# Structural Colors Based on Amorphous Arrays Comprised Solely of Silica Particles
## 3 Experimental Results and Discussion
### Coating of Silica Solutions  
Figure 7 shows the SEM images of the silica solutions coated on a glass slide. Figure 7a shows a crystal lattice structure of a silica solution consisting of homogeneously sized, monodispersed, spherical silica nanoparticles. However, in the case of Figure 7b-d, silica particles are arranged in amorphous form instead of a lattice structure. The reason is that the particles of uniform size and shape were arranged in a crystal lattice without disturbing other particles during the self-assembly process. Meanwhile, the spherical silica nanoparticles did not form a lattice structure due to the presence of atypical silica.  
Figure 8 shows photographs of the coated silica solutions at three viewing angles and photographs of spherical silica nanoparticles rubbed on a black substrate. Figure 8a shows that the coated silica solution changes color to blue, green, and red at viewing angles of 90\({}^{\circ}\), 60\({}^{\circ}\), and 40\({}^{\circ}\). These changes occurred because the crystal lattice structure in case 1 satisfied the Bragg's equation (Equation (1) [11, 22]).  
\[\lambda=2D\sqrt{\frac{2}{3}(n_{eff}{}^{2}-\sin^{2}{\theta})} \tag{1}\]  
where \(D\), \(\lambda\), \(\theta\), and \(n_{eff}\) denote the size of the spherical silica nanoparticle, the reflection wavelength, the angle of light incidence, and the effective refractive index, respectively. As shown in Figure 4a, the average size of the spherical silica nanoparticles is 435 nm, and the effective refractive index is 1.35 [18]. The sizes of the particles were calculated theoretically from 438 nm to 704 nm with colors, as shown in Figure 8a. In contrast, in Figure 8b-d, the silica solutions coated on glass slides show a different color depending on the size of the spherical silica nanoparticles, and the same color as the silica powder is observed. Furthermore, the colors did not change with the change in the viewing angle. These results occurred because spherical silica nanoparticles did not form a crystal lattice structure, but formed an amorphous array due to particle aggregation, as shown in Figure 7b-d. That is, atypical silica particles interfered with the crystal arrangement of spherical silica nanoparticles. This amorphous array was similar to the arrangement induced by the addition of carbon black particles, and similar  
Figure 7: SEM photographs of the silica solution coatings: (**a**) No added phenol-formaldehyde resin (Case 1); (**b**) 0.027 g of added phenol-formaldehyde resin (Case 2); (**c**) 0.030 g of added phenol-formaldehyde resin (Case 3); (**d**) 0.033 g of added phenol-formaldehyde resin (Case 4).  
results were reported in Reference [14]. Figure 8e indicates that various colored membranes comprise solely of spherical silica nanoparticles. The average sizes of the particles were 300 nm, 400 nm, and 500 nm (from the left in the figure). It is confirmed that the color appeared differently according to the size of the spherical silica nanoparticles. The color of the silica solution coated in this study and the membrane color composed only of spherical silica nanoparticles showed similar trends to Reference [15].  
Figure 8: Photographs of the silica solution coatings under three viewing angles: (**a**) Case 1 (various colors depending on angles); (**b**) Case 2 (blue); (**c**) Case 3 (green); (**d**) Case 4 (red); (**e**) Colored membranes consist of solely of spherical silica particles.