Application of representative layer theory to near-infrared reflectance spectra of powdered samples

The diffuse reflectance near-infrared (NIR) spectrum of a powdered sample includes the contribution of specular and diffuse reflectance, which is a function of absorbance and scattering. The fraction of light scattered depends in a complex manner on the physical properties of the sample such as particle size, refraction index, etc. Several theories to study the dependence of NIR spectra on the particle size have been proposed. The best known is the Kubelka-Munk model, an approach based on continuous mathematics. Recently Dahm and Dahm put forward an alternative method, the representative layer theory (RLT), which uses discontinuous mathematics as a basis. This approach can be used to identify and disentangle the scattering and absorbance signals as well as their dependence on the particle size. The scattering and absorption coefficient of NaCl (a nonabsorbing material) and of potassium hydrogen phthalate, KHP (a strong absorber), have been estimated through the application of the representative layer theory, working on a particle size range from 63 to 450 microm. In both samples, the absorption coefficient of the sample (K) remains constant and practically independent of the particle size, while the scattering coefficient of the sample (S) decreases when the particle diameter increases, becoming stable around a diameter of 250 microm.