## 3 Experimental Outcomes  
### Analyses of SEM Images  
Figure 1a,b, illustrates the pictorial presentation of SEM images. The dye adsorption onto the NIFGS surface can be depicted from these pictures. The NIFGS surface texture has a porous and fibrous structure which resembles a honeycomb shape, it enhances the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Eq. No.** & **Equation** & **Description** & **Parameter** \\ \hline \multicolumn{4}{c}{**General Adsorption Studies**} \\ \hline (1) & \(q_{e}=\frac{(C_{e}-C_{e})\ V}{W}\) & Adsorption capacity at equilibrium & \(q_{e}\): equilibrium adsorption capacity (mg L\({}^{-1}\)) \\ \hline (2) & \(q_{t}=\frac{(C_{e}-C_{e})\ V}{W}\) & Adsorption capacity at time \(t\) & \(C_{o}\): initial concentration of adsorbent (mg L\({}^{-1}\)) \\ \hline (3) & \(RE\%\ =\ \left[\frac{C_{e}-C_{e}}{C_{e}}\right]*100\) & Percentage removal efficiency (\(RE\)) & \(C_{e}\): time \(t\) adsorbent concentration \\ \hline \multicolumn{4}{c}{**Adsorption isotherm studies**} \\ \hline (4) & \(q_{e}=\frac{Q_{m}K_{e}C_{e}}{1+K_{e}C_{e}}\) & Langmuir isotherm [30] & \(Q_{m}\): monolayer adsorption capacity (mg g\({}^{-1}\)) \\ \hline (5) & \(R_{L}=\frac{1}{1+K_{e}C_{6}}\) & Separation factor of Langmuir isotherm & \(R_{L}\) factor implies whether the adsorption is when (\(R_{L}>1\)): unfavourable (\(R_{L}=1\)): linear (\(0<R_{L}<1\)): favourable and (\(R_{L}=0\)): irreversible \\ \hline (6) & \(q_{e}=K_{F}C_{e}^{\frac{1}{1+}}\) & Freundlich isotherm [31] & \(R_{F}\) is adsorption constant of Freundlich isotherm (mg/g) \\ \hline (8) & \(q_{t}=\frac{q_{t}^{2}k_{F}}{1+q_{e}k_{F}!}\) & Pseudo-second order Equation [33] & \(R_{2}\): rate constant of pseudo-second order (mol\({}^{-1}\) L\({}^{-1}\) s\({}^{-1}\)) \\ \hline \multicolumn{4}{c}{**Adsorption kinematic studies**} \\ \hline (7) & \(q_{t}=q_{e}\left(1-e^{-k_{t}t}\right)\) & Pseudo-first order Equation [32] & \(q_{t}\): time \(t\) adsorption capacity (mg L\({}^{-1}\)) \\ \hline (7) & \(q_{t}=q_{e}\left(1-e^{-k_{t}t}\right)\) & Pseudo-first order equation [32] & \(q_{t}\): equilibrium adsorption capacity (mg L\({}^{-1}\)) \\ \hline (8) & \(q_{t}=\frac{q_{t}^{2}k_{F}!}{1+q_{e}k_{F}!}\) & Pseudo-second order Equation [33] & \(R_{2}\): rate constant of pseudo-second order (mol\({}^{-1}\) L\({}^{-1}\) s\({}^{-1}\)) \\ \hline \multicolumn{4}{c}{**Adsorption thermodynamic studies**} \\ \hline (9) & \(\Delta G^{\circ}=\Delta H^{\circ}-\Delta S^{\circ}T\) & Standard Gibbs free energy & \(\Delta G^{\circ}\): standard free energy (mol\({}^{-1}\)) \\ \hline (10) & \(\Delta G^{\circ}=-RT\ln K_{\text{eq}}\) & Standard Gibbs free energy at chemical equilibrium & \(\Delta H^{\circ}\): enthalpy change (J mol\({}^{-1}\)) \\ \hline (11) & \(K_{eq}=\frac{C_{e}}{C_{e}}\) & Thermodynamic equilibrium constant & \(R\): ideal gas constant (J mol\({}^{-1}\) K\({}^{-1}\)) \\ \hline (12) & \(\ln K_{eq}=\frac{\Delta S^{\circ}}{R}-\frac{\Delta H^{\circ}}{R}\) & Variant of standard Gibbs free energy & \(C_{o}\): initial adsorbent concentration (mg L\({}^{-1}\)) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mathematical equations used in the manuscript and their significance.  
adsorption of the substrate (dye) on it. Figure 1a describes the structure of the pores which help to fasten the adsorption process, while Figure 1b shows the limited filling of pores by the dye.