## 3 Results and Discussion
### Underwater Oil Contact Angle Behavior  
The polished surface of the C84400 was oleophilic, with an oil contact angle of \(54^{\circ}\pm 2^{\circ}\). However, after the thermal oxidation process in the N\({}_{2}\)-O\({}_{2}\) gas mixtures, the surfaces became oleophobic, with the underwater oil contact angles showing superoleophobicity with an increase in the thickness of the oxide layers. The contact angle of the oil (\(\theta_{\rm o}\)) increased and peaked at \(154^{\circ}\pm 1^{\circ}\) after 3 h of thermal oxidation in the N\({}_{2}\) 5 wt. % O\({}_{2}\) gas mixture. The roughness of the thermally oxidized surfaces, as well as the surface tension at the oil-oxide interface causes the oleophobicity of the oil contact angles on the samples when placed under water. The oxide layers act as low energy surfaces under water, due to surface tension. The average roughness values, \(R_{\rm a}\), of the surfaces were comparable irrespective of the N\({}_{2}\)-O\({}_{2}\) gas mixture used. Therefore, the increase in the underwater oil contact angles is dependent on other factors beyond the surface roughness and surface tension effects. To this end, the underwater oil contact angles, as well as the resultant underwater superoleophobicity can be explained from two perspectives, namely: the low fractional surface area of surfaces, due to the surface morphology of the oxide granules, as well as the porosity of the thermally grown oxide layer of varying thicknesses. Based on the Cassie-Baxter model [20] as stated in Equation (2), the fractional surface area of the oxide granules (\(f_{\rm so}\)) in contact with the oil must be small for the surface to exhibit high oil contact angles and superoleophobicity. \[\cos\ \theta_{\rm o}=f_{\rm so}\left(\cos\ \theta+1\right)-1 \tag{2}\]  
Using the Cassie-Baxter model, with \(\theta\) equal to the underwater oil contact angle on the polished C84400 copper alloy surface (\(\theta=54^{\circ}\pm 2^{\circ}\)) and \(\theta_{\rm o}\) equal to the measured underwater oil contact angle values on the thermally oxidized surfaces, the fractional surface areas of the oxide granules were calculated. The calculated values of \(f_{\rm so}\) were within the range of 0.32-0.39 and 0.06-0.35 for the C84400 copper alloy samples oxidized in the N\({}_{2}\)-0.75 wt.% O\({}_{2}\) and N\({}_{2}\)-5 wt.% O\({}_{2}\) gas mixtures, respectively, as stated in Table 1. The nano-sized oxides generated hierarchical surface layers, as can be seen in the SEM images, due to their irregular parking and size differences. The small granules of CuO, PbO and ZnO provided a very small surface area for wetting by the oil. Beyond the small fractional surface area of the oxide granules, the porosity of the oxide layers aided in the increment of the underwater oil contact angles into the superoleophobic region. As stated earlier, there is a pronounced distribution of pores in the samples that were oxidized in the N\({}_{2}\)-5 wt.% O\({}_{2}\) gas mixture, as shown by the SEM images in Figure 2e-f. The distribution of the pores was insignificant in the samples that were thermally oxidized in the N\({}_{2}\)-0.75 wt.% O\({}_{2}\) gas mixture, due to the morphology of the oxides and the thinness of the oxide layers. As the thickness of the oxidized surface layer increased to 25.69 \(\pm\) 9.14 \(\upmu\)m, the underwater oil contact angles on the surfaces shifted from oleophobicity to superoleophobicity. This dependence of the underwater oil contact angles with the oxide layer thickness is shown in Figure 7.  
As can be noted in the plot, the samples oxidized in the N\({}_{2}\)-5 wt.% O\({}_{2}\) gas mixture showed underwater superoleophobicity on the thicker oxide scales formed after the 3 h of thermal oxidation. To effectively explain this trend, the porosities of the oxide layers are estimated based on the effective sizes of the pores, D, and the average sizes of the oxide granule, \(\alpha\).