## 3 Results and Discussion  
Figure 3 shows the configurations of free-standing and supported GO layers on PVDF, PAI, and PAI-cr films. Within water, the layers appeared highly dispersed due to the oxygen-containing functionalities. The water content on the surface enhanced the repulsive nature of the interlayer interactions, making the GO nanosheets shift their rotation angle. In the case of the supported systems the inner layers were more anchored to the polymeric films. Several water molecules were encountered between the polymer and the nanosheets of the first layer. The immobilization of the nanosheets should be attributed to non-covalent bonds of the water molecules that bridge the polymeric surface and the GO. It has been observed in the literature that these interactions are associated with strong hydrogen bonds formed between the water hydrogens and the oxygens of the functional groups of the nanosheets [49; 50]. Representative hydrogen bonds of water  
Figure 3: GO sheets at the beginning and end of the simulation: (**a,b**) GO in water; (**c,d**) PVDF (pink); (**e,f**) PAI (orange); (**g.h**) PAI–cr (yellow). In all pictures, the colors are O = red; H = white, GO layer = deep grey. molecules bridging the polymer and the first GO layer are shown in Figure 4, as snapshots corresponding to the initial and final configurations of the NPT equilibrations. Figure 5 shows the density profiles of water molecules as a function of the distance from the top edge of the simulation box and through the graphene oxide layers. The profile curves depict the water densities in the initial and the final configurations of the NPT simulations. The boundary of the stacks with the graphene oxide layers is highlighted using two vertical yellow dashed lines. Both the supported and the unsupported systems display highly ordered structures of water molecules in the interlayer space at the initial configurations. These structures reflect the parallel orientation of the graphene nanosheets. The density plateau on the left side of the plots corresponds to the bulk density of water. On the right side of the plots, we encounter a negligible density. This density corresponds to a small amount of water molecules inserted inside the polymeric layer upon solvation. Figure 4: Examples of hydrogen bonds between polymer–water–GO in the lower layer of GO at the beginning of the simulation (**left column**) and at the end (**right column**). GO in colored in gray, PAI in purple, PVDF in green, and crosslinked PAI in blue. Some atom types are colored differently in order to highlight their atom type: oxygen in red, hydrogen in white, fluorine in light blue. The orange dotted line represents the hydrogen bonds. Figure 5: Density profile perpendicular to GO sheets at the beginning of the simulation (blue lines) and at the end (orange lines) for (a) GO in water; (b) PVDF; (c) FAJ; and (d) PAI-or, as a function of the distance from the top edge of the box. The yellow dashed lines denote the boundaries of the stacks of the GO layers. On the other hand, the water density profiles at the final configurations show that the water structure has been disturbed due to oscillations of the GO layers after a simulation over 4 ns. The interlayer distance is similar to that of the initial configuration. However, this value corresponds to the center-of-mass distance of the GO layers. The nanosheets on the layers were not oriented exactly parallel. Nevertheless, using a hydrophilic support, the initial ordering of the GO layers was partially maintained throughout the equilibration. The situation was even better for the GO-PAI-cr system. This is also depicted by the shape of the corresponding water density profiles in the interlayer range of distances. Figure 6 shows the position and the orientation angle of the individual GO nanosheets of the different membrane systems.