## 1 Introduction  
Carbon-based membranes are considered promising alternatives to membrane materials currently applied in water treatment and nanofiltration technology [1, 2, 3, 4]. This is due to the unique properties of a miscellany of carbon nanoparticles and carbonaceous frameworks, which exhibit different textures and nanosized pore networks, having large surface areas, excellent thermal and mechanical strengths, competitive antibacterial performances, and adequate adsorption/selectivity capacities. Specifically, graphene oxides (GOs) are two-dimensional (2D) layered materials, with oxygen-containing functional groups (epoxy, hydroxyl, and carboxyl) grafted on the basal plane and the periphery of graphene nanosheets. The GO sheets pile up in multilayer formations via \(\pi\)-complexation interactions with tunable interlayer distances [5, 6]. The \(\pi\) complexes involve the non-covalent bonding of the sp2 carbons of the adjoining GO sheets. Multilayer formations of GOs can operate like molecular sieves [7, 8, 9, 10], likely letting only the water molecules pass through their nanosized spacings, while excluding the metal ions from an aqueous solution. In this regard, GO materials are widely applied in seawater desalination and purification [5, 7, 8, 9, 10, 11], energy storage and conversion [12], solvent dehydration, and gas separation [13]. Free-standing graphene oxides suffer from poor mechanical strength and swelling defects in polar and aqueous environments [14, 15]. The reason is that the oxygen groups make the graphitic surface hydrophilic. Water molecules may access the inner core of the GO matrix and be adsorbed by the functional groups between the layers. Water loading may limit the strength of the \(\pi\) interactions of the adjoining nanosheets and, locally, increase the interlayer distance. This may cause the GO layers to detach from the initial columnar structures producing few-layer GO assemblies [15, 16]. The tendency of GOs to delaminate in aqueous solvents reduces the applicability of GO membranes in water-related processes. Several methods have been suggested to overcome this hurdle, such as chemical crosslinking [17; 18; 19], molecular bridging [20], physical confinement using polymer matrix [6], cationic bonding and intercalation [7; 21], and the formation of a graphene-polyelectrolyte multilayer [22]. Recently, our group produced a water-stable GO membrane [23]. The sample was prepared using solvent evaporation of dispersed GO deposited on a crosslinked co-poly(amide-imide) film (PAI-cr) [24]. Different supports were also tried for comparison. In this respect, hydrophilic supports were used such as polyether sulfones (PES), cellulose acetate (CA), co-poly(amide-imide) Torlon(r) (PAI), and its crosslinked derivative (PAI-cr). Hydrophobic polymeric films were also used, such as polyvinylidene fluoride (PVDF), polypropylene (PP), and polytetrafluoroethylene (PTFE). It was demonstrated that the hydrophobic supported systems were unstable due to the unfavored interactions between the films and the dispersed GOs. For instance, Figure 1a shows that the GO-PVDF sample appeared fragmented and crushed on contact with water, whereas other systems having a hydrophilic support such as GO-PAI (Figure 1b) and GO-PAI-cr (Figure 1c) appeared rather compact and uniform. We noticed some cracks on the edge of the GO-PAI sample, whereas the rest of the structure appeared condensed. Evidently, the crosslinked GO-PAI-cr membrane remained stable after prolonged contact time with water (>30 days). Figure 1d,e show the cross section of a membrane in which the GO was deposited on a PVDF support. The GO layer immediately detached from the support on contact with water (the red arrow indicates the GO layer detached form the support). On the contrary, when the GO was deposited under similar conditions on a PAI-cr membrane, good adhesion between the GO and the support was observed thanks to the electrostatic interaction between the two oppositely charged materials.