Optical properties of deposit models for paints: full-fields FFT computations and representative volume element

Abstract

A 3D model of microstructure containing spherical and rhombi-shaped inclusions ‘falling’ along a deposit direction is used to simulate the distribution of nanoscale color pigments in paints. The microstructure’s anisotropy and length scales, characterized by their covariance functions and representative volume element, follow that of transversely isotropic or orthotropic media. Full-field computations by means of the fast Fourier method are undertaken to compute the local and effective permittivity function of the mixture, as a function of the wavelength in the visible spectrum. Transverse isotropy is numerically recovered for the effective permittivity of the deposit model of spheres. Furthermore, in the complex plane, the transverse and parallel components of the effective permittivity tensor are very close to the frontiers of the Hashin–Shtrikman’s domain, at all frequencies (or color) of the incident wave. The representative volume element for the optical properties of paint deposit models are studied. At fixed accuracy, it is much larger for the imaginary part of the permittivity than for the real part, an effect of the strong variations of the electric displacement field, exhibiting hot-spots, a feature previously described in the context of conductivity.