*3.3. Interfacial Formation Energy*

In order to investigate the stability of the interface in the presence of NGOs at three temperatures, the interaction energy between nanoparticles and water molecules was calculated, the calculation process is shown in Equation (7):

$$
\Delta E = \frac{(E\_{\text{Nano}} + E\_{\text{Water}}) - E\_{\text{Total}}}{V\_{\text{Nano}}} \tag{7}
$$

where: Δ*E* is interaction energy per unit volume; *ETotal* is the total energy of the nanoparticle and water phase system; *ENano* is the energy of the nanoparticle; *EWater* is the energy of the water phase; and *VNano* is occupied volume of the nanoparticle.

From Table 5, it can be observed that the interaction energy between nanoparticles and water becomes smaller as the temperature increases, indicating that an increasing temperature can reduce the resistance to movement between nanoparticles and water, making them easier to transport to the oil–water interface.

**Table 5.** The interaction energy of nanoparticles with water per unit volume.

