Mie scattering theory applied to light scattering of large nonhomogeneous colloidal spheres

Colloidal suspensions made of smart core-shell structures are of current interest in many fields. Their properties come from the possibility of varying the core and shell materials for modifying the composite particles' chemical, biological, and optical properties. These particles are formed with a material with a constant refractive index core and a shell with a refractive index decaying until it matches the solvent refractive index. Poly(N-IsoPropyl AcrylaMide) (PNIPAM) is a typical example of materials forming shells. In this report, we present how to apply Mie scattering theory to predict and understand the static light scattering of large nonhomogeneous colloidal particles with spherical symmetry whose size is comparable with or larger than the light wavelength used for developing scattering experiments, where the Rayleigh-Gans-Debye approximation is not valid. Here, the refractive index decay was approximated by a Gaussian RI profile numerically evaluated through a multilayer sphere. We calculated the form factor functions of suspensions of PNIPAM microgels previously reported and core-shell suspensions made of polystyrene/PNIPAM at 20 and 40 °C synthesized by us. In all the cases, our method succeeded in providing the scattering intensity as a function of the angle. The software for using the numerical method is fairly straightforward and is accessible as an open-source code. The results can not only help predict and understand the photonic properties of microgels with large core-shell structures but also for any particle with a refractive index distribution with spherical symmetry, as in the case of microgels with super chaotropic agents, hollow microgels, or microparticles.