## 2 Results and Discussion
Figure 4: (**a**) CV Profile of Ce/GOCNIO NPs; (**b**) CV Profile of Yb/GOCNIO NPs; (**c**) Influence of scan rates on specific capacitance of Ce/GOCNIO NPs; and (**d**) Influence of scan rates on specific capacitance of Yb/GOCNIO NPs. The gravimetric capacitance of all the electrodes was calculated using Equation (2):  
\[\text{Cg}=\text{i}\ \times\Delta\text{t} \tag{2}\]  
where 'i' is the current density, \(\Delta\text{t}\) is the discharge time, and \(\Delta\text{V}\) is the potential drop. The gravimetric capacitance of Yb/GOCNIO NPs was 219 \(\text{Fg}^{-1}\) as compared to Ce/GOCNIO NPs (169 \(\text{Fg}^{-1}\)). Electrochemical impedance spectroscopy (EIS) results provide information about various reaction resistances. The charge transfer resistance (\(\text{R}_{\text{ct}}\)) ascribes the diameter of the semicircled curve of impedance. EIS studies of prepared electrodes were conducted using an AC circuit. Results were obtained by using a 3M KOH electrolyte within the frequency range of 100 kHz to 100 mHz. The Nyquist plot of both Ce/GOCNIO NP and Yb/GOCNIO NP electrodes shows the non-vertical portion of the impedance plot taken at a lower frequency, which is observed due to an uneven pathway for the transport of electrolytic ions from the bulk electrolyte to the porous active surface of electrode, by the irregular distribution of pore size and coarseness of the electrode [38]. The larger diameter of the semicircled Ce/GOCNIO NPs shows a greater charge transfer resistance (\(\text{R}_{\text{ct}}\)) and possesses a larger value for Warburg resistance (\(\text{R}_{\text{w}}\)). In the case of Yb/GOCNIO NP electrodes, the curve possesses a very small semicircle and gives a lower \(\text{R}_{\text{ct}}\) value. Yb/GOCNIO NPs also have a vertical impedance line at a low frequency, indicating the lowest Rw value and also representing EDLC behavior. Hence, the electrolyte's ions diffused quickly and improved the capacitance (Figure 5a). For the confirmation of surface area and pore size, Brunauer Emmett Teller (BET) analysis was also conducted. Figure 5c,d indicate the nitrogen adsorption desorption  
Figure 5: (a) GCD Profile of Ce/GOCNIO NPs and Yb/GOCNIO NPs; (b) EIS Nyquist Plots of Ce/GOCNIO NPs and Yb/GOCNIO NPs; (c) BET profile of Ce/GOCNIO NPs; (d) BET profile of Yb/GOCNIO NPs. patterns of as-synthesized nanocomposites, being measured at \(-196.03\)\({}^{\circ}\)C in order to quantify the sorption of nitrogen contents. The hysteresis loop formed for Yb/GOCNIONNPs showed a larger surface area of 103 m\({}^{2}\) g\({}^{-1}\) as compared to Ce/GOCNIONPs with a specific surface area of 89 m\({}^{2}\) g\({}^{-1}\), thus confirming the availability of enhanced surface area and porosity within the nanomaterial. A type IV BET hysteresis loop, classic for mesoporous 2-D nano-architectures, was observed in both nanocomposites as shown in Figure 5c,d. The photocatalytic activity of cerium- and ytterbium-based nanocomposites was checked by using the rhodamine B and methylene blue dyes, respectively (Figure 6a-d). Dyes were prepared as 2.5 mg/250 mL using distilled water separately. The \(\lambda_{\text{max}}\) of both dyes was first measured using a UV-visible spectrophotometer; MB dye showed a \(\lambda_{\text{max}}\) of 665 nm and the RhB that of 554 nm [39; 40]. A nanocomposite (5 mg) in a 500 mL dye solution was mixed and placed in the dark to attain equilibrium. After 2 h, the mixture was exposed to light under vigorous stirring. The time interval was set to 5 min for every reading in order to measure the percentage of degradation of RhB and MB repeatedly. Nearly 3 mL for each reading was used and showed a noticeable decrease in absorbance values, thus confirming the degradation of dyes [41; 42].