This example shows how SPRAY can be used to predict colors of paints. In most cases paints consist of a transparent host material (resin) with embedded particles that scatter and absorb light. For the design of paints it is important to know how the amount of reflected light and its spectral composition depend on the concentrations and types of inclusions. Problems of this kind are often approached applying the so-called Kubelka-Munk theory. This rather old concept is a two-flux radiation transfer model. In its simplest form it assumes diffuse illumination, isotropic scattering and perfect interfaces air-resin and resin-substrate. The probabilities per distance for absorption K(l) and scattering S(l) must be known - these are the input quantities of the model. The Kubelka-Munk theory returns the diffuse reflection coefficient of the paint for each wavelength.
Using SPRAY you can do the same - but with less approximations and much more realisitic results. The required input quantities are the scattering and absorption properties of each particle species, the optical constants of all materials involved and - of course - the geometry of the setup like the thickness of the resin or the direction of the incident radiation. You can increase the complexity of the model as you like - approaching more and more the real paint.
This SPRAY application example investigates a very simple model paint. Spherical inclusions are embedded in a resin with a constant and real refractive index of 1.5 - the resin itself does not absorb light. The following inclusions are used:
The scattering and absorption properties of the inclusions are summarized in their individual sections (just double-click the links above).
The SPRAY configuration used to investigate the paint properties is described in the section 'The test system'. Before the actual work is done some short initial tests confirm the consistency of the setup.
The TiO2 spheres will be used to create diffuse light scattering almost independent of wavelength. In a first exercise we will learn how much inclusions we have to take in order to get a white paint covering a black substrate. The required amount strongly depends on the particle size. This is demonstrated comparing the case of large and small TiO2 spheres.
In a second step CdS clusters are added. They mainly function as absorbers in the blue and will be responsible for the color of the paint.