Kubelka-Munk corrections

Figure 10.20—Devices allowing the study of samples by reflection, a) Diffuse reflection device b) attenuated total reflection (ATR) device c) comparison of the spectra of benzoic acid obtained by transmission (KBr disc) and by diffuse reflection using the Kubelka Munk correction. The depth of penetration of the IR beam depends on the wavelength. The absorbance for longer wavelengths would be overestimated if no correction was applied.

Figure 3. LSF calibration curve of vinyl silanized kaolin clay standards at 3066 cm 1 (Kubelka-Munk corrected)—from Reference 2.

Figure 6. Spectra of various concentrations of vinyl silanized aluminum hydroxide powders used as analytical standards (Kubelka-Munk corrected).

Figure 10.18 Spectra by reflection, (a) From a sample of plexiglass, three types of reflection are displayed. Left, crude spectra and right, spectra after correction. Above, crude signal of specular reflection and the result in units of K following application of the Kramers-Kronig (transformation of the reflectance) calculation middle, spectrum obtained by diffused hght comparison of the crude spectrum with the Kubelka-Munk correction below, spectrum obtained by ATR, the latter requiring a fine correction to reduce the absorbance at higher wavelengths which would be overestimated (b) comparison of two spectra of benzoic acid, one obtained through transmission, the other by diffused reflection and subsequent K-M correction.

Diffuse Reflection. Using a set of flat and elliptical mirrors, this device can measure a sufficient amount of light diffused by a sample dispersed in KBr powder (Fig. 10.20). By comparing the diffused reflection obtained with neat KBr, a result resembling the transmission spectrum is obtained. Kubelka-Munk s correction can be used to improve the spectrum. 

In a previous publication [2], the authors have demonstrated that excellent quantitative FT-IR measurements could be made on various silanized kaolin clays. Figure 1, for example, shows superimposed calibration spectra at various concentrations of vinyl silanized clay from [2], and Fig. 2, the corresponding least squares fit (LSF) plot showing a correlation coefficient of 0.9951 which is comparable to the Kubelka-Munk (KM) corrected LSF data shown in Fig. 3 since the Alog (1/R) values are small. 

Given the limitations of Kubelka-Munk, a more complex equation was developed by J. L. Saunderson that contrasted the refractive index of the sample to that of air. With the addition of surface or specular (K,) and internal (K2) correction factors the equation became more practical for use in opaque systems. 

The reflectance spectra were recorded in the geometry R0,d (4) in the frequency range 5000-40,000 cm-1 in a previously described apparatus (4, 6). The absorbance is represented by the logarithm of the Schuster-Kubelka-Munk (SKM) function, F(RX) = (1 — RX)2/2RX, where Rx is the reflectance measured against a white standard. Since the comparison of the reflectance spectra with the transmission spectra of complexes in molecular sieves revealed that the scattering coefficient is a constant independent of the wavelength (4), the logarithm of the SKM function is, but for an additional constant, a correct representation of absorbance. 

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. 

The UV/vis spectra were recorded on a Perkin-Elmer Lambda 900 UV/vis spectrometer equipped with a diffuse reflectance and transmittance accessory (PELA-1000). The accessory is essentially an optical bench that includes double-beam transfer optics and a six-inch integrating sphere. Background corrections were recorded using a Labsphere SRS-99-020 standard. The reflectance data from were converted to k/s values by using the Kubelka-Munk theory (1931). The Kubelka-Munk equation describes the infinite reflectance as a function of absorption and scattering ... 

The disturbance by specular reflection may be reduced considerably by technical means (trapping) on the reflection attachment. The resulting diffuse reflection spectrum then has to be corrected in order to correspond to the absorbance of a transmission spectrum. This mathematical procedure is generally performed according to the Kubelka-Munk theory. For a comprehensive and critical discussion of this theory the reader is referred to the Further reading section. 

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