## 3 Results and Discussion
### CMC Determination of Fatty Acids with Different Alkyl Chains
month of measurement, FA-unC18, with its long alkyl chain, exhibited the highest stability (Figure S11b). We also characterized the chemical compounds in the TiO2 dispersions with 1 wt% of the four fatty acid treatments. Bands at 600-700 cm\({}^{-1}\) associated with TiO2 and the C-H bands of fatty acids at 2916 and 2848 cm\({}^{-1}\) were observed, indicating that the fatty acids were adsorbed on the TiO2, creating a well-dispersed TiO2 dispersion (Figure S12). To examine the characteristics of the particle surface, size and zeta potential were analyzed (Figure S13). As the chain length increased, the particle size also increased, indicating a thicker adsorption layer. This trend was consistent with the results observed in the zeta potential analysis (Figure S14). To correlate the degree of dispersion stability and the potential of the viscous W/O formulation, the viscosity of the TiO2 dispersion was measured according to the fatty acid concentration. For both the non-polar (DC345) and polar (CEH) oils, anionic fatty acids showed an increasing trend of viscosity with increasing treatment concentrations (Figure 7). Fatty acids with relatively shorter alkyl chains (FA-C6 and FA-C12) produced a higher-viscosity TiO2 dispersion than fatty acids with longer alkyl chains (FA-C18) did. Surfactants with shorter alkyl chains have more molecules per unit mass than those with longer alkyl chains, resulting in faster adsorption onto TiO2. Consequently, a more rapid increase in viscosity occurred than for longer alkyl chains. However, for surfactants with shorter hydrophobic chains, the length of the chains protruding into the external oil is shorter, making them less effective at capturing oil and thus less stable compared to longer alkyl chains [41; 42; 43]. Figure 6: TiO2 dispersions using different surfactants after 24 h storage. (**a**) 0.01 wt% TiO2 was added to non-polar oil (DC345):water (8:2) with surfactant. (**b**) 0.01 wt% TiO2 was added to polar oil (CEH):water (8:2) with surfactant. Table of the degree of TiO2 dispersion (O: >80% dispersed, X: <80% dispersed) in a mixture of (**c**) DC345 and water and (**d**) CEH and water. Effect of Fatty Acids with Different Alkyl Chains on the UV-Blocking Efficacy of TiO\({}_{2}\) Dispersion  
The UV-blocking efficacy of the TiO\({}_{2}\) dispersion was evaluated based on the concentration of anionic fatty acids with different alkyl chains. The UV absorption (\(\lambda_{\text{abs}}\) = 300 nm) gradually increased corresponding to the increasing concentration of treated fatty acids (Figure 8). Among them, fatty acids with relatively longer alkyl chains (FA-C\({}_{12}\), FA-C\({}_{18}\), and FA-unC\({}_{18}\)) resulted in relatively more effective UV-blocking than those with shorter alkyl chains (FA-C\({}_{6}\)). In the case of surfactants with longer alkyl chains in the W/O formulations, the length of the alkyl chain protruding into the external oil was longer than that of the other surfactants, allowing it to successfully trap oil. This oil forms a spatial barrier by filling the gaps between the droplets, thereby increasing stability and enhancing UV-protection efficacy. Surfactants with double-bond structures have a higher affinity for polar oils, leading to greater oil-trapping capability and the formation of an even stronger spatial barrier [41; 43].