## 1 Introduction  
In the last decades, climate change has become one of the major challenges of the modern world. Rising sea levels, droughts, increases in greenhouse gas emissions, and scarcity of resources confront the current generations with grave and pressing challenges. For those reasons, a new technological revolution towards clean and sustainable transport, energy sources, and industries is taking place [1]. The development of direct methanol fuel cells (DMFCs) and artificial photosynthesis is part of that technological revolution. The purpose of DMFCs is to generate energy using methanol as fuel, and artificial photosynthesis is used to generate fuel from energy with the aid of sunlight. Both technologies make use of an electrochemical cell, commonly equipped with a proton exchange membrane (PEM). Within a DMFC, methanol is oxidized in the anode compartment, which generates electrons and protons. The electrons carrying the free energy travel via an external circuit towards the cathode, which generates a potential difference. To maintain the charge balance, the protons also need to be transported to the cathode compartment through a semi-permeable membrane, i.e., a PEM [2, 3]. On the other hand, within artificial photosynthesis, CO\({}_{2}\) is reduced in the cathode compartment under the influence of an external potential difference and sunlight. Possible reaction products are methanol, ethanol, and ethylene. Similarly to DMFCs, the charge balance is maintained by transporting protons from the anode to the cathode compartment using a PEM [4; 5]. PEMs are dense, semi-permeable membranes commonly fabricated from polymers containing fixed, negatively charged groups that give preference to proton transport while rejecting other compounds. Nowadays, perfluorinated PEMs, such as the commercial Nafion membranes, are the most commonly employed PEMs for DMFC and artificial photosynthesis [2; 4; 5; 6]. They show high proton conductivities due to their phase-separated morphology, i.e., a hydrophobic backbone combined with hydrophilic side chains, and their high ion exchange capacity (IEC) [2; 5; 7; 8]. Furthermore, these membranes have high thermal and chemical stability. However, Nafion has certain limitations, making it unsuitable for a broader application range. The main drawbacks are its high methanol permeability [6; 9; 10] and high production cost [9; 10; 11; 12]. In addition, it contributes to global PFAS pollution, endangering human health and the environment [13; 14; 15; 16]. Extensive research has been undertaken on alternative polymers to replace the perfluorinated membranes. Polyether ether ketone (PEEK) is a low-cost polymer, showing good film-forming properties and easy sulfonation [17; 18; 19; 20; 21; 22; 23]. Generally, sulfonic acid groups are used as the functional groups in PEMs. The combination of these polar groups and the hydrophobic aromatic backbone provides the membrane with a phase-separated structure [24]. Recently, many efforts have been devoted to preparing the membranes with dense structures to minimize the solvent absorption rates and swelling degrees [25]. Crosslinking the polymer leads to a dense, tortuous 3D network with steric effects, which leads to decreased swelling. Additionally, a crosslinked membrane structure shows increased cation/anion permeation, lowers the hydrogen and methanol crossover, and enhances the thermal and mechanical stability [26; 27]. Various studies on employing sulfonated PEEK (sPEEK) as the polymer backbone have already been performed [17; 18; 19; 20; 21; 22; 23]. For example, [PERSON] et al. [21] synthesized self-crosslinked sPEEK membranes with sulfonic acid groups on the aliphatic side chains. They used concentrated sulfuric acid to perform the sulfonation, after which the sPEEK was reduced with borohydride. The pending sulfoalkoxy groups were added by using 1,3-propane sulfone. Their results showed an even higher proton conductivity than Nafion 212.