## 3 Results and Discussion
### Stability of TiO\({}_{2}\) Dispersion upon Adding Surfactants  
For cosmetic formulations containing TiO\({}_{2}\), such as sunscreens, W/O fabrication processes have mostly been considered [23]. As a model study of the W/O formulation, the stability of TiO\({}_{2}\) dispersion in a mixture of two liquids (oil:water = 8:2) was evaluated by the percentage ratio (degree) of single-phase dispersion per total suspension (values as 0-100%) and change in trend of viscosity in the dispersed formulation. Two types of oils--nonpolar (DC345) and polar (CEH)--were chosen owing to them being the most studied regarding TiO\({}_{2}\) formulations in the published literature [24]. Ruelle TiO\({}_{2}\) was selected because it functions as a UV-blocking compound in cosmetic formulations, with fewer skin toxicities [25]. TiO\({}_{2}\) particles contain hydroxyl groups on their surfaces and are hydrophilic, which is appropriate for use in W/O formulations [26; 27; 28]. We compared the degree of single-phase dispersion of TiO\({}_{2}\) suspensions by adding different surfactants. The liquid phase of the TiO\({}_{2}\) dispersions was observed 24 h after preparation (Figure 2). Without adding surfactants, TiO\({}_{2}\) powder (0.01 wt%) could not be dispersed in the mixture of oil and water (Figure 2a). In the case of TiO\({}_{2}\) dispersed in a mixture of nonpolar oil (DC345) and water, the addition of SDS produced a well-dispersed solution in all ranges of the treated surfactant concentration (0.001-2 wt%). The anionic surfactant SDS enables electrostatic stabilization, as recognized by the Derjaguin-Landau-Verwey-Overbeek theory [29; 30; 31]. For CTAB, DDAPS, and Tween 20, a higher degree of single-phase dispersion was observed with increasing surfactant concentration (starting from 0.05 wt%). Exceptionally, the 2 wt% CTAB treatment resulted in phase separation, indicating an unstable dispersion. The reason for this instability is as follows: when the concentration of the added surfactant increases, the adsorption layer becomes thicker than the distance between the particles. Then, the driving force to form micelles between the surfactants increases the aggregation between the surfactants [32; 33]. Based on the photographic images, the qualitative results of whether single-phase dispersion was maintained (criteria for stable dispersion were defined as more than the height of 80% single-phase dispersion) are summarized in Figure 2c. Quantitative values of the degree of dispersion stability (percentage ratio between the height of a single-phase dispersion and the height of the initial suspension) were recorded in detail (Figure S4). Based on references, the CMC value and degree of dispersion stability are closely related; the dispersion capability is optimized at the CMC or higher concentrations of the surfactant [32; 33; 34]. Anionic SDS produced a TiO\({}_{2}\) dispersion of \(\sim\)100% in all ranges of treated concentrations. In the case of CTAB and DDAPS, the degree of dispersion stability increased from 70-80% to 100% as the treatment concentration increased. For non-ionic Tween 20, TiO\({}_{2}\) was dispersed with a degree of 100% in treated surfactant concentration (0.01-2 wt%). After one month, TiO\({}_{2}\) dispersion by adding SDS exhibited the highest stability, followed by the case of adding Tween 20, which also kept stable dispersion. In contrast, most of the CTAB- and DDAPS-added samples separated and precipitated (Figure S5). In the case of TiO\({}_{2}\) dispersion in a mixture of polar oil (CEH) and water, SDS produced a well-dispersed solution in the range of treated surfactant concentration (0.1-2 wt%) as shown in Figure 2b. In the cases of CTAB, DDAPS, and Tween 20, higher dispersion stability was observed with increasing surfactant concentration (starting from 0.01 wt%). Exceptionally, 0.1-2 wt% DDAPS treatment resulted in phase separation, which is explained by the same principle of surfactant aggregation when over-concentration was applied [32; 33].