## 2 Modelling
### Polymeric Models  
We considered three polymeric materials to be used as supports to deposit the GO layers, namely a polyvinylidene fluoride (PVDF), a pristine and a crosslinked polyamide-imide (PAI and PAI-cr). The polymeric supports are presented in Table 1.  
We built a long chain of n monomers of each material (n\({}_{\text{PVDF}}\) = 300, n\({}_{\text{PAI}}\) = 50, n\({}_{\text{PAI-cr}}\) = 25) by branching the monomers to each other with a random torsion [43; 44; 45]. The chain conformations of the macromolecules were sampled in 1000 steps. We set the macromolecules to fill a confined amorphous layer using a density of 2.3 g/cm\({}^{3}\), at 300 K. In practice, we used a simulation box with one side that was one-third of the desired box size to speed up the sampling of polymer conformations. The dimensions of the actual simulation box were obtained using a super cell of the smaller box. We used the amorphous cell algorithm [37; 46] to grow the macromolecule by inserting one segment at each Monte Carlo step. [47]. The trial conformations of the inserted segments were sampled according to [PERSON]'s RIS theory [48]. We used argon as a spacer to promote uniform growth in the cell and prevent segment accumulations in local high-density areas. The PVDF film contained 5 chains and 900 argon atoms. The PAI films contained 2 chains and 300 argon atoms. The argon atoms were deleted prior the NPT equilibration of the polymeric chains. The polymeric films were also put between two layers of graphene to prevent the chains fluctuating over the plane of the membrane. The positions of the graphenes were restrained during the equilibration. We performed Forcite annealing dynamics in five cycles. The initial temperature was 300 K, and the mid-cycle temperature was 600 K. We used five heating ramps per cycle with 1000 NVT (constant number of particles, volume, and temperature) steps each. The resulting configuration was further equilibrated using an NPT simulation over 3 ns at 298 K and 1 bar. At the end of the equilibration the graphene layers were deleted, and the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Name** & **Abbr.** & **Chemical Structure** & **Monom.** & **\# Atoms per** & **Chain in a** \\  & & & **in a Chain** & **Chain** & **Layer** \\ \hline Polyvinylidene fluoride & PVDF & & & 300 & 1802 & 5 \\  & & & & & \\ Polyamide-imide (PAI) & PAI & & & 50 & 1787 & 2 \\  & & & & & \\ crosslinked Polyamide-imide & PAI-cr & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Chemical structures of supporting polymers (numbers refer to the initial boxes, not the supercells). box sizes were adjusted to exclude the resulting empty space. The final layer dimensions were (112.73 \(\times\) 74.66 \(\times\) 41.91) A\({}^{3}\) for PVDF and (114.02 \(\times\) 75.35 \(\times\) 39.20) A\({}^{3}\) for PAI. The crosslinked PAI was created starting from 25-monomer-long 180 torsion chains of PAI and DAMP molecules as linkers. PAI chains were modified to a semi-reacted state where the imide groups were opened; the monomers were linked by a single amide group with a simple carbon atom in its ortho position. In addition, DAMP molecules were modified so that they carry the amide group at both their ends. Four PAI chains and 50 DAMPs were inserted into a confined amorphous layer normal to the z axis at a density of 2 g cm\({}^{-3}\) together with 300 Argon atoms as spacers. Graphene walls were inserted on the top and on the bottom of the layer to prevent chain exiting from z-perpendicular faces. A custom-made code was used to perform the actual crosslink of the chains. The crosslinking code detected the available reactive atoms and analyzed their mutual positions. The closest couple of atoms was analyzed. If their distance was below a set threshold, a second check regarding the possible bond-angle was performed. When the possible bond-angle values lay within a pre-set range of the actual value, a bond was formed, and the geometry was optimized over 10\({}^{4}\) steps of conjugate gradient minimization.