Theoretical study of the scattering efficiency of rutile titanium dioxide pigments as a function of their spatial dispersion

We propose an original theoretical framework to model the scattering efficiency of white paint films as a function of the volume fraction and spatial state of dispersion of rutile titanium dioxide pigments, taking into account electromagnetic couplings. Numerical calculations are performed using a multiple T matrix formalism on an "elemental" volume extracted from the bulk of the paint and which we model as pigments and fillers in a polymer matrix. Qualitative studies show that, due to the dependent scattering phenomenon, the size of fillers can modulate the magnitude of loss in scattering efficiency by modifying the spatial state of dispersion of the pigments in the polymer matrix. In particular, fillers whose size is comparable to the dimension of the pigments improve the scattering efficiency by impeding crowding. It is also shown that the optical properties of the bulk material at arbitrary concentration can be approximated by extrapolating the optical properties calculated on a limited number of scatterers.