Anti-reflection (AR) is important in enhancing the display effect of display panels and the photovoltaic conversion efficiency of solar cells. The construction of AR structures using hollow silica (SiO₂) particles (HSPs) as an effective method has been attracting related researchers. Plastic substrates, represented by polycarbonate (PC) and polymethyl methacrylate (PMMA), have broad market potential in replacing inorganic glass. However, due to the great differences between the surface properties of plastic substrates and inorganic materials, many AR coating technologies that can be easily industrialized on inorganic materials are difficult to be transferred to plastic substrates. In this context, a big challenge in constructing AR structures on plastic substrates is how to fix HSPs on organic substrates at low temperatures. Anchoring HSPs with low-temperature curable resin is a very promising strategy for industrialization with low cost and easy operation. However, the quality of AR coatings prepared by this strategy is greatly affected by the physical and chemical properties of the coating solution and the complex hydrodynamic effects during coating and drying. Many factors should be considered and optimized to obtain AR coatings with excellent performance. There are too many uncertain factors, long optimization cycle, and poor repeatability and reliability, so optimizing conditions by experimental methods willbe time-consuming and laborious. In contrast, optimizing the surface structures through simulations has incomparable advantages over traditional experimental strategies. The simulation results can point out the direction for further experimental research and accelerate experimental processes.

The effects of HSPs and HSP-solid SiO₂ particle hybrid on the optical properties of as-prepared AR surfaces in the visible light range are studied by COMSOL Multiphysics. Some specific factors are examined, including the diameter of HSPs, hollowness degree, spacing between particles, resin coverage height, incidence angle, and particle arrangement pattern. A three-dimensional model is employed for simulation. The model consists of PC substrate, HSPs, resin (PMMA), and air. The minimum cell structures are studied under periodic boundary conditions. Three patterns of particle arrangements are considered (Fig. 1): square lattice arrangement, where HSPs are arranged in the X-Y plane in a square lattice; hexagonal lattice arrangement, where HSPs are arranged in the X-Y plane in a hexagonal lattice; HSP-solid SiO₂ particle hybrid arrangement, where small size solid SiO₂ particles are inserted into the gaps of HSP hexagonal lattice. For the square lattice arrangement, the effects of some factors on the reflectivity of the coatings are investigated, including the HSPs' size, the HSPs' hollowness degree, spacing between particles, the height of resin coverage, and incidence angle.

When the HSPs with a radius of 10-100 nm and hollowness of 0.7 are arranged in the form of square lattice and the resin covers half the height of the particles, coatings with low reflectance in the visible light range (380-780 nm) can be obtained (Fig. 2). The coating with the best AR effect is the one using HSPs with hollowness of 0.7. The hollowness is defined as the ratio of cavity radius to particle radius. Smaller spacing between particles facilitates lower reflectance over a broader wavelength range. When the radius of HSPs is 100 nm and the resin coverage height is 100-125 nm, the coating has the lowest reflectance in the whole visible light band (Fig. 3). The reflectance of the coatings constructed by all sizes of HSPs is lower than that of the bare PC substrate in the incidence angle range of 0°-85° (Fig. 4). For those three different patterns, the reflectance at 550 nm is 0.17% for square lattice arrangement, 0.03% for hexagonal lattice arrangement, and 0.12% for HSP-solid SiO₂ particle hybrid arrangement. The average reflectance in the visible light range (380-780 nm) is 0.57% for square lattice arrangement, 0.51% for hexagonal lattice arrangement, and 0.24% for HSP-solid SiO₂ particle hybrid arrangement, respectively. The changes of effective refractive indexes in the Z-direction are calculated by effective medium theory under different resin coverage heights, different degrees of hollowness of HSPs, and three particle arrangement modes. The results show that the HSP-solid SiO₂ particle hybrid arrangement has one more refractive index variation gradient than the other two arrangement modes in the height of 0-40 nm (Fig. 6). However, since the effective medium theory can only qualitatively explain part of the results, the simulation via COMSOL Multiphysics is a strategy that can quickly and accurately optimize the experimental scheme of AR coatings.

The AR performance of coatings constructed by resin-anchored SiO₂ particles is studied by COMSOL Multiphysics. The results show that the average reflectance of the coating constructed by HSPs (radius of 100 nm, hollowness degree of 0.7) arranged in a square lattice can be reduced to 0.57% in the visible light band. Compared with the bare PC substrate, the reflectance of the coating is reduced by 79.7% with the incidence angle of 0°-75°. The conditions such as hollowness degree of 0.7-0.8, resin coverage height of half the height of HSPs, and small spacing between particles are favorable to the construction of surfaces with outstanding AR performance. The hexagonal lattice arrangement of HSPs results in lower reflectivity in the 500-780 nm band, while the square lattice arrangement leads to lower reflectivity in the 380-500 nm band. When the gaps between the HSPs arranged in hexagonal lattice mode are doped with solid SiO₂, the AR performance of the coating can be further improved in a broader wavelength range, and the average reflectance in the whole visible light range can be as low as 0.24%. Finally, the effective medium theory is adopted to further explore the AR mechanism of the coating. Some qualitative results are consistent with the simulation results.