DRIFTS Kubelka-Munk equation

Specifically, data was presented describing moisture desorption and intermediate temperature air oxidation of a powdered sub-bituminous coal. In comparison to its companion method, PA-IR, DRIFT spectroscopy would appear to be the technique of choice for the study of such reaction processes involving powdered samples since the temperature and environment of the sample are more conveniently controlled. Also PA-IR in general requires longer data acquisition times than DRIFT to produce a similar quality S/N ratio (34), No effort has been made in this report to treat in any way the quantitative aspects which most surely at some point must be considered. Most quantitative work involving DR spectra has utilized the Kubelka-Munk Equation to mathematically treat the data. This Equation seems to apply mainly to species in highly reflecting matrices at low dilution. Therefore, it remains to be determined what treatment may be required for DR spectral data obtained from neat materials such as coal. 

In diffuse reflectance spectroscopy, there is no linear relation between the reflected light intensity (band intensity) and concentration, in contrast to traditional transmission spectroscopy in which the band intensity is directly proportional to concentration. Therefore, quantitative analyzes by DRIFTS are rather complicated. The empirical Kubelka -Munk equation relates the intensity of the reflected radiation to the concentration that can be used for quantitative evaluation. The Kubelka-Munk equation is defined as ... 

Diffuse reflectance IR spectroscopy has become an attractive alternative to mulls with the introduction of DRIFT cell by Griffiths,29 later modified by Yang.30 Since materials are dispersed in a nonabsorbing medium and not subjected to thermal or mechanical energy during sample preparation, DRIFT spectroscopy is especially suitable for the qualitative/quantitative analysis for polymorphs, which are prone to solid-state transformations. The Kubelka-Munk (K-M) equation,31 which is analogous to Beer s law for transmission measurements, is used to quantitatively describe diffusely-reflected radiation ... 

As you can see, the peaks in the Kubelka-Munk spectrum are smaller and have different relative intensities than those in the absorbance spectrum. To be clear, the only difference between these two spectra is how the y-axis units are plotted peak positions are the same. The equation derived by Kubelka and Munk relates the intensity of diffusely reflected light to concentration [8]. If you are going to perform quantitative DRIFTS you must measure the spectra in Kubelka-Munk units to obtain a calibration line, similar to how absorbance spectra must be used for quantitation in transmission experiments (see Chapter 5). However, if one is doing qualitative analysis, DRIFTS spectra plotted in absorbance or Kubelka-Munk units may be used. Since the DRIFTS experiment does not produce a true absorbance spectrum, it is best to call the y-axis units of a DRIFTS spectrum plotted in absorbance diffuse absorbance. All the DRIFTS spectra in this chapter are plotted in diffuse absorbance. 

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