## 3 Results and Discussion
### Oil-in-Water Emulsion Separation and Reusability Performance  
A series of oil-in-water emulsions, including crude oil, diesel oil, and kerosene-in-water emulsions, were prepared and filtered through the AM-NaA/PVDF membranes. For the crude oil-in-water emulsion, as shown in Figure 10a, the permeate flux of the membranes exhibited an increasing trend, reaching a maximum of 6579 L/m\({}^{2}\cdot\)h when the monomer mass ratio of AM to NaA was adjusted from H-2 to H-5. However, further increasing the proportion of NaA monomer units (AM/NaA) to H-6 resulted in a gradual decline in permeate flux to 5874 L/m\({}^{2}\cdot\)h while maintaining nearly zero oil fouling, as demonstrated in Figure S6. This behavior can be attributed to the ionic strength of acrylate monomers and the surface morphology of membranes. This result demonstrates the successful separation of the oil-in-water emulsion by achieving a separation efficiency of 99.5%. Consequently, the AM-NaA/PVDF membrane fabricated at H-6 was employed for the subsequent experiments and analyses.  
The cycling performance of the AM-NaA/PVDF membrane was evaluated by monitoring permeate flux and oil content during multiple separation cycles (with a cycle period of 30 s) of a crude oil-in-water emulsion. After each cycle, the membrane was rinsed with water for 1-2 min to remove any residual oil. As shown in Figure 10b, the membrane maintained a removal efficiency of more than 99% within five-run separations, and the permeate flux decreased by about 12%, i.e., from 5874 L/m\({}^{2}\cdot\)h to 5180 L/m\({}^{2}\cdot\)h. These results can be attributed to the formation of an oil layer on the membrane surface that  
Figure 10: (**a**) Permeate flux and oil rejection performance of AM-NaA/PVDF membranes with different monomer mass ratios for the separation of crude oil-in-water emulsions. (**b**) The reusability of the H-6 membrane over multiple cycles for crude oil-in-water emulsion separation.  
increases with reusability and consequently raises the resistance of the membrane against the flow. This phenomenon is particularly pronounced in dead-end filtration processes, as the absence of hydrodynamic forces prevents the removal of the deposited oil layer [70; 71].  
The oil-in-water microscopic and optical images of the crude oil-in-water emulsion, diesel oil-in-water emulsion, and kerosene-in-water emulsion, before and after separation, are presented in Figure 11a-c. The milky white diesel oil- and kerosene-in-water emulsions, as well as the turbid brown crude oil-in-water emulsion, became transparent and clear after one cycle of separation using the AM-NaA/PVDF membrane. The oil content in the permeate for all three oil-in-water emulsions was below 10 mg/L, corresponding to a separation efficiency of just above 99% (Figure 11d). These results indicate that the AM-NaA/PVDF membrane can meet the safe environmental discharge limits of oil and grease content in wastewater across various regions, including China, the USA, and others [72], by removing almost all oil droplets from the oil-in-water emulsion, demonstrating its high separation efficiency. The high oil rejection of the AM-NaA/PVDF membrane is attributed to its superior underwater oil-repellent properties and proper mean pore size. The AM-NaA/PVDF membrane also exhibited high permeate flux during the separation of oil-in-water emulsions: 5874 L/m\({}^{2}\)-h for crude oil-in-water emulsion, 5276 L/m\({}^{2}\)-h for diesel oil-in-water emulsion, and 5798 L/m\({}^{2}\)-h for kerosene-in-water emulsion. This high flux is further supported by the superabsorption properties of the AM-NaA hydrogel, as evidenced by its water uptake capacity of 98 g H\({}_{2}\)O per gram of gel (Figure S7).