# Effect of Pore Size Distribution and Amination on Adsorption Capacities of Polymeric Adsorbents
## 3 Results and Discussion
### Static Adsorption Equilibrium  
We used a three-parameter multilayer adsorption model to describe the adsorption data [24]. The equation was as follows:  
\[Q_{e}=\frac{Q_{m}K_{1}C_{e}}{(1-K_{2}C_{e})[1+(K_{1}-K_{2})C_{e}]} \tag{2}\]  
Figure 5: Adsorption kinetic curves of the three adsorbates. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Pseudo-First-Order Rate Equation**} & \multicolumn{3}{c}{**Pseudo-Second-Order Rate Equation**} \\ \cline{2-7}  & \(\mathbf{Q_{e}}\) & \(\mathbf{K_{1}}\) & \(\mathbf{R^{2}}\) & \(\mathbf{Q_{e}}\) & \(\mathbf{K_{2}}\) & \(\mathbf{R^{2}}\) \\  & (\(\mathbf{L}\)-mmol\({}^{-1}\)) & (\(\mathbf{L}\)-mmol\({}^{-1}\)) & (\(\mathbf{L}\)-mmol\({}^{-1}\)) & (\(\mathbf{L}\)-mmol\({}^{-1}\)) & \(\mathbf{R^{2}}\) \\ \hline NDA-2 phenol & 0.583 & 0.102 & 0.963 & 0.611 & 0.284 & 0.969 \\ NDA-3 phenol & 0.459 & 0.069 & 0.949 & 0.489 & 0.213 & 0.963 \\ NDA-2 ABS acid & 0.364 & 0.005 & 0.974 & 0.477 & 0.011 & 0.980 \\ NDA-3 ABS acid & 0.350 & 0.004 & 0.939 & 0.467 & 0.008 & 0.951 \\ NDA-2 RBB4 & 0.267 & 0.002 & 0.957 & 0.384 & 0.003 & 0.958 \\ NDA-3 RBB4 & 0.189 & 0.002 & 0.972 & 0.260 & 0.006 & 0.976 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The corresponding parameters of the adsorption kinetic curves. where \(C_{e}\) (mmol\(\cdot\)L\({}^{-1}\)) is the equilibrium concentration of adsorbate, \(Q_{e}\) (mmol\(\cdot\)g\({}^{-1}\)) is the adsorption capacity of resin, \(Q_{m}\) (mmol\(\cdot\)g\({}^{-1}\)) is the maximum first-layer adsorption capacity of resin, \(K_{1}\) (L-mmol\({}^{-1}\)) is the first-layer adsorption equilibrium constant, and \(K_{2}\) (L-mmol\({}^{-1}\)) is the multilayer adsorption equilibrium constant. The three-parameter multilayer adsorption model can be used to describe almost all S-type adsorption isotherms, including the BET isotherm and the Freundlich isotherm, which are typical for gas adsorption and organic matter adsorption. The equilibrium adsorption isotherms are shown in Figure 6, and Table 4 summarizes the corresponding parameters. The adsorption isotherms of phenol were approximately straight lines in the concentration range of our study and could not be simulated by this model. Figure 6a shows the adsorption isotherms of phenol on the four resins. The order of adsorption capacity was NDA-2 > NDA-1 > NDA-3 > NDA-4. The NDA-2 resin had the highest adsorption capacity because it had the largest specific surface area. Although NDA-1, NDA-3 and NDA-4 had similar specific surface areas, the pore diameter distribution of NDA-1 was mainly concentrated in the small mesopore region. This resin is suitable for the adsorption of micromolecules such as phenol. However, the opposite was true for NDA-4, which had lowest adsorption capacity for phenol. Figure 6b shows the adsorption isotherm of ABS acid on the four resins. The order of adsorption capacity was NDA-2 > NDA-3 > NDA-4 > NDA-1. Different from phenol, the adsorption capacity of NDA-1 for ABS acid was much lower than that of the other three resins. This was because the adsorption of ABS acid to NDA-1 was affected by pore hindrance, making part of the pore volume unusable. One reason for this phenomenon is that the pore size of NDA-1 was smaller than that of the adsorbate molecule; thus, the molecule cannot be adsorbed within the resin pores. Second, in the process of diffusion from the surface to the inner channels of the resin, the adsorbate molecules are partly adsorbed onto the pore walls. This can cause the channels become blocked, preventing the adsorbate from passing through the channels. As can be seen from the pore diameter distribution diagram, the pore diameter of NDA-1 was mainly distributed around approximately 3 nm, this is 2-3 times larger than the diameter of ABS acid. Therefore, the adsorption of this molecule caused pore obstruction. Figure 6c shows the adsorption isotherm of RBB4 on the four resins. The order of adsorption capacity was NDA-3 > NDA-4 > NDA-2 > NDA-1.