“…This was because the volume fraction of the high-refractive-index ZrO 2 ( n = 2.16) decreased relatively and that of the low-refractive-index SiO 2 ( n = 1.46) increased with the increasing reaction time during the surface modification of NPs, considering the same NP weight content in aqueous solutions. The shell thicknesses of the SiO 2 layers of the ZrO 2 @SiO 2 NPs for each reaction time of 0, 3, 9, 18, 27, and 54 h were calculated as 0.0, 0.1, 0.7, 1.3, 2.1, and 4.2 nm, respectively (the red line in Figure 4 c) [ 34 , 46 , 47 , 48 , 49 ]. In particular, the calculated shell thickness of the ZrO 2 @SiO 2 NPs for the reaction time of 18 h (ZrO 2 @SiO 2 -18h) was consistent with that given by the TEM analysis, as described above ( Figure 2 b,e).…”