On the Effective Medium Theory for Silica Nanoparticles with Size Dispersion

Silica nanoparticles (SNPs) are pivotal in designing functional optical films, but accurately modeling their properties is hindered by the limitations of classical effective medium theories, which break down for larger particles and complex morphologies. We introduce a robust, effective medium theory that overcomes these limitations by incorporating full Mie scattering solutions, thereby accounting for size-dependent and multipolar effects. Our model is comprehensively developed for unshelled, shelled, mixed, and hollow SNPs randomly dispersed in a host medium. Its accuracy is rigorously benchmarked against 3D finite-element method simulations. This work establishes a practical and reliable framework for predicting the optical response of SNP composites, significantly facilitating the rational design of high-performance coatings, such as anti-glare layers, with minimal computational cost.