# Removal of Metal Ions in Spin-on Hardmask Using Functionalized Porous Silica Adsorbents
## 3 Result and Discussion
### Adsorption Isotherm  
To better understand the ion adsorption mechanism involved, adsorption isotherms for ions were obtained by plotting the equilibrium concentration (C\({}_{e}\), mmol L\({}^{-1}\)) versus  
Figure 6: Adsorption of metal ions by (**a**) amine-functionalized MCM-41 and (**b**) amine-functionalized SBA-15 under monomer-containing conditions. Figure 7: Adsorption of metal ions by (**a**) amine-functionalized MCM-41 and (**b**) amine-functionalized SBA-15 under polymer-containing conditions. the amount of metal ion removed at equilibrium state (qe, mmol g\({}^{-1}\)), as shown in Figure 8. The amount of removed metal ion was calculated using the following equation:  
\[q_{e}=\frac{C_{i}-C_{e}}{C_{m}}\times V \tag{2}\]  
where \(C_{i}\) and \(C_{e}\) represent the initial and equilibrium concentration, measured before and after the adsorption process, respectively, and expressed in mmol L\({}^{-1}\). \(V\) is the volume of the solution (L); and \(m\) is the mass of the adsorbent (g). The obtained adsorption isotherms were fitted to three common models: Langmuir, Freundlich, and Dubinin-Radushkevich (D-R) models. The Langmuir adsorption isotherm model, which assumes monolayer adsorption onto a homogeneous surface, is expressed as [32,33]:  
\[q_{e}=\frac{(q_{m}b)}{1+\ bC_{m}}\ C_{e} \tag{3}\]  
\[\frac{C_{e}}{q_{e}}=\frac{1}{q_{e}b}+\frac{1}{q_{m}}\ C_{e} \tag{4}\]  
where \(q_{m}\) represents the maximum adsorption capacity (mmol g\({}^{-1}\)), and \(b\) is the Langmuir constant, a parameter associated with the adsorption energy. The maximum adsorption capacities (\(q_{m}\)) for Al\({}^{3+}\), Cu\({}^{2+}\), Fe\({}^{3+}\), and Ni\({}^{2+}\) were found to be 0.6206, 0.8672, 0.5179, and 0.3653 mmol g\({}^{-1}\), respectively, indicating the order of Cu\({}^{2+}\) Al\({}^{3+}\)\(>\) Fe\({}^{3+}\)\(>\) Ni\({}^{2+}\) as shown in Table 2. Furthermore, the negative values of Gibbs free energy (\(\Delta\)G) for all metal ions  
Figure 8: Adsorption isotherms of (**a**) Al\({}^{3+}\), (**b**) Cu\({}^{2+}\), (**c**) Fe\({}^{3+}\), and (**d**) Ni\({}^{2+}\) on amine-functionalized MCM-41, fitted with Langmuir, Freundlich, and Dubinin–Radushkevich isotherm models. Experimental data are shown as points, and the fitted curves are represented by dashed lines. indicate that the adsorption processes onto amine-functionalized MCM-41 are spontaneous in nature. The Freundlich isotherm, which assumes multilayer adsorption on heterogeneous surfaces, is given as [32]:  
\[log(q_{e})=logK_{F}+\frac{1}{n}log(C_{e}) \tag{5}\]  
where \(K_{F}\) is the adsorption capacity, and \(n\) is indicating adsorption intensity or surface heterogeneity. The Dubinin-Radushkevich Isotherm (D-R) is expressed as follows [32]. \[lnq_{e}=lnq_{m}-\beta\epsilon^{2} \tag{6}\]  
Figure 7:0  
Figure 7:1  
where \(\epsilon\) is Polanyi potential, \(\beta\) is Dubinin-Radushkevich constant, \(R\) is gas constant (8.31 J mol\({}^{-1}\cdot\)k\({}^{-1}\)), \(T\) is absolute temperature, and \(E\) is mean adsorption energy. The experimental isotherm data for four metal ions (Al\({}^{3+}\), Cu\({}^{2+}\), Fe\({}^{3+}\), and Ni\({}^{2+}\)) were obtained and fitted to the previously described isotherm models. Among these, the Langmuir isotherm consistently provided the best fit across all ions, indicating that the adsorption process was characterized by monolayer adsorption on the surface of the adsorbent with uniform energy distribution. This agreement with the Langmuir model suggests that the adsorption mechanism was primarily governed by chemical interactions between the metal ions and the surface of the functionalized mesoporous silica, rather than a physical one. In particular, the nature of the surface functional groups appears to play a decisive role in determining the overall adsorption efficiency. These results underscore the importance of functional group selection and surface chemistry in designing mesoporous adsorbents for effective metal ion removal in complex chemical environments [30; 33; 34; 35; 36].