## 3 Materials and Methods
### Liquid Extrusion Porometry (LEP) Method  
In order to obtain the capillary pressure curves, the same commercial device, an IFTS fluid porometer, used in previous CFP experiences was used, but now docked to an external module consisting of an appropriate sample holder and a precise analytical balance (Figure 5). The role of the CFP equipment was now to supply a stable pressure above the sample, while the balance was able to monitor the drained mass from the wetted membrane. This IFTS designed commercial setup allowed for the conversion of CFP equipment to accomplish such LEP experiments, and was adapted to characterize gas diffusion layers (GDL) integrated into polymer electrolyte membrane fuel cells (PEMFC) [22; 23; 24; 25; 26; 27].  
The experimental device for the generation of capillary pressure curves was the drainage and further imbibition of the wetting liquid. Using the CFP porometer, the capillary pressure slowly increased and the wetting liquid flowed out of the sample onto an analytical balance (accuracy \(\pm 0.1\) mg). As the system reached the equilibrium condition (\(\Delta m/\Delta t\)-0) at each capillary pressure, the volume (mass) of liquid drained is recorded before the pressure is again increased. Once the maximum desired pressure has been reached, the capillary pressure is slowly relieved and the wetting fluid flows back into the sample. Using this data, a capillary pressure curve (and drainage) can be generated.  
The capillary pressure can be defined from the next equation [26].  
\[Pc=P\ (\text{wetting liquid})-P\ (\text{non-wetting fluid})=\rho gh+P_{Atm}-P_{G} \tag{3}\]  
where the gas pressure \(P_{G}\) (Pa) is controlled by the porometer above the sample, and \(h\) (cm) is the distance between the liquid reservoir level and the sample surface, which was roughly 5 cm. Therefore, during the experiment, there was a small column of liquid open to barometric pressure \(P_{Atm}\) (Pa) and acted on the surface of the liquid reservoir. Concerning the role of the capillary barrier needed to properly apply LEP, a hydrophilic membrane (Sartorius, 0.2 \(\upmu\)m nominal pore size, made of CN and  
Figure 5: Schematic diagram of liquid extrusion porometer system setup.  
having \(\mathcal{O}\) = 25 mm) was placed below the measured sample and performed this role as long as its pores were clearly smaller than those of the membrane to be analyzed. The main characteristics required of the wetting liquid used in the LEP experiments were very similar to those used for CFP. In addition, ideal flow properties (low viscosity) and low propensity for evaporation at room temperature are required. Evaporation is not desirable as it can lead to pores in both the sample and the hydrophilic barrier membrane becoming not wet, therefore allowing for air to breakthrough.  
In the case of the MF Sartorius membrane analyzed, the mixture consisted of the aqueous phase (see Section 3.1) from the water/isobutanol mixing. This liquid was successfully used as a wetting liquid with a surface tension value of 29.6 mN/m. Ultra-pure water was used as the wetting liquid for FM to obtain a better resolution with a low pressure manometer.  
The plot of contributions to total mass drained was considered only for positive capillary pressure of the drained liquid for each opened pore and converted into PSD, in terms of normalized differential mass drained divided by differential diameter \(dm/dD\) (mg/\(\upmu\)m) (%).  
\[\left(\Delta m/\Delta d\right)_{k}(\%)=\frac{\left(\Delta m/\Delta d\right)_ {k}}{\sum\left(\Delta m/\Delta d\right)_{k}}100 \tag{4}\]  
The pore sizes obtained by LEP were the average \(d_{p}\) (m) from the gas capillary pressure curve.