Flocculation gradient technique in terms of Kubelka-Munk coefficients: Quantifying black-pigmented dispersions

The diffuse reflectance from a painted layer depends upon the layer thickness. The rate of change of diffuse reflectance when thickness increases is the flocculation gradient, which is valuable information about the degree of pigment dispersion in paint. The simple determination method is called the flocculation gradient technique and is suitable to quantify the pigment dispersions in low-absorptive and high-scattering paints. To make the method useful for black-pigmented paints as well, we modified it by applying the Kubelka-Munk theory. This makes it possible to solve the problem of the very narrow linearity region that appears in the diffuse reflectance vs. thickness curve because of high absorption. The modified method allows one to quantify the degree of dispersion in black thickness-sensitive spectrally selective paints, which are used as absorbers in solar collectors.