## 3 Results and Discussion
### Electrochemical Studies  
The electrochemical behavior of the as-prepared template-free electrode samples was studied via Cyclic voltammetry (CV), galvanostatic charge-discharge (GCD), and electrochemical impedance spectroscopy (EIS). The CV spectra of the electrode materials INS0, INS1, INS2, and INS5 in three electrode systems at various scan rates are depicted in Figure 5a. All the sample electrode materials show reversible redox peaks in their 3T CV curves. The nonrectangular curve shape indicates the presence of pseudocapacitance [50]. The enclosed areas under the CV curve for the three samples are comparatively illustrated  
Figure 4: FESEM images corresponding to the sample (**a**) INS0, (**b**) INS1, (**c**) INS2, and (**d**) INS5, (**e**) HRTEM image, and (**a1**) their magnified areas, which are illustrated by (**a1**) FFT line, (**a2**) FFT images, and (**a3**) SAED pattern for INS1 sample. at 10 mVs\({}^{-1}\). The sample, INS1, exhibits the highest curve area under the CV curve, leading to better charge storage capacity. Figure 5b depicts the calculated specific capacitance from the CV curve at various scan rates, ranging from 10 mVs\({}^{-1}\) to 100 mVs\({}^{-1}\) for all prepared electrode samples. At a scan rate of 10 mVs\({}^{-1}\), the values of the specific capacitance for INS0, INS1, INS2, and INS5 are found to be 897 F\(\cdot\)g\({}^{-1}\), 1268 F\(\cdot\)g\({}^{-1}\), 1076 F\(\cdot\)g\({}^{-1}\), and 963 F\(\cdot\)g\({}^{-1}\), respectively. While at 100 mVs\({}^{-1}\), the values of maintained specific capacitance are 306 F\(\cdot\)g\({}^{-1}\), 484 F\(\cdot\)g\({}^{-1}\), 444 F\(\cdot\)g\({}^{-1}\), and 425 F\(\cdot\)g\({}^{-1}\), respectively. More accessible electrochemical kinetics and a higher surface area in sample INS1 lead to a higher charge storage capacity [51]. The reversible redox reaction of the In\({}_{2}\)S\({}_{3}\) ionic charge storage behavior with hydroxide counter anions (OH\({}^{-1}\)) in the electrolyte (KOH) can be expressed as follows:  
\[\text{In}_{2}S_{3}+\text{OH}^{-}\leftrightarrow\text{In}_{2}S_{5}\text{OH}+ \text{e}^{-} \tag{4}\]  
At all scan rates, the linear connection between the redox peak current and the scan rate (Figure 5c) indicates that the electrode surface reaction is diffusion-controlled [52]. Figure 5d depicts a comparative GCD curve for all the prepared electrode samples. Nonlinear GCD curves in all samples indicate that the electrode material exhibits obvious pseudocapacitive charge storage behavior [53]. Higher discharge times associated with INS1 suggest better charge storage capacity. Figure 5e illustrates the specific capacitance plot against the current density's values. The excellent capacitance value in the INS1 electrode is (i) due to an optimal layering structure, the layered facets of 2D In\({}_{2}\)S\({}_{3}\) enable highly accessible interfacial contacts, leading to greater use of ion accumulation, and (ii) due to thin-layered interfaces, there is a  
Figure 5: (**a**) Comparative CV curve of all prepared electrode samples, (**b**) calculated specific capacitance values at various scan rates, (**c**) comparative oxidation peak position of all prepared electrode samples, (**d**) comparative GCD curve of all prepared electrode samples, (**e**) calculated specific capacitance values at various scan rates, (**f**) EIS spectra of sample INS1, (**g**) Ragone plot, (**h**) cyclic retention plot (inset: scheme of conjugated INS5 for high retention) for all the prepared samples. reduction in internal material resistance, and the short electron diffusion length is associated with this phenomenon during the charge/discharge process [54; 55]. The Nyquist plot was accomplished to understand better the frequency response and material charge transportation (Figure 5f).