Wavelength dependence of Kubelka–Munk scattering spectra for studies of TiO2 microstructure and aggregation in paints

Abstract

The wavelength exponent β is easily determined from diffuse reflectance spectra as the gradient of a log–log plot of the Kubelka–Munk scattering coefficient (S) against wavelength. Previous work suggests that β provides a useful relative measure of the size of scattering units applicable to many particulate systems. This article examines the applicability of β to paints, specifically studies of TiO2 aggregation, and comments on its wider use for pigmented coatings. Modelling using multisphere T-matrix Mie methods shows that β varies nearly linearly with the mean aggregate size. Experimental data shows good correlation between the state of aggregation and β. However, β depends strongly on the volume fraction of TiO2 owing to the effects of dependent scattering arising from crowding, therefore comparisons between paints can only be made at constant effective TiO2 volume fraction. A simple effective medium refractive index model in conjunction with Mie scattering appears to give a good account of the behavior of both S and β with increasing TiO2 volume concentration. When air is incorporated into the coatings at high pigment volume fractions, scattering is much more complicated. In this case it appears very difficult to relate β directly to coating microstructure properties such as pore diameter.