## 3 Results and Discussion
### CMC Determination of Fatty Acids with Different Alkyl Chains  
To evaluate the effect of surfactant alkyl chains on the degree of TiO\({}_{2}\) dispersion stability, anionic fatty acids of different chain lengths (FA-C\({}_{6}\), FA-C\({}_{12}\), FA-C\({}_{18}\), and FA-unC\({}_{18}\)) were selected. Their chemical structures are shown in Figure 5a. A comparison between FA-C\({}_{18}\) and FA-unC\({}_{18}\) revealed the effect of the presence of a double bond in the middle of the alkyl chains on dispersion quality. Figure 4: UV-Vis absorption intensities of (**a**) 10 wt% TiO\({}_{2}\) in non-polar oil (DC345): water (8:2) with various concentrations of surfactant (SDS, CTAB, DDAPS, and Tween 20); (**b**) 10 wt% TiO\({}_{2}\) in polar oil (CEH):water (8:2) with various concentrations of surfactant (SDS, CTAB, DDAPS, and Tween 20). The CMC of FA-C\({}_{6}\) is approximately 1 M; however, FA-C\({}_{6}\) is not soluble in water (solubility \(<\) 0.2 M), making it impossible to measure via conductivity measurements [40]. CMC of FA-C\({}_{12}\), FA-C\({}_{18}\), and FA-umC\({}_{18}\) were determined at the point of intersection between different linear slopes: 27.4 mM (0.609 wt%), 1.08 mM (0.033 wt%), and 1.98 mM (0.06 wt%), respectively (Figure 5b). Effect of Addition of Fatty Acids with Different Alkyl Chains on the Stability of TiO\({}_{2}\) Dispersion  
We evaluated the degree of single-phase dispersion of TiO\({}_{2}\) after the fatty acid treatment. In a mixture of non-polar oil (DC345) and water, FA-C\({}_{6}\) could not disperse TiO\({}_{2}\) at any concentration (Figure 6a). This is attributed to the fact that the alkyl chains of the fatty acids were too short to be adsorbed onto the surface of TiO\({}_{2}\). In the case of FA-C\({}_{12}\), as the treated fatty acid concentration increased (starting from 1 wt%), a higher dispersion height was observed. In the case of FA-C\({}_{18}\) and FA-umC\({}_{18}\), the degree of dispersion stability reached 100% at 3-5 wt% treated concentrations. The quantitative values of the degree of dispersion stability are presented in Figure S10a. Anionic FA-C\({}_{12}\) produced a TiO\({}_{2}\) dispersion with a nearly 100% degree of dispersion stability over a range of treated concentrations (1-5 wt%). In the case of FA-C\({}_{18}\) and FA-umC\({}_{18}\), TiO\({}_{2}\) was dispersed with a degree of dispersion stability of 100% at treated surfactant concentrations (3-5 wt%). After one month of measurement, FA-C\({}_{18}\), with its long alkyl chain, demonstrated the highest stability. This is because long chains more effectively maintain steric hindrance compared to shorter chains, resulting in such outcomes (Figure S11a). In a mixture of polar oil (CEH) and water, FA-C\({}_{6}\) could not disperse TiO\({}_{2}\) in solution at all tested concentrations (Figure 6b). In the case of FA-C\({}_{12}\) and FA-C\({}_{18}\), single-phase dispersion was not achieved at low concentrations (0.001-2 wt%), although the dispersion showed approximately 100% of dispersion height at high concentrations (3-5 wt%). In the case of FA-umC\({}_{18}\), as the treated fatty acid concentration increased (starting from 0.1 wt%), a higher dispersion height was observed. The quantitative values of the degree of dispersion stability are presented in Figure S10b. Anionic FA-C\({}_{12}\) and FA-C\({}_{18}\) produced a TiO\({}_{2}\) dispersion with a nearly 100% degree of dispersion stability at the range of treated concentrations (3-5 wt%). In the case of FA-umC\({}_{18}\), TiO\({}_{2}\) was dispersed with a degree of dispersion stability of 85-100% at treated surfactant concentrations (1-5 wt%). After one  
Figure 5: (**a**) Chemical structures of sodium hexanoic acid (FA-C\({}_{6}\)), sodium lauric acid (FA-C\({}_{12}\)), sodium stearic acid (FA-C\({}_{18}\)), and sodium oleic acid (FA-umC\({}_{18}\)). (**b**) Critical micelle concentration determination of FA-C\({}_{12}\), FA-C\({}_{18}\), and FA-umC\({}_{18}\) by conductivity measurement.