General Method for Determining Light Scattering and Absorption of Nanoparticle Composites

Abstract

Scattering and absorption from nanoparticles are of major importance in optical research as well as in a range of applications. The Kubelka–Munk two‐flux radiative transfer model gives a simple description of light scattering in nanoparticle composite materials, but inversion of experimental transmittance and reflectance data to obtain backscattering and absorption coefficients remains challenging. Here, a general method for evaluating these parameters from transmittance and reflectance spectra, combined with spectral angle resolved light scattering measurements is developed. The angular dependence is approximated by an extension of the empirical Reynolds–McCormick phase function, which is fitted to the experimental angle resolved light scattering data. This approach is verified by measurements on three typical nanoparticle/polymer composites containing plasmonic Au, ferromagnetic Fe3O4, and dielectric TiO2 particles. An approximation to the angular scattering pattern is further demonstrated, which can be applied to obtain the optical parameters using only reflectance and transmittance data, in cases where angle‐resolved measurements are not available. These results can be extended to a wide range of isotropic, anisotropic, and multiple scattering systems, and will be highly useful in the fields of light scattering coatings/metamaterials, UV‐shielding films, displays, absorption/scattering layers in solar cells and biological scatterers.

Scattering and absorption cross sections of light diffusing materials retrieved from reflectance and transmittance spectra of collimated radiation

“…An experimental sample configuration is considered in this Section: a polymeric medium containing submicron sized anatase (TiO 2 ) particles between two glass slides. We analyze reflectance and transmittance measurements in the wavelength range from 0.3 to 1.3 μm [28] carried out on this configuration. Besides the optical constants of the glass slides and of the PVP/water medium, those of the anatase (TiO 2 ) particles are required for theoretical modelling of the optical properties.…”

“…The Kubelka-Munk model was used to obtain S and K from diffuse reflectance measurements of paints containing submicron sized black carbon or FeMnCuO x particles [24] and of TiO 2 pigmented paints [25]. An extended Kubelka-Munk approach [26] has been used to retrieve scattering and absorption coefficients of suspended particle devices [14,27] and nanoparticle-polymer composites [28]. The Reichman model was applied to retrieve scattering and absorption coefficients of powder glass and porous sintered glass from reflectance and transmittance measurements [29].…”

“…Despite the fact that the present paper considers only two collimated fluxes, these must be considered within the formalism of the four-flux radiative transfer model (with two collimated and two diffuse fluxes), in order to avoid confusion with two-flux radiative transfer models of the Kubelka-Munk type, which focus on the diffuse fluxes. We consider a system consisting of TiO 2 particles dispersed in a matrix containing a weight ratio of polyvinylpyrrolidone (PVP) to water [28] of 0.8:1. Reflectance (R) and transmittance (T) spectra for these samples as well as for pure water and PVP/water were measured by using a Perkin Elmer Lambda 900 spectrometer [28].…”

“…We consider a system consisting of TiO 2 particles dispersed in a matrix containing a weight ratio of polyvinylpyrrolidone (PVP) to water [28] of 0.8:1. Reflectance (R) and transmittance (T) spectra for these samples as well as for pure water and PVP/water were measured by using a Perkin Elmer Lambda 900 spectrometer [28]. Section 2 describes the experimental sample arrangement, consisting of the layer under study sandwiched between two glass slides.…”

Effective backscattering and absorption coefficients of light diffusing materials retrieved from reflectance and transmittance spectra of diffuse radiation

“…According to the scanning electron microscope analysis, the average diameter of the particles is close to 0.20 μm, with a log-normal size distribution characterized by a standard deviation σ o = 0.15. Hence the values for the particle diameter vary between 0.16 and 0.25 μm, and their volume concentration is f = 0.066% [49,50]. As shown previously, some agglomeration seems to be present in the samples [14].…”