Absorption and scattering properties of nanoparticles in an absorbing medium: modeling with experimental validation

Abstract

Absorption and scattering properties of nanoparticles immersed in an absorbing medium are essential in understanding the overall properties of composites and in designing materials with expected functionalities. In this paper, we establish a model based on both Kubelka-Munk theory and Mie theory that links the absorption and scattering properties of individual particles with the reflectance and transmittance spectra of its thin-film composite, supported by detailed experiments. Thin films consisting of TiO$_2$ nanoparticles embedded in PMMA are fabricated on glass substrates using spin-coating and then peeled off to form standalone samples for spectroscopy measurements. By using the Kubelka-Munk theory in combination with the Saunderson correction, the absorption $K$ and scattering $S$ coefficients of multiple nanoparticles are extracted from the measured transmittance and reflectance. On the other hand, the absorption $K$ and scattering $S$ coefficients are the sum of absorption and scattering cross-sections of individual particles, which are calculated from the Mie theory specified for particles in an absorbing medium, with the scattering $S$ coefficient further modulated by the anisotropy factor $g$. The effect of the particulate medium is incorporated through an effective refractive index. The overall model is validated by matching well between the $K-S$ coefficients extracted from experimental data and theoretical calculations. This agreement provides deep insight into the significant attenuating effect of absorption and scattering on each particle due to the surrounding medium. The validated model of nanoparticles immersed in an absorbing medium can be used to obtain preliminary results for materials designed in a number of applications, such as radiative cooling.