## 3 Results and Discussion
### Electrochemical Analysis
EIS experiments were carried out to investigate the inherent features, such as solution resistance (R\({}_{\text{s}}\)) and charge transfer resistance (R\({}_{\text{ct}}\)). The EIS analysis in Figure 6c shows the Nyquist plot, in which the absence of a semicircle could be due to the faradaic reactions and excellent chemical stability of all MnO\({}_{2}\) phases. The solution resistance (R\({}_{\text{S}}\)) determined through electrochemical circuit fitting was 7.50, 7.56, and 7.59 \(\Omega\) for \(\alpha\)-, \(\beta\)-, and \(\gamma\)-MnO\({}_{2}\), respectively. The nearly straight line in the low-frequency region of the Nyquist plot for \(\alpha\)-, \(\beta\)-, and \(\gamma\)-MnO\({}_{2}\) indicated that the reactions were limited by diffusion resistance (constant-phase element (CPE)) rather than charge transfer resistance (R\({}_{\text{ct}}\)) [26]. Also, the straight line inclined towards the imaginary z-axis indicated the perfect capacitive behavior of MnO\({}_{2}\). The charge transfers resistance (R\({}_{\text{ct}}\)) was found to be 2.24, 2.45, and 2.56 \(\Omega\) for \(\alpha\)-, \(\beta\)-, and \(\gamma\)-MnO\({}_{2}\), respectively. Despite the fact that \(\alpha\)-MnO\({}_{2}\) has a large band gap, it has the lowest charge transfer resistance due to its well-organized tunnel-shape nanostructure. The Bode plot shown in Figure 6d from the EIS analysis shows that the negative phase angle was found to be 64.5\({}^{\circ}\), 62.4\({}^{\circ}\), and 58.0\({}^{\circ}\) for \(\alpha\)-, \(\beta\)-, and \(\gamma\)-MnO\({}_{2}\), respectively. It was observed that \(\alpha\)-MnO\({}_{2}\) had the highest phase angle among all the phases, and hence it can be considered a good supercapacitor electrode material. It was observed that in the case of \(\gamma\)-MnO\({}_{2}\), the phase angle had a low value as compared to \(\alpha\)-MnO\({}_{2}\) and \(\beta\)-MnO\({}_{2}\), indicating that it had poor conductivity. It is clear that the slopes obtained in the high-frequency region were almost zero, which is a salient characteristic of a pure resistor. However, the slope increases in the low-frequency region correspond to the characteristics of a pseudocapacitor [26]. All these results demonstrate that the material behaves like a resistor in the high-frequency range, whereas it behaves like a pseudocapacitor in the low-frequency region. Further, the Bode plot of the phase angle is shown in Figure 6d. The phase line strongly deviated from that of an ideal capacitor (an ideal capacitor shows a phase angle of 90\({}^{\circ}\)). Such a non-ideal behavior further substantiates the pseudocapacitive nature of MnO\({}_{2}\). The EIS plots show that \(\alpha\)-MnO\({}_{2}\) had the lowest R\({}_{\text{ct}}\) as compared to the other phases, resulting in a high specific capacitance. Based on these results, the best working electrode material (\(\alpha\)-MnO\({}_{2}\)) was chosen for the device fabrication. The electrochemical analysis of the fabricated symmetric device was tested using a two-electrode set-up; one acts as a cathode and the other as an anode. Figure 7a depicts the CV analysis of the symmetric \(\alpha\)-MnO\({}_{2}\)/\(\alpha\)-MnO\({}_{2}\) device in the potential window of 1.2 V with diverse scan rates (10 to 100 mV s\({}^{-1}\)). The plots demonstrate capacitive performance with a distorted quasi-rectangular shape, which is preserved even when the voltage window is changed, exhibiting the characteristics of EDLC with the pseudocapacitive combination. With an increased scan rate, the CV curve shape hardly varies, confirming the excellent cyclability and high-speed capabilities of the symmetric \(\alpha\)-MnO\({}_{2}\)/\(\alpha\)-MnO\({}_{2}\) supercapacitor. Figure 7b shows the GCD plots at different specific current densities (1 to 10 Ag\({}^{-1}\)) for the symmetric \(\alpha\)-MnO\({}_{2}\)/\(\alpha\)-MnO\({}_{2}\) supercapacitor device over a potential range of 1.2 V. Using the GCD technique, the specific capacitance of 86 Fe\({}^{-1}\) was obtained at a current density of 1 Ag\({}^{-1}\).