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International audienceWe 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

We demonstrate the interest of combining finite element calculations with the vector partial wave formulation (used in T-matrix and Mie theory) in order to characterize the electromagnetic scattering properties of isolated individual scatterers. This method consists of individually feeding the finite element problem with incident vector partial waves in order to numerically determine the T-matrix elements of the scatterer. For a sphere and a spheroid, we demonstrate that this method determines the scattering matrix to high accuracy. Recurrence relations for a fast determination of the vector partial waves are given explicitly, and an open-source code allowing the retrieval of the presented numerical results is provided.

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