## 3 Results
### The Influence of Different Nafion Membrane Specifications on VRFB Performance  
In a VRFB, the cathode and anode are divided by a membrane. In order to finish the redox reaction, it also makes ion movement easier [57]. The production of protons in a vanadium redox flow battery occurs technically through two processes: the dissociation of sulfuric acid, the electrolyte's supporting medium, and the reaction of water with VOSO4 to form protons. To balance the charge on both sides for the charging and discharging processes, the generated protons then move through a membrane. Proton imbalances on both sides can lead to the generation of the vanadium cross-over. The driving forces of diffusion, migration, osmotic force, and electroosmotic convection can produce the vanadium cross-over [58]. The losses in open circuit voltage and voltage efficiency are caused by the vanadium cross-over [59; 60]. A membrane's primary property requirements are good ion conductivity, high chemical resistance, a wide temperature range for application, high mechanical properties for supporting pressure generated by pumps, and good ion selectivity to protect against crossover, a problem that reduces capacity and energy. Proton mobility through the membrane to balance charges on both sides for the charging and discharging processes is required to finish the electrochemical reactions. Therefore, to provide strong corrosion resistance, low vanadium crossover, and high proton conductivity, a membrane must be used. A cation exchange membrane, such as Nafion, has been used for VRFBs. Nafion is a sulfonated perfluorinated polymer with a copolymer molecule structure that consists of two major parts: a hydrophobic backbone (fluorocarbon), and a hydrophilic domain (sulfonate group). During the electrochemical reaction, \(\mathrm{SO_{3}}^{-}\) groups interact with water molecules by electrostatic forces in the membrane to form hydronium ions with hydrogen bonding ((\(\mathrm{(H_{3}O)^{+}}\)) (\(\mathrm{SO_{3}H+H_{2}O\to SO_{3}^{-}(H_{3}O)^{+}}\)). Thus, the number of sulfonate groups should influence the redox reaction capability. Theoretically, three mechanisms, namely, the surface mechanism, the vehicle mechanism, and the Grothus mechanism, have been used to describe the proton conduction through a sulfonated membrane. Protons react with water molecules to generate hydronium ions in the case of the surface process, and they repeatedly hop on sulfonate groups on ionomer surfaces. The hydronium ions can move freely on the sulfonate group structure because the intermolecular force between sulfonate groups and hydronium ions is smaller than the molecular force between protons and sulfonate groups. In terms of the driving mechanism, protons interact with several water molecules to produce the hydronium ion. The hydronium ions migrate to balance charges through hydration and osmosis processes because the charge on both sides is unbalanced [61]. This transport process is directly influenced by the thickness of a membrane. A thick membrane has a low driving force and a high proton mobility resistance. According to the Grothus mechanism, protons interact with water molecules to generate hydronium ions, which are then transported by hopping along the water molecules absorbed in the chemical structure of the membrane. It is worth noting that these three mechanisms were proceeded simultaneously. According to the aforementioned transport mechanism, this part of the work addressed selecting a commercial Nafion membrane for use in the VRFB, and the selection criterion was related to membrane thickness and the number of sulfonate groups. Regarding the thickness issue, Nafion 112, Nafion 1135, Nafion 115, and Nafion 117 are commercial Nafion membranes that were considered for the first selection because they contain the same number of sulfonate groups while their thicknesses are different. Nafion 112, Nafion 1135, Nafion 115, and Nafion 117 have thicknesses as follows: 50, 88, 125, and 175 \(\mathrm{\SIUnitSymbolMicro m}\), respectively.