## 3 Results and Discussion
### Solvent Absorptivity of AEMs in Electrolyte Solutions  
In general, the solvent absorption of AEMs calculated from Equation (1) is feasible at low concentrations, as the mass of the solution is nearly equal to that of the solvent in dilute solutions. However, as the concentration of the absorption solution increases, this assumption becomes less valid. Therefore, the water uptake is appropriately expressed by the following equation, which quantifies the swelling of the polymer:  
\[W\,\%_{0}=\frac{m_{\text{wet}}-m_{\text{dry}}-m_{\text{mob}}}{m_{\text{dry} }-m_{\text{b}}} \tag{5}\]  
where the \(m_{\text{mob}}\) is the mass of the solute in the absorption solution.  
Based on this, the solvent absorption of three types of AEMs (ACLP-2%, ACLP-3%, and ACLP-4%) in NaCl and NaBr solutions was obtained. The experimental results are presented as a function of the molality of the external solution and the water uptake of the ion-exchange polymer (solvent absorptivity), as shown in Figure 3.  
As observed in the trend shown in Figure 3, the deswelling effect of cross-linked polyelectrolytes in the electrolyte solution is evident in the ACLP materials used in this experiment [46]. With increasing concentration of the external electrolyte solution, the degree of swelling of the ion-exchange polymer in ACLP exhibited a downward trend. This trend was significant at concentrations above 0.3 mol\(\cdot\)kg\({}^{-1}\), while it was less pronounced at concentrations below 0.1 mol\(\cdot\)kg\({}^{-1}\), which can be attributed to the swelling force of the polymer being partially supported by the PP fibers.  
In addition, the water absorption of the three AEMs in NaBr solution was consistently lower than that in NaCl solution, which may be due to the different hydration numbers between them, which will be further explored in future studies. However, the difference gradually decreased as the degree of cross-linking increased. For ACLP-2%, the difference in water uptake between the two electrolytes was approximately 25%; for ACLP-3%, it was about 18%; and for ACLP-4%, the difference was less than 5%. These results indicate that the swelling degree of the polymer in AEM decreases progressively with increasing  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**AEM**} & **Thickness** & **IEC** & & \multirow{2}{*}{\(\mathbf{m}_{\text{A}}^{\text{m}}\)} & \\  & **[mm]** & **[mmol\(\cdot\)g\({}^{-1}\)]** & & & **[mol\(\cdot\)kg\({}^{-1}\)]** & \\ \hline ACLP-2\% & 0.35–0.40 & 1.4–1.8 & 51–58\% & 3.2 & 2.41 \\ ACLP-3\% & 0.32–0.35 & 1.2–1.5 & 30–36\% & 4.8 & 3.00 \\ ACLP-4\% & 0.28–0.30 & 0.9–1.2 & 15–20\% & 5.4 & 3.27 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The properties of the membranes (Cl combined) prepared in this experiment are presented as follows: \(m_{\text{A}}^{\text{m}}\) represents the mean value of the fixed group concentration relative to the water uptake (\(W\%\)); \(\xi\) is the linear charge density, with specific calculations provided later. The reported values for the ion-exchange capacity (IEC) and \(W\%\) in this table are ranges derived from sixteen separate measurements.  
cross-linking, which also reduces the disparity in swelling behavior of AEM in different electrolyte solutions [47; 48; 49].