## 2 Materials and Methods
### Performance Testing  
1. Methanol diffusion coefficient and permeability: To measure the methanol crossover of the membrane, the membrane was first soaked in water for 24 h. Then, the membrane was placed in a two-compartment diffusion cell. Both compartments had the same dimensions, having a thickness of 1 cm and a circular cross-section with a diameter of 6 cm. The concentrate side was filled with a 2 M methanol solution and the dilute side with demineralized water. The setup was left unattended for 90 min to make the methanol diffuse through the membrane. The compartments were emptied in separate beakers and the solutions were intensely mixed before taking three samples of 20 \(\upmu\)L. It is important to note that the mixing of the solution is crucial since methanol-water mixtures can have microscopic configurational inhomogeneities [37]. The methanol concentration of the samples was analyzed via GC-FID (TurboMatrix HS 40, PerkinElmer), with helium as the carrier gas. The methanol diffusion coefficient [38] and the methanol permeability are calculated as follows: \[Methanol\ diffusion\ coefficient:\ D\ \left(\text{cm}^{2}/\text{min}\right)=\frac{\Delta C}{t \cdot C_{0}}\frac{V_{B}*L}{A}\] \[Methanol\ permeability\ P\ (1/\text{min})=\frac{\Delta C}{t\cdot C_{0}}\]  
\(\Delta C\), \(t\) and \(C_{0}\) are the average concentration changes in the concentrate and dilute compartment (mol/L), time of the experiment (min) and the methanol concentration of the concentrate compartment at the start (mol/L), respectively. V\({}_{B}\), L and A represent, respectively, the volume in the dilute compartment (cm\({}^{3}\)) (which is similar to the concentrate compartment), the thickness of the membrane (cm) and the surface area of the membrane (cm\({}^{2}\)). The diffusion coefficient D describes the diffusion of methanol through the membrane, normalized by membrane surface area and by membrane thickness. Therefore, this parameter gives insight into the performance of the membrane material since the thickness of the membrane does not influence this parameter. The permeability parameter P describes the methanol crossover through the complete membrane. The membrane thickness does have an influence on this parameter; therefore, the methanol permeability represents a more general membrane performance.
2. Proton resistance: AC impedance spectroscopy with a frequency range from 200 kHz to 1 Hz and an oscillating voltage between \(-\)10 and 10 mV (Biologic Sp-150 instrument) was used to determine the proton resistance of the membranes. Before performing the experiment, the membrane was soaked in a 1 M H\({}_{2}\)SO\({}_{4}\) solution for 24 h. The membrane (active area = 1 cm\({}^{2}\)) was put in a two-compartment cell sandwiched between two platinum electrodes. During the experiment, a 1 M H\({}_{2}\)SO\({}_{4}\) solution was pumped through both compartments at a flow rate of 49 mL/min. The blank measurement was performed following the same procedure without the membrane. The resistance value was derived from the intersect at high frequencies on a complex impedance plane with the Re(Z) axis. The proton resistance normalized by thickness was obtained by dividing that resistance value by the membrane thickness.