## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Membranes**} & **Thickness** & **Contact Angle** & **WC(\%)** & **IEC** & \(\sigma^{1}\)** & **EAR**2 & \(t_{\cdot}\)3 & \(t_{\cdot}\)4 & **WL**5 \\  & **(\(\mu\)m)** & **(Degree)** & **WU (\%)** & **(meq,/g)** & **(S/cm)** & **(\(\Omega\) cm\({}^{2}\))** & **(\(c_{\cdot}\))** & **(\(c_{\cdot}\))** & **(\(c_{\cdot}\))** \\ \hline AMX (Aatom Corp.) & 135 & 44.8 & 21.1 & 1.40 & 0.015 & 0.93 & 0.975 & 0.853 & 10.2 \\ Hydrophobic-PFAEM & 82 & 93.2 & 13.2 & 1.46 & 0.010 & 0.84 & 0.984 & 0.926 & 0.32 \\ Hydrophilic-PFAEM & 40 & 70.7 & 21.1 & 1.42 & 0.019 & 0.21 & 0.990 & 0.954 & 0.45 \\ \hline \hline \end{tabular}  
* Membrane conductivity obtained by 2-point probe impedance measurement (in a 1.0 M KOH aqueous solution at 25 \({}^{\circ}\)C). 2 Membrane electrical resistance measured using a clip cell and an impedance analyzer (in a 1.0 M KOH aqueous solution at 25 \({}^{\circ}\)C). 3 Transport number for anion (Cl\({}^{-}\)) determined by emf method (in 0.001/0.005 M NaCl aqueous solutions) (initially measured). 4 Transport number for anion (Cl\({}^{-}\)) determined by emf method (in 0.001/ 0.005 M NaCl aqueous solutions) (measured after 500 h in the alkaline stability test). 5 Weight loss (%) after the soaking test using the [PERSON]’s reagent at 80 \({}^{\circ}\)C for 1 h.  
\end{table} 
Table 2: Various characteristics of commercial and prepared membranes. hydrophobic-PFAEM. It is believed that the more hydrophilic nature of the membrane increases the diffusion rate of the hydrophilic molecules. This means that the energy conversion efficiency of the hydrophilic-PFAEM is expected to be poorer than that of the hydrophobic-PFAEM, in terms of the fuel crossover rate. Therefore, it could be concluded that the dramatic improvement of the power density by employing the hydrophilic-PFAEM mainly resulted from the facilitated hydroxyl ion transport through the membrane. Figure 5: Time course changes in weight loss during the Fenton oxidation tests of anion-exchange membranes (AEMs). Figure 6: Power generation performances of the MEAs employing different PFAEMs (open symbols = cell potential; closed symbols = power density). \begin{table}
\begin{tabular}{c c} \hline \hline
**Membranes** & **Diffusion Coefficient (\(\times\)10\({}^{9}\), cm\({}^{2}\) s\({}^{-1}\))** \\ \hline Hydrophobic-PFAEM & 5.75 \\ Hydrophilic- PFAEM & 6.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Diffusion coefficients of hydrazine (N\({}_{2}\)H\({}_{4}\)) through the PFAEMs prepared by using different porous PTFE substrates. VRFB experiments were also performed to investigate the influence of the membranes on the battery characteristics, as shown in Figure 7. The charge--discharge performances were revealed to be largely affected by the membrane properties, and the efficiencies are summarized in Table 4. The hydrophobic-PFAEM showed the highest value of coulombic efficiency (CE) among the membranes tested, indicating that the crossover of redox species through the membrane was effectively suppressed owing to its high cross-linking degree and hydrophobic nature. The crossover rate of vanadyl ions (VO\({}^{2+}\)) through the membranes could be estimated from a two-compartment diffusion cell experiment, by recording the time-course change of VO\({}^{2+}\) concentration (Figure 8). The overall dialysis coefficient (\(K_{A}\)) values calculated from Equation (7) are also summarized in Table 4. The hydrophobic-PFAEM showed almost similar \(K_{A}\) values, despite its considerably reduced thickness compared to that of the commercial AMX membrane. However, the hydrophilic-PFAEM revealed a \(K_{A}\) value increased by about three times, owing to its hydrophilic nature and much-reduced thickness compared to the hydrophobic-PFAEM. As a result, it can be seen that the lowest CE value of the hydrophilic-PFAEM among the membranes compared, is due to the high crossover rate of the vanadium redox species.