## 2 Methods
### Structural Analysis  
To select SG of different grain sizes for water vapor sorption studies, structural studies were performed first. LPA studies aimed to indicate materials for further research with the most favorable pore space parameters. The equilibrium points of N2 adsorption on the tested silica gels had the shape of type I isotherms (Figure 6a,b). In the case of SG2, the hysteresis loop was obtained [58]. The total adsorption capacity at \(p/p_{0}=1\) for SG1 samples was in the range of 8.1-11.1 mmol/g (Figure 6a), while for SG2 in the range of 10.3-12.1 mmol/g (Figure 6b). The tests showed that the grain size of the SG used affects their sorption capacity in relation to gases. The highest sorption capacity was obtained for silica gel with a granulation of 100-160 \(\upmu\)m (SG1a and SG2a) and these samples were selected for further tests on water vapor sorption. The N2 adsorption isotherms on CNT had the shape of type III and a small area of hysteresis loops were obtained (Figure 6c). Total sorption capacity for CNT (\(p/p_{0}=1\)) was 24.4 mmol/g.  
Based on the sorption LPA equilibrium points, structural parameters have been determined (Table 2). Due to different isothermal shapes for SGs and CNT, different models were used to describe the values of their structural parameters. The selected silica gels had a type I isotherm shape--typical for the Langmuir model [58], and the monolayer specific surface area (\(SSA_{L}\)) was in the range of 1127-1334 m\({}^{2}\)/g. Total pore volume (\(V_{t}\)) was 0.38-0.44 cm\({}^{3}\)/g, while volume in micropores with diameters smaller than 1 nm was 0.15 cm\({}^{3}\)/g. In the CNT, where the shape of the isotherm was type III, which is best fitted by the BET model, the specific surface area of \(SSA_{BET}\) was 186.6 m\({}^{2}\)/g. The total pore volume was 0.24 cm\({}^{3}\)/g, of which the micropore volume was negligibly low.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Unit** & **SG1** & **SG2** & **CNT** \\ \hline BET Surface Area (\(SSA_{BET}\)) & m\({}^{2}\)/g & 713.3 \(\pm\) 10.9 & 706.8 \(\pm\) 9.2 & 186.6 \(\pm\) 0.9 \\ Langmuir Surface Area (\(SSA_{L}\)) & m\({}^{2}\)/g & 1126.7 \(\pm\) 8.8 & 1334.4 \(\pm\) 31.3 & 429.9 \(\pm\) 24.5 \\ Volume in Pores (\(V\)) & cm\({}^{3}\)/g & 0.151 \({}^{*}\) & 0.146 \({}^{*}\) & 0.022 \({}^{**}\) \\ Total Volume in Pores (\(V_{t}\)) & cm\({}^{3}\)/g & 0.380 \({}^{*}\) & 0.441 \({}^{*}\) & 0.237 \({}^{**}\) \\ Area in Pores (\(SSA_{NLDFT}\)) & m\({}^{2}\)/g & 0.3 \({}^{*}\) & 4.4 \({}^{*}\) & 0 \({}^{**}\) \\ Total Area in Pores & m\({}^{2}\)/g & 435.2 \({}^{*}\) & 467.3 \({}^{*}\) & 99.4 \({}^{**}\) \\ (\(SSA_{t}\)\(NLDFT\)) & & & & \\ Standard Deviation of Fit & & & & \\ (\(NLDFT\)) & cm\({}^{3}\)/g STP & 0.80 & 1.08 & 1.05 \\ Characteristic Energy & kJ/mol & 14.9 & 12.7 & 20.6 \\ \hline \hline \end{tabular} Where: results marked with \({}^{*}\): volume in pores \(<\) 1.0 nm; total volume in pores \(\leq\) 23.7 nm; area in pores \(>\) 23.7 nm; total area in pores \(\geq\) 1.0 nm; results marked with \({}^{**}\): volume in pores \(<\) 2.5 nm; total volume in pores \(\leq\) 18.1 nm; area in pores \(>\)18.1 nm; total area in pores \(\geq\) 2.5 nm.  
\end{table}
Table 2: Structural parameters of SGs and CNT.  
Figure 6: Nitrogen adsorption/desorption isotherms in 77 K of (**a**) SG1, (**b**) SG2, (**c**) CNT.  
The NLDFT model was used to determine the pore size distribution for the tested materials. The pore size distributions in both silica gels (Figure 7a) had similar shapes. The presence of pores with diameters of single nanometers was found (Figure 7b). The first peak shows the presence of increased pore volume with a diameter of 1-1.5 nm and had a higher value for SG1. The second volume increase was observed for pores with diameters from 2 nm to 6 nm in SG1 and from 2 nm to 10 nm in SG2. In CNT (Figure 7b), peaks of increased volume were observed in the pore range with diameters of 3-4 nm and above 5 nm.