Kubelka—Munk function

Strictly speaking the Kubelka-Munk function is only applicable und ing conditions [67 — 73] ... 

These general requirements also apply to adsorbents laden with s these requirements are not fulfilled to the same extent in thin-layer ( phy. So the Kubelka-Munk function does not apply without qualif... 

The intensity of the emitted fluorescence In is, therefore, directly proportional to the amount of substance applied a This relationship is much simpler than the Kubelka-Munk function and always leads to a linear calibration curve passing through the origin If this is not true then interference is occurring [5]... 

Ultraviolet-visible (UV-vis) diffuse reflectance spectra of supported WOx samples and standard W compounds were obtained with a Varian (Cary 5E) spectrophotometer using polytetrafluoroethylene as a reference. The Kubelka-Munk function was used to convert reflectance measurements into equivalent absorption spectra [12]. Spectral features of surface WOx species were isolated by subtracting from the W0x-Zr02 spectra that of pure Z1O2 with equivalent tetragonal content. All samples were equilibrated with atmospheric humidity before UV-vis measurements. 

To continue the derivation, the next step is to determine the variation of the absorbance readings starting with the definition of absorbance. The extension we present here, of course, is based on Beer s law, which is valid for clear solutions. For other types of measurements, diffuse reflectance for example, the derivation should be based on a suitable function of T that applies to the situation, for example the Kubelka-Munk function for diffuse reflectance should be used for that case ... 

The term on the left side of Eq. (4) is often termed the remission function (or the Kubelka-Munk function), and it is frequently denoted by f(Rx). Equation (4) indicates that a linear relationship should exist between f(Rx) and the sample absorption. 

Take the logarithm of the Kubelka-Munk function yields... 

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 ... 

If the scattering coefficient does not depend on the infrared frequency, the Kubelka-Munk function transforms the measured spectrum RJ V) into the absorption spectrum K v). In situ cells for DRIFT studies of catalysts have been described [10] and are commercially available. 

The Kubelka-Munk function (f (r)), the remission function, is often used to relate diffuse reflectance spectra to absorption and scattering parameters. This function is the ratio of the absorption, k, and the scattering, s, coefficient and is related to the diffuse reflectance, r, by... 

If over the region of interest, the scattering coefficient hardly varies with wavelength, the shapes of the remission spectrum and the absorption spectrum should be very similar. The relationship between the remission function and the reflectance spectrum is shown in Figure 7.2 left, and the Kubelka-Munk functions of the different iron oxides are illustrated in Figure 7.2, right. 

Fig. 7.2 Left Relationships between diffuse reflectance (r), the specular reflectance (R) and Kubelka-Munk function (f(r)) of maghemite. Right Kubelka-Munk function of various Fe oxides (Strens. Wood, 1979, with permission).

From this expression (Kubelka Munk function) it follows that, within the range of validity of the theory, q,/ depends only on the ratio of the absorption coefficient to the scattering coefficient, and not on their individual values. The equation has been most useful where reflectance measurements are used to obtain information about absorption and scattering (e.g., in textile dyeing, thin layer chromatography, and IR spectroscopy). 

Present data illustrate the technique for an in situ determination of surface areas. Related methods had been applied primarily to the study of site distributions in clay minerals, particularly by Russian workers (66), and they were used by Bergmann and O Konski in a detailed investigation of the methylene blue-montmorillonite system (3). In fact, changes in electronic spectra arising from surface interactions received sufficient attention in the past to warrant their review by A. Terenin (65). Most of these investigations involved transmittance spectra but new techniques in reflection spectrophotometry and applications of the Kubelka-Munk relation have facilitated the quantitative evaluation of spectra in highly turbid media (35, 69, 77). Thus, in agreement with the work of Kortiim on powders and anhydrous dispersions (31, 32, 33), our results demonstrate the applicability of the Kubelka-Munk function... 

Fig. II. UV-Visible reflectance spectra (Kubelka-Munk function vs. wavenumber) of (a) silicalite-1 (b) TS-1. (From Boccuti et al., 1989.)...

Fig. 1. (a) Diffuse reflectance spectra of P25 (thin line), TH (thick line), 3% [PtClJ/P25 (dashed line) and 4.0% H2[PtCl6]/TH (dotted line). The Kubelka-Munk function, F(R00), is used as the equivalent of absorbance, (b) Transformed diffuse reflectance spectra of P25 (thin line), TH (thick line), 3% [PtCl4]/P25 (dashed line) and 4.0% H2[PtCl6]/TH (dotted line). The bandgap energy was obtained by extrapolation of the linear part. 

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