Diffuse-reflectance spectroscopy Kubelka-Munk function

In the diffuse reflectance mode, samples can be measured as loose powders, with the advantages that not only is the tedious preparation of wafers unnecessary but also diffusion limitations associated with tightly pressed samples are avoided. Diffuse reflectance is also the indicated technique for strongly scattering or absorbing particles. The often-used acronyms DRIFT or DRIFTS stand for diffuse reflectance infrared Fourier transform spectroscopy. The diffusely scattered radiation is collected by an ellipsoidal mirror and focussed on the detector. The infrared absorption spectrum is described the Kubelka-Munk function ... 

It is usually considered more difficult to evaluate and quantify diffuse reflectance data than transmission data, because the reflectance is determined by two sample properties, namely, the scattering and the absorption coefficient, whereas the transmission is assumed to be determined only by the absorption coefficient. The absorbance is a linear function of the absorption coefficient, but its counterpart in reflection spectroscopy, the Kubelka-Munk function (sometimes also called remission2 function), depends on both the scattering and the absorption coefficient. Often, researchers list a number of prerequisites for application of the Kubelka-Munk function, but, in contrast, transmittance is routinely converted without comment into absorbance. 

Generally, the assumption is made that scattering does not depend on the wavenumber so that the conversion of the measured reflectance spectrum R by means of the Kubelka-Munk function F R), results in an absorption-proportional representation. As for ATR and reflection-absorption spectroscopy, also the diffuse-reflectance spectmm does not consist of dispersion features but band-like structures. For changes in low absorption, the sensitivity of diffuse reflectance is greater than the one of transmittance, while strong absorption bands are less pronounced in the diffuse-reflection (see Fig. 6.4-18). Therefore, diffuse-reflection spectra resemble poorly resolved transmittance spectra. For diffuse reflectance spectra where R is in the order of 0.01 or below, the function -log R or just I / R is equally well suited for conversion (Olinger and Griffiths, 1988). Such level are found with compact samples such as polymer foams or varnishes with filler (Otto, 1987 Korte and Otto, 1988). 

Ground-state absorption studies of the probe molecules adsorbed within zeolites were performed by UV-visible diffuse reflectance spectroscopy. Cationic form of the zeolite without probe molecule was used as a comparison sample. The remission function was calculated by using the Kubelka-Munk equation. Steady-state photoluminescence studies were carried out with the Hilger spectrofluorimeter. The spectra were recorded at room temperature and 77 K, respectived. 

UV-Vis spectroscopy in solution is probably one of the most frequently applied spectroscopic methods in the quantitative analysis of pharmaceuticals (see other chapters of this book). In solid-state analysis, this situation is quite the opposite since most solids are too opaque to permit the use of this technique in the conventional transmission mode. UV-Vis spectroscopy on solids can only be realized via diffuse-reflection techniques connected with mathematical corrections (e.g. Kubelka-Munk function) and lacking the high reproducibility of UV-Vis spectroscopy in solution owing to particle dispersion effects. The number of published papers on the application of UV-Vis spectroscopy to solid pharmaceuticals is very small and these papers include topics such as photo-stabihty of dyes and active ingredients in tablets, drug-excipient interactions in dmg products, quantitative measurements on discolouration in dmg products, and others. For further reading we refer to Brittain [26] and the literature cited therein. 

This function has become the fundamental law of diffuse reflectance spectroscopy. It relates the diffuse reflectance R of an infinitely thick, opaque layer and the ratio of the absorption and scattering coefficients K/S. Since the scattering coefficient is virtually invariable in the presence of a chromatographic band, the Kubelka-Munk equation can be written in the form ... 

For diffuse reflectance spectroscopy the Kubelka-Munk function, f Roo), is most appropriate [128, 129]. The K-M theory indicates that linear relationships of band intensity vs. concentration should result when intensities are plotted as the K-M function f Roo) = k/S, where k is the absorption coefficient and S is the scattering coefficient (cfr. Chp. 1.2.1.3). The use of the K-M equation for quantitative analysis by diffuse reflectance spectroscopy is common for measurements in the visible, mid-IR and far-IR regions of the spectrum. Measurement of scattered light (ELSD) allows quantitative analysis. 

The samples were characterized by UV-visible reflectance spectroscopy using a Varian-Carry-5 spectrometer equipped with a double monochromator. Diffuse reflectance spectra were recorded in air at room temperature in the range 200-800 nm against alumina as reference. Spectra are presented indicating the frequency of the Schulz-Munk-Kubelka equation as function of the wavelength. 

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