# Ex-Situ Evaluation of Commercial Polymer Membranes for Vanadium Redox Flow Batteries (VRFBs)
## 3 Results and Discussion
### Membrane Conductivity, Area Resistance and Ion Selectivity  
Membrane conductivity is another important factor determining the voltage efficiency (VE) of a VRFB since it controls the ohmic resistance of the cell. Table 4 shows the in-plane membrane ionic conductivity measured in water at RT. Generally, when the perturbation amplitude of the AC signal is applied by EIS, either protons or OH\({}^{-}\) ions are transported within the ionic channel of a hydrated CEM or AEM. They can also migrate along the  
Figure 4: Concentration of the V\({}^{4+}\) of eight (8) membranes at different times on the deficiency side. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Membranes**} & **Slope/k** & **Diffusion Coefficient** \\  & **(mol\(\cdot\)L\({}^{-1}\cdot\)h\({}^{-1}\cdot\)10\({}^{-4}\))** & **(cm\({}^{2}\cdot\)s\({}^{-1}\cdot\)10\({}^{-7}\))** \\ \hline AMV & 0.3 & 0.0025 \\ \hline AHA & 1 & 0.032 \\ \hline CMV & 4 & 0.035 \\ \hline FAP-450 & 15 & 0.070 \\ \hline DF & 18 & 0.092 \\ \hline N212 & 27 & 0.11 \\ \hline FS-930 & 76 & 0.18 \\ \hline VAN & 82 & 1.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Diffusion coefficients of VO\({}^{2+}\) ions for different membranes. network formed by the hydrogen bond between water molecules and ionic functional groups in the membranes [41]. The degree of transport of ions through the membrane is defined as ionic conductivity. Specifically, the in-plane ionic conductivity measured in this work for CEM or AEM refers to proton conductivity or OH\({}^{-}\) conductivity, respectively. The proton conductivities among PFSA dense membranes (NRE-212, FS-930 and DF) are comparable (60-84 mS-cm\({}^{-1}\)) due to their analogous chemical structures, while the slight variances are mainly attributed to the difference in IEC (0.9-1.1 meq\(\cdot\)g\({}^{-1}\)). For CEMs, the PFSA-based dense membranes exhibited higher proton conductivities than the reinforced CEM (VAN, 0.54 mS-cm\({}^{-1}\)) and the hydrocarbon-based CEM (CMV, 4.6 mS-cm\({}^{-1}\)) on account of the differences in the physical and chemical structure of the membranes. Moreover, the proton conductivities of PFSA dense membranes are higher than the OH\({}^{-}\) conductivities of AEMs because protons have higher mobility than hydroxyl ions (the intrinsic diffusion rate: H\({}^{+}\) (9.31 \(\times\) 10\({}^{-5}\) cm\({}^{2}\cdot\)s\({}^{-1}\)) vs. OH\({}^{-}\) (5.27 \(\times\) 10\({}^{-5}\) cm\({}^{2}\cdot\)s\({}^{-1}\))) [7]. The OH\({}^{-}\) conductivities for AEMs were in the range of 2.4-38 mS-cm\({}^{-1}\). In summary, the ionic conductivities of the membranes (\(\sigma\)) are in the following order: FS-930 \(\approx\) N212 \(\approx\) DF \(>\) FAP-450 \(>\) CMV \(>\) AMV \(>\) AHA \(>\) VAN. The membrane area resistance was also measured in 2 M H\({}_{2}\)SO\({}_{4}\) in an H-cell with two carbon rods as electrodes. PFSA-based membranes (N212, DF, FS-930) exhibited comparable area resistance with hydrocarbon membranes (FAP-450 and CMV), showing superior ion conductivity compared to VAN, AMV and AHA. It is worth mentioning that the thickness of the membrane is not taken into account in the calculation of membrane area resistance. In summary, the area resistance of each membrane is in the following order: DF \(\approx\) N212 \(<\) FS930\(\approx\)FAP-450 \(<\) CMV \(<\) VAN \(<\) AMV\(<\) AHA. To minimize energy loss, it is essential for the membranes to acquire high ionic conductivity while preventing undesired ion crossover to ensure high VE and CE. Ion selectivity (S) is used to evaluate this sentiment and defined as the ratio of ionic conductivity (H\({}^{+}\) or OH\({}^{-}\)) over vanadium ion permeability. Table 4 summarizes the calculated ion selectivity of eight (8) investigated membranes based on Equation (6).