## 3 Results
### Characterization of Mesoporous Silica
#### 3.1.4 Nitrogen Adsorption-Desorption Isotherms  
The adsorption isotherms for both materials are type IV according to the IUPAC, in the isotherms, an abrupt increase in adsorbed volume occurs at a relative pressure (P/P\({}_{0}\)) of approximately 0.4, indicative of nitrogen capillary condensation within the mesopore structure. The isotherms also show that the adsorption volume is higher in the case of MCM-41 due to its larger pore volume. The hysteresis loop presented by MCM-41 and MSU-2 is of type H1 according to the IUPAC classification, which is associated with porous materials consisting of regular-shaped aggregates or compacts and a narrow pore size distribution [35; 36]. This is consistent with what has been observed in the SEM and TEM images for these materials. The average BJH pore diameter for MCM-41 is 26.6 A, and the wall thickness is 26.32 A. On the other hand, for MSU-2, pore diameter of 33.6 A and wall thickness of 18.58 A was found. In the case of the functionalized materials, it can be seen that the attachment of organic ligands to the pore walls has increased the effective thickness of the walls. This does not significantly alter the pore diameter but has reduced the internal volume of the pores and surface area as can be seen in the data on their textural properties. These data on wall thickness, volume, and pore diameter demonstrate why MCM-41 has a higher number of pores per gram of material. All these physical parameters obtained from nitrogen isotherms, such as the BET surface area, average BJH pore diameter, pore volume, and wall thickness of the materials are presented in Table 2, where it is observed that the MCM-41 has a larger surface area (1101 m\({}^{2}\)/g) than the MSU-2 (852 m\({}^{2}\)/g). Figure 6 shows the pore size distribution using the BJH method in the desorption branch of the functionalized and unfunctionalized materials. It can be observed that MCM-41 presents a narrower pore distribution than MSU-2 (Figure 6a), indicative of a higher uniform mesoporosity in the structure. After functionalization (Figure 6b), a decrease in SBET, BJH pore diameter, and pore volume took place (see Table 2) in both materials. The adsorbed volume in the adsorption isotherms of the two materials decreased, and the hysteresis loops were reduced (Figure 6c,d). These changes can be attributed to the presence of sulfonic groups on the surface and pores of the materials, which partially block nitrogen molecule adsorption. Additionally, it is observed that the inflection point of the isotherm in the adsorption branch is shifted slightly toward lower relative pressures because of the earlier filling of the monolayer due to the reduction in the pore volume of the material [37]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & **BET Specific Surface** & **Pore Diameter** & **Pore Volume \({}^{\mathrm{c}}\)** & **Wall Thickness \({}^{\mathrm{d}}\)** & **L\({}_{\mathrm{0}}\)\({}^{\mathrm{e}}\)** \\  & **Area \({}^{\mathrm{a}}\) (m\({}^{2}\)/g)** & **BJH \({}^{\mathrm{b}}\) (Å)** & **(cm\({}^{3}\)/g)** & **(Å)** & **(mmol SO\({}_{3}\)H/g)** \\ \hline MCM-41 & 1101 & 26.6 & 1.03 & 26.32 & - \\ MCM-41- & 870 & 25.3 & 0.69 & - & 1.12 \\ SO\({}_{3}\)H & 852 & 33.6 & 0.78 & 18.58 & - \\ MSU-2-SO\({}_{3}\)H & 648 & 25.6 & 0.52 & - & 1.08 \\ \hline \hline \end{tabular}  
* BET: Specific surface area calculated by the Brunauer–Emmett–Teller method. \({}^{\mathrm{b}}\) BJH: Pore size distribution obtained using the Barret–Joyner–Halenda model on the desorption branch. \({}^{\mathrm{c}}\) Pore volume: Total pore volume measured at relative P/P\({}^{0}\) = 0.97. \({}^{\mathrm{d}}\) Wall thickness for MCM-41 = a\({}_{0}\)—pore size, where \(e_{0}=\frac{2}{\sqrt{3}}\cdot d_{100}\) and Wall thickness for MSU-2 = d\({}_{100}\)—BJH pore diameter. \({}^{\mathrm{e}}\) L\({}_{\mathrm{0}}\): Degree of functionalization estimated through the sulfur percentage determined by elemental analysis.  
\end{table}