## 3 Results
### Structural and Optical Characterization of TiO\({}_{2}\) Nanospheres  
The surface morphologies of Am- and An-TiO\({}_{2}\) NSs synthesized by solution-based synthesis method are observed by SEM as shown in Figure 2a,b, respectively. Figure 2a,b shows the uniformly distributed sizes and morphologies of as-synthesized and calculated TiO\({}_{2}\) NSs. The average diameters of Am- and An-TiO\({}_{2}\) NSs were measured as 498 \(\pm\) 5 nm and 496 \(\pm\) 5 nm, respectively, as depicted in the inset of Figure 2. The summary of the size dependence of TiO\({}_{2}\) NSs with respect to the mixed solution ratio is depicted in Table S1. Generally, the solution-based synthesis of TiO\({}_{2}\) NSs is governed by a hydrolysis process [26]. Initially, the stepwise hydrolysis forms primary TiO\({}_{2}\) hydrates with sizes of a few nanometers, which have high surface energy and small electrostatic charges. Hence, TiO\({}_{2}\) hydrates agglomerate spontaneously owing to van der Waals attractive forces and hydrogen bonding among the individuals [27]. As the mass of the TiO\({}_{2}\) hydrates increases by gradual aggregation of the individual hydrates, the electrostatic charges build up in the aggregated TiO\({}_{2}\) hydrates. When TiO\({}_{2}\) spheres achieve a certain critical size, the repulsive interaction becomes sufficiently strong to block the Brownian aggregation, leading to each TiO\({}_{2}\) sphere being completely separate and without further increase in size. To investigate the phase conversion of the TiO\({}_{2}\) spheres from as synthesized to after annealing at different temperatures, we analyzed the XRD patterns. Figure 3a shows the XRD spectra of the Am- and An-phase TiO\({}_{2}\) NSs drop-casted on the Al\({}_{2}\)O\({}_{3}\) substrate. For the Am-TiO\({}_{2}\) NSs, there are no strong peaks in the XRD pattern, indicating that there is no crystallized phase, as shown (black line) in Figure 3a. By increasing the annealing conditions to 450 \({}^{\circ}\)C for 4 h, strong 20 peaks appeared at the diffraction peaks placed at 25.2\({}^{\circ}\), 37.8\({}^{\circ}\), 48\({}^{\circ}\), 55\({}^{\circ}\), 62.6\({}^{\circ}\), 70.3\({}^{\circ}\), and 75\({}^{\circ}\), which are well matched with crystal planes (101), (103), (200), (105), (204), (220), and (215) of An-structured TiO\({}_{2}\) (JCPDS No. 21-1272), as  
Figure 1: Process flow from formation of TiO\({}_{2}\) monolayer to its transfer on LED chips. (**a**) Formation of TiO\({}_{2}\) NSs ML on a PDMS, (**b**) drop-casting of DI water and flip of TiO\({}_{2}\)/PDMS pad, (**c**) removing of PDMS from TiO\({}_{2}\) NSs ML, (**d**) formation of arrays of TiO\({}_{2}\) NSs ML on LED chips. shown (red line) in Figure 3a. According to the XRD results, we know that as-synthesized Am-TiO\({}_{2}\) NSs changed to An-TiO\({}_{2}\) via heat treatment [28]. Transmission electron microscopy (TEM) images further reveal that the Am- and An-TiO\({}_{2}\) NSs have clustered structures and consist of a number of tiny nanocrystals, as shown in Figure 3b,c. Figure 3b shows the TEM image of An-TiO\({}_{2}\) NSs with particle diameters of 496 \(\pm\) 5 nm. The selected area electron diffraction (SAED) patterns of An-TiO\({}_{2}\) NSs show the crystallized An-TiO\({}_{2}\) NSs with indexing of (101), (103), (200), (105) and (204). The lattice-resolved HRTEM image clearly demonstrates that the crystal interplanar spacing  
Figure 3: (**a**) XRD patterns of as-synthesized and thermally annealed TiO\({}_{2}\) NSs and HR-TEM images and SAED patterns of (**b**) anatase and (**c**) amorphous spheres. Figure 2: SEM images of (**a**) Am- and (**b**) An-TiO\({}_{2}\) NSs. The inset figure shows the size distributions of used TiO\({}_{2}\) NSs. distance of (101) planes of An-TiO\({}_{2}\) is d = 3.492 A within the primary nanocrystals [29]. Am-TiO\({}_{2}\) NS, by contrast, does not present any diffraction pattern except for the blurry ring shape, as in XRD analysis, confirming the amorphous nature of this material.