## 3 Results and Discussion
Figure 3: High-resolution X-ray photoelectron spectroscopy (XPS) scan of as-obtained Co\({}_{3}\)O\({}_{4}\): (a) Co 2p region; (b) O 1s region. Figure 2: (a) XRD patterns and (b) energy-dispersive X-ray (EDX) spectrum of the obtained Co\({}_{3}\)O\({}_{4}\). On the basis of Equation (1), the specific capacitances were determined to be 948.9, 931.8, 920.2, 912.4, and 900.6 F/g at scan rates of 5, 10, 20, 50, and 100 mV/s respectively, as shown in Figure 4b. The prominent specific capacitances most probably benefit from the porous hollow sphere nanostructure. The decrease in specific capacitances with an increasing scan rate can be understood in terms of the circuitous diffusion of OH\({}^{-}\) ions into the Co\({}_{3}\)O\({}_{4}\). At a low scan rate, both the inner and outer surface of the material can be utilized for charge storage. At a high scan rate, the diffusion of OH\({}^{-}\) ions is more likely happen on the outer surface and only a small fraction of OH\({}^{-}\) ions can penetrate into the inner surface [37]. Nevertheless, the inevitable decrease of specific capacitances is not drastic, which demonstrates an excellent rate capability (maintaining almost 95% capacitance from 5 to 100 mV/s). This phenomenon illustrates that the Co\({}_{3}\)O\({}_{4}\) is able to act as a \"reservoir\" of ions [38; 39] to accommodate OH\({}^{-}\). The reservoir can guarantee the efficient proceeding of the faradic reactions at high scan rates (or high current densities) and in turn relieves the fading of the specific capacitances. Further evidence is provided by GCD measurement. The discharge curves of the Co\({}_{3}\)O\({}_{4}\) measured at different current densities in a voltage window of 0-0.55 V are presented in Figure 5a. In comparison with the discharge curves of electric double-layer capacitors (which are almost a straight line), two evident plateaus are well displayed. These coincide with the sequential redox reactions described by Equations (3) and (4), indicating the pseudocapacitive property of the Co\({}_{3}\)O\({}_{4}\). According to Equation (2), specific capacitances of 988, 960, 947.9, 939.4, and 925 F/g can be delivered at current densities of 1, 2, 5, 10, and 20 A/g respectively, as depicted by Figure 5b. Due to the relatively insufficient active material involved in redox reactions under higher current densities, the boosting of the current densities results in the fading of specific capacitances. At a low current density, the OH\({}^{-}\) ions have adequate time to transfer at the interface between electrode and electrolyte than they do at a high current density [40]. It is worth noting that the rate performance of the Co\({}_{3}\)O\({}_{4}\) is impressive (maintaining 925 F/g at 20 A/g, representing a 93.6% capacitance retention), which is significant for practical use of the material. An EIS study is depicted in Figure 6. The first intersection point of the Nyquist plot with the real axis reflects the resistances (\(R_{\mathrm{s}}\)), including the ionic resistance of the electrolyte, contact resistance at the interface of electrolyte and electrode, and intrinsic resistance of the material [39]. The Co\({}_{3}\)O\({}_{4}\) modified electrode exhibits a very low \(R_{\mathrm{s}}\) of 0.52 Ohms. In the high frequency region, the charge-transfer resistance (\(R_{\mathrm{ct}}\)) and double-layer capacitance (\(C_{\mathrm{dl}}\)) correspond to the semicircle arc. The inset of Figure 6 shows that the semicircle has a small diameter, expressing a low charge-transfer resistance and a low interfacial resistance between the current collector and electroactive material [22; 41]. In the low frequency range, the slope of the plot corresponds to the diffusive resistance of OH\({}^{-}\) ions (Warburg impedance, \(W\)) within the Co\({}_{3}\)O\({}_{4}\). The plot presents an evident straight line with a slope greater than 45\({}^{\circ}\), which indicates a valid electrolyte ion diffusion [30; 34].