_{\text{s}}\)), double-layer capacitance (\(C_{\text{dl}}\)), charge-transfer resistance (\(R_{\text{ct}}\)), Warburg element (\(W\)) and pseudocapacitance (\(C_{\text{ps}}\)). Figure 7: Cycling performance and coulombic efficiency of Co\({}_{3}\)O\({}_{4}\)-2 electrode. The insets are GCD curves at the first and last 10 cycles.