## 3 Results
### Membrane Characterization  
The H-NMR spectra of sPEEK sulfonated at 60 \({}^{\circ}\)C for 24 h is shown in Figure 4a. The same peaks, corresponding to the aromatic hydrogen peaks as in the work of [PERSON] et al. [31], were observed, i.e., at 7.88-7.7 ppm (A, A\({}^{\prime}\)), 7.56-7.5 ppm (E) and 7.31-6.92 ppm (C, D, B, B\({}^{\prime}\)). The hydrogen E peak corresponds to the hydrogen of the -SO\({}_{3}\)H group. After sulfonation at 60 \({}^{\circ}\)C for 24 h, a sulfonation degree of 65% was reached. FTIR analysis was used to obtain a qualitative confirmation of the sulfonation of PEEK in the crosslinked membranes. Figure 4b shows the FTIR spectra of sPEEK and the four crosslinked sPEEK membranes. Peaks originating from the PEEK backbone are present in the fingerprint region of the spectra. The peak at 1648 cm\({}^{-1}\) belongs to the C=O group in the backbone, whilst the peaks at 1595 cm\({}^{-1}\) and 1415 cm\({}^{-1}\) correspond to skeletal ring vibrations. The peak at 1307 cm\({}^{-1}\) shows the bending motion of the C-C(=O)-C group, while the peak at 1185 cm\({}^{-1}\) is due to asymmetric stretching of the diphenyl ether group. The peaks at 1217 cm\({}^{-1}\) and 1159 cm\({}^{-1}\) show the aromatic hydrogens in plane deformation, and the peak at 928 cm\({}^{-1}\) refers to the aromatic hydrogens out of plane bending mode. The presence of the sulfonic acid groups is confirmed due to the presence of the peaks at 1080 and 1030 cm\({}^{-1}\), which correspond to the symmetric stretching of O=S=O and the stretching vibrations of S=O, respectively. The split peaks in the range between 860 and 840 cm\({}^{-1}\) are due to the isolated hydrogen in a 1,2,4-trisubstituted ring [40]. In addition, the peaks at 1179 and 1405 cm\({}^{-1}\) correspond to the S=O bond [41; 42; 43]. Furthermore, the intensity of the peak around 1480 cm\({}^{-1}\) is more enhanced for the membranes sPEEK/DCX-CX190\({}^{\circ}\)C and sPEEK/DCX-CX24h. Since this peak is located at the edge of the fingerprint region, it might correspond to the C-H bond of a methylene group. A methylene group would only be present in this membrane structure when the crosslinking reaction has occurred (see Figure 3). This would indicate that those two membrane types have an enhanced crosslinking. However, the quantitative determination of the crosslinking degree via the FTIR analysis remains complex, and the main focus of the FTIR analysis is the qualitative confirmation of the presence of sulfonic acid groups. The surface and cross-section SEM images of the considered membranes in this work are shown in Figures 5 and 6, respectively. Based on both figures, it can be stated that the membrane surfaces are smooth without defects, holes, or pores. However, the membranes  
Figure 4: (a) NMR images of sPEEK; (b) FTIR images of the membranes synthesized in this work. became brittle due to the dry conditions during the SEM sample preparation and analysis. The brittleness made the membranes very sensitive to cracks during the handling. Those cracks can be seen in the cross-section image and show the importance of handling the membranes in wet conditions. Furthermore, the intensity of the peak around 1480 cm\({}^{-1}\) is more enhanced for the membranes sPEEK/DCX-CX190\({}^{\circ}\)C and sPEEK/DCX-CX24h. Since this peak is located at the edge of the fingerprint region, it might correspond to the C-H bond of a methylene group. A methylene group would only be present in this membrane structure when the crosslinking reaction has occurred (see Figure 3). This would indicate that those two membrane types have an enhanced crosslinking. However, the quantitative determination of the crosslinking degree via the FTIR analysis remains complex, the main focus of the analysis is the qualitative confirmation of the presence of sulfonic acid groups. Photoelectron spectroscopy (XPS) analysis was performed on the synthesized membranes to investigate the surface elemental composition before and after crosslinking with DCX.