# Ex-Situ Evaluation of Commercial Polymer Membranes for Vanadium Redox Flow Batteries (VRFBs)
## 3 Results and Discussion
### Membrane Vanadium Crossover  
It is inevitable that vanadium ions will pass through any of the membranes, leading to the reduction of CE and EE of a VRFB due to the overlapped hydrated ionic clusters and the complex interactions among different ions being transported in the membrane. In order to achieve durable and high-performance VRFB, a membrane possessing low vanadium ion crossover rate is desperately required. The crossovers of VO\({}^{2+}\) ions across the selected membranes were compared and their diffusion coefficients of vanadium ions were calculated using Equation (3):  
Figure 4 shows the concentration of the VO\({}^{2+}\) of each membrane against the time on the deficiency side. The calculated slopes (k) and diffusion coefficients (\(D\)) are listed in Table 3. In principle, the vanadium permeability across a membrane depends on the membrane properties of IEC, water uptake, thickness and microstructure [8]. Compared to  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Sample Name**} & **Peak Load (N)** & **Peak Stress (MPa)** & **Peak Stress Loss** \\ \hline \multirow{2}{*}{N212} & Before & 4.3 \(\pm\) 0.1 & 28.9 \(\pm\) 0.5 & \multirow{2}{*}{20\%} \\ \cline{2-4}  & After & 3.5 \(\pm\) 0.3 & 23.2 \(\pm\) 1.9 & \\ \hline \multirow{2}{*}{DF} & Before & 5.3 \(\pm\) 0.2 & 29.3 \(\pm\) 1.3 & \multirow{2}{*}{25\%} \\ \cline{2-4}  & After & 4.3 \(\pm\) 0.3 & 21.9 \(\pm\) 1.5 & \\ \hline \multirow{2}{*}{FS-930} & Before & 2.7 \(\pm\) 0.2 & 30.0 \(\pm\) 2.0 & \multirow{2}{*}{18\%} \\ \cline{2-4}  & After & 2.2 \(\pm\) 0.3 & 24.6 \(\pm\) 3.1 & \\ \hline \multirow{2}{*}{FAP-450} & Before & 5.5 \(\pm\) 0.0 & 36.7 \(\pm\) 0.2 & \multirow{2}{*}{40\%} \\ \cline{2-4}  & After & 3.7 \(\pm\) 0.6 & 22.0 \(\pm\) 3.6 & \\ \hline \multirow{2}{*}{VAN} & Before & 12.5 \(\pm\) 0.5 & 16.9 \(\pm\) 0.7 & \multirow{2}{*}{6\%} \\ \cline{2-4}  & After & 11.7 \(\pm\) 0.9 & 15.9 \(\pm\) 1.2 & \\ \hline \multirow{2}{*}{AHA} & Before & 34.3 \(\pm\) 1.7 & 46.7 \(\pm\) 2.3 & \multirow{2}{*}{4\%} \\ \cline{2-4}  & After & 28.8 \(\pm\) 2.9 & 44.6 \(\pm\) 4.6 & \\ \hline \multirow{2}{*}{CMV} & Before & 9.9 \(\pm\) 1.3 & 28.6 \(\pm\) 3.8 & \multirow{2}{*}{32\%} \\ \cline{2-4}  & After & 6.7 \(\pm\) 1.0 & 19.4 \(\pm\) 2.9 & \\ \hline \multirow{2}{*}{AMV} & Before & 9.3 \(\pm\) 0.1 & 27.1 \(\pm\) 0.2 & \multirow{2}{*}{7\%} \\ \cline{2-4}  & After & 9.0 \(\pm\) 1.3 & 25.1 \(\pm\) 3.5 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Tensile strength of the selected membranes before and after chemical stability testing.  
PFSA membranes (9.2 \(\times\) 10\({}^{-9}\) to 1.62 \(\times\) 10\({}^{-7}\) cm\({}^{2}\cdot\)s\({}^{-1}\) in Table 3), the AEMs showed lower diffusion coefficients (1.5 \(\times\) 10\({}^{-8}\) to 4.2 \(\times\) 10\({}^{-7}\) cm\({}^{2}\cdot\)s\({}^{-1}\)), due to the Donnan exclusion effect between the immobilized positively charged functional groups and the electroactive species. Meanwhile, the hydrocarbon membranes (3.5 \(\times\) 10\({}^{-9}\) cm\({}^{2}\cdot\)s\({}^{-1}\) for CMV) more effectively suppress vanadium permeability than PFSA membranes for the sake of their microstructural distinction. It was reported that the fraction of 'open' ionic domains at the surface of the sulfonated hydrocarbon membranes, as measured by conductive probe microscopy, is much smaller than the surface of the PFSA membrane [40]. The diffusion coefficient of VO\({}^{2+}\) ions is in the order of AMV < AHA < CMV < FAP-450 < DF < N212 < FS-930 < VAN.