Extending the applicability of the four-flux radiative transfer method

A generalized four-flux method capable of modeling and tuning the spectral reflectance of a diverse range of complex composite coatings is presented. An example application is exploring and maximizing the visible and near-infrared (IR) spectral reflectance available from the diverse structures arising from combinations of the many practical paint ingredients that are available or can be made when applied to different substrates. This requires consideration of scatterers that can differ in composition, particle size, size distribution, and fill factor, and are held in place by a variety of organic binders, which typically partially absorb in the near IR. This extended model is further enhanced by an explicit matrix algorithm that allows analysis of diverse multilayer stacks. This is applied to a multilayer and is designed to model useful changes that result from varying the pigment fill factor as a function of depth within a layer. What we believe is a novel feature is the way the scattering affects matrix absorptance. The model includes contributions to total absorptance from the scattering pigments and from the paint binder that can arise in different bands or simultaneously at the same wavelengths. Model accuracy is demonstrated by example results when compared to experimental data on dried single layer paint profiles using imaged cross sections. The model input covering the actual pigment and binder properties used are material, shape, size, and size distributions, mass added, and the measured optical constants from 400 nm to 2,500 nm of the undoped binder resin layer. One interesting result is the comparison of a two-layered stack, with bigger particles in the first layer and smaller ones in the second, to one with the opposite depth profile.