## 1 Introduction
Coating filter membranes with hydrogels effectively combines the inherent hydrophilicity of the hydrogel with the high permeability of the membrane, enhancing both separation efficiency and antifouling properties [42; 43]. Prior studies highlight the potential of hydrogel coatings. [PERSON] et al., 2018 [44] coated a thin hydrogel film onto the surface of a PAA-g-PVDF ultrafiltration membrane through layer-by-layer self-assembly of sodium alginate and Cu\({}^{2+}\). The resulting filtration film achieved a high water flux of up to 1230 L/m\({}^{2}\)-h.bar, with separation efficiency exceeding 99.8% and outstanding antifouling and cyclic performance. [PERSON] et al., 2011 [45] coated micro-scale porous metal substrates with rough nanostructured hydrogel instead of directly applying a hydrogel coating to the filtration membrane surface. The hydrogel-coated mesh demonstrated excellent selective and effective separation of water from various oil/water mixtures, including crude oil, with separation efficiency exceeding 99. However, this method faces two key challenges: (1) controlling the coating thickness, because exceeding the optimal thickness of the layer can lead to pore blockage, reducing filtration efficiency;and (2) ensuring long-term stability, as weak adhesion can cause delamination or degradation over time [46; 47]. Therefore, developing an effective and versatile surface modification strategy remains a critical challenge in advancing membrane technology. Acrylamide (AM) and acrylic acid (in the form of sodium acrylate (NaA)) are two important raw monomers that form superior synthetic copolymer hydrogels that have separation ability for oil-in-water emulsions, metal ions, and organic dyes, along with notable antibacterial properties, thanks to the role of their functional groups, making them highly suitable for treating oilfield-produced water [48; 49; 50; 51]. The ratio of these monomers significantly influences polymer chain packing, thereby controlling the thickness of the coated hydrogel layer. The presence of carbon-fluorine (C-F) bonds with strong bond energy (110 kcal.mol\({}^{-1}\)) in PVDF complicates chemical modification, resulting in weak interactions between the substrate and coating layer [52]. To address this issue, applying the low-temperature plasma treatment before the hydrogel coating process effectively enhances the wettability and chemical bonding between the PVDF membrane surface and the hydrogel. The mechanism involves the introduction of polar functional groups and an increase in the number of available binding sites, thereby facilitating improved interfacial interactions [53; 54; 55]. This work integrates atmospheric pressure low-temperature plasma treatment with AM/NaA copolymer hydrogels to develop a superhydrophilic and underwater superhydrophobic PVDF microfiltration membrane with coating stability and antifouling performance. The hydrogel is synthesized from AM and NaA copolymer in different AM/NaA monomer mass ratios by free radical polymerization in aqueous solutions. The hydrogel is coated onto a plasma-preconditioned PVDF surface and optimized by treatment time. The modified membranes are tested for crude oil-in-water emulsion separation, assessing reusability and antifouling with the optimal monomer ratio. This work also explores separation efficiency across oil types (kerosene and diesel) and the role of salts (calcium chloride, magnesium chloride hexahydrate, and sodium chloride) in promoting demulsification of crude oil-in-water emulsions within the membrane system. The superior performance and fabrication method make our AM-NaA/PVDF membrane an effective solution for industrialization.