## 2 Materials and Methods
### Membrane Characterizations  
The membrane electrical resistance (MER) of IEMs is related to the internal resistance of the VRFB system and is a factor that dominantly determines the voltage efficiency (VE). To measure the MER, the membrane sample was first immersed in 0.5 M NaCl solution for at least 5 h to reach its equilibrium state. First, the blank resistance (\(R_{2}\)) of the 0.5 M NaCl solution was determined using a lab-made clip cell connected to a potentiostat/galvmostat with electrochemical impedance spectroscopy (SP-150, Bio-Logic Science Instruments, France). The membrane sample was then inserted into the clip cell and immersed in 0.5 M NaCl solution to measure the membrane + solution resistance (\(R_{1}\)). Finally, the membrane electrical resistance was calculated by substituting the measured \(R_{1}\) and \(R_{2}\) values into the following Equation (1) [30]:  
\[\text{MER}=(R_{1}-R_{2})\times A\ \Big{[}\Omega\cdot\text{cm}^{2}\Big{]} \tag{1}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Property** \\ \hline Structure & Single layer \\ Composition & Polyethylene \\ Thickness (\(\upmu\)m) & 25 \\ Gurley (s) & 21 \\ Porosity (\%) & 40 \\ \(T_{m}\) (\({}^{\circ}\)C) & 138 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specifications of the porous PE substrate used for this study [29]. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Membrane**} & \multicolumn{2}{c}{**Monomer Mole Ratio**} & \multicolumn{2}{c}{**Weight Ratio**} \\ \cline{2-4}  & **VBC:Sty:OFPMA** & **Cross-Linker (DVB)** & **Initiator (BPO)** \\ \hline PFAEM-0 & 3:1:0 & & \\ PFAEM-1 & 2:0:1 & & \\ PFAEM-2 & 3:0:1 & & \\ PFAEM-3 & 4:0:1 & & \\ \hline PFCEM-0 & 0:1:0 & & \\ PFCEM-1 & 0:2:1 & & \\ PFCEM-2 & 0:3:1 & & 20 wt\% & 2 wt\% \\ PFCEM-3 & 0:4:1 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Composition of monomers for fabricating PFAEMs and PFCEMs. where \(A\) is the effective area of Pt electrodes constituting the clip cell. Meanwhile, the ion conductivity (\(\sigma\)) of the IEMs was obtained from the following Equation (2) [31]:  
\[\sigma=\frac{L}{\text{MER}}\left[\frac{\text{S}}{\text{cm}}\right] \tag{2}\]  
where \(L\) is the thickness of the membrane sample. To measure the water uptake (WU), a membrane sample having a size of 2 \(\times\) 2 cm\({}^{2}\) was immersed in distilled water to reach an equilibrium state. After removing the water present on the sample surface with filter paper, the wet weight (\(W_{wet}\)) was measured and then dried in a dry oven at 80 \({}^{\circ}\)C for more than 6 h to measure the dry weight (\(W_{dry}\)). The WU values were determined using the following Equation (3) [31]:  
\[WU=\frac{W_{wet}-W_{dry}}{W_{dry}}\times 100\ [\%]. \tag{3}\]  
The swelling ratio (\(SR\)) of the prepared membranes was determined with the following Equation (4) by measuring the volume of the dried membrane (\(V_{dry}\)) and the volume of the wet membrane (\(V_{wet}\), swelled with the electrolyte solution used for VRFB tests) [31]:  
\[SR=\frac{V_{wet}-V_{dry}}{V_{dry}}\times 100\ [\%]. \tag{4}\]  
The ion-exchange capacity (IEC) of the prepared membranes was measured with a sample having a size of 2 \(\times\) 2 cm\({}^{2}\). In the case of an AEM, the sample was immersed in 0.5 M NaCl solution for more than 6 h so that the ion-exchange groups were exchanged with Cl\({}^{\prime}\), and then washed several times with distilled water, and the wet weight was measured. Then, it was immersed in 0.25 M Na\({}_{2}\)SO\({}_{4}\) aqueous solution for 3 h or more so that Cl\({}^{-}\) ions of the ion-exchange groups were fully replaced with SO\({}_{4}\)\({}^{2-}\) ions. The amount of Cl\({}^{-}\) present in the solution was determined by [PERSON]'s method using a K\({}_{2}\)CrO\({}_{4}\) indicator and 0.01 M AgNO\({}_{3}\) aqueous solution as titrant. In the case of a CEM, the sample was immersed in 0.5 M HCl solution for more than 6 h to reach an equilibrium state.