## 3 Results and Discussion
The vanadium ion permeability values of the commercial membranes and the prepared PFIEMs are listed in Table 5. As a result, it was confirmed that the permeability of vanadium ions increased as the ratio of VBC and Sty in the prepared PFIEMs increased. That is, the permeability of the vanadium active material is elevated because the water uptake and the free volume increase by increasing the IEC in the membranes. However, despite the thin film thickness compared with the commercial membranes, the vanadium ion permeability in the PFIEMs was shown to be relatively low due to the low water uptake (wettability) and surface hydrophilicity. As a result, the vanadium ion permeability was lowest when the ratio of fluorine moieties was highest in both the PFAEMs and PFCEMs. In addition, when comparing both types of IEMs, it can be seen that the vanadium ion permeability in the PFAEMs is relatively low compared with that of the PFCEMs. This result demonstrates that in the case of the PFAEMs, the crossover of cations (i.e., vanadium ions) can be effectively reduced by means of the Donnan exclusion. The VRFB performance evaluation results with various IEMs are summarized in Figure 11 and Table 6. The results show a tendency to increase the VE by increasing the VBC or Sty molar ratio of the membrane owing to the reduced electrical resistance [52]. As a result, PFAEM-1 and PFCEM-1 having the highest fluorine content exhibited the lowest VE among the membranes tested, but did not show a significant difference from other membranes. On the other hand, the CE was shown to increase by elevating the fluorine content in the membrane, and therefore, PFAEM-1 and PFCEM-1 showed the highest values. The capacity loss of the VRFB showed a tendency to increase as the number of cycles increased, and it is known that this capacity loss originates from the crossover of the active materials through the IEMs and the irreversibility of the oxidation-reduction reactions [53]. In conclusion, PFAEM-1 and PFCEM-1, which have the most fluorine content, showed the highest EE values, and it was confirmed that they had better charge-discharge performance than the commercial membranes. Although it may seem that the difference among the membranes is not large in the results of such a single cell, it is expected that the significant performance difference will occur in a practical system with a large membrane area. Although it is difficult to make an accurate comparison due to the different experimental conditions, the energy efficiency of the fluorine-containing PFIEMs developed in this study was shown to be superior to those of the investigated commercial membranes listed in Table 7. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Membrane** & **CE (\%)** & **VE (\%)** & **EE (\%)** \\ \hline AMX & 92.6 & 93.2 & 86.2 \\ PFAEM-0 & 95.0 & 94.6 & 89.9 \\ PFAEM-1 & 96.4 & 93.2 & 89.9 \\ PFAEM-2 & 94.7 & 93.4 & 88.4 \\ PFAEM-3 & 93.3 & 94.4 & 88.0 \\ \hline CMX & 90.9 & 91.3 & 83.0 \\ PFCEM-0 & 94.3 & 92.1 & 86.8 \\ PFCEM-1 & 94.8 & 92.3 & 87.6 \\ PFCEM-2 & 93.5 & 92.5 & 86.5 \\ PFCEM-3 & 92.4 & 93.5 & 86.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Battery efficiencies of commercial membranes and PFIEMs. Figure 11: The charge–discharge curves in VRFB systems employing different IEMs ((**a**) PFAEM-0, (**b**) PFAEM-1, (**c**) PFAEM-2, (**d**) PFAEM-3, (**e**) PFCEM-0, (**f**) PFCEM-1, (**g**) PFCEM-2, and (**h**) PFCEM-3, respectively). The characteristics of PFAEM-1 and PFCEM-1, which showed the best VRFB performance, are compared with each other as a spider chart in Figure 12. It can be seen that PFAEM-1 shows better performance than PFCEM-1 in all evaluation criteria. In summary, the PFAEM was not disadvantageous in terms of electrical resistance compared with traditional CEMs when applied to the VRFB due to its thin film thickness.