Kubelka-Munk method

While direct, this method is the most difficult experimentally due to the diminutive nature of fiber diameters and the uncertainty involved with contact angle measurements and hysteresis. The value i ) can also be measured on flat sheets of the fiber material but due to fabric finishes and different surface properties incurred during manufacture, the surface energetics of the sheet and fiber may be very dissimilar. Therefore, the value of co8i i was determined in the following manner from detergency data. The Kubelka-Munk Equation (12-13),... 

The method can be rationalized by means of the Kubelka-Munk theory. For standards, see Table 1 ( Tinting strength, relative Photometric ). 

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... 

Diffuse reflection from powder sample is a complex combination of transmission, internal and external reflections, and scattering. It is dependent on the particle size, absorption and refractive indices of the studied material. The case of proper prepared powder diffuse reflection R carries the information primarily about the transmission spectrum of the sample (Willey 1976 Fuller and Griffiths 1978). The traditional method of the absorption spectra (K) calculation on the base of the diffuse reflection R is the Kubelka-Munk equation K = (1 - R)2S/2Rc, where S is the scattering coefficient, concentration of the studied material is c = 1 in our case. 

Is it a real absorption It is well known that analysis on the base of the Kubelka-Munk equation is applicable at diffuse reflection R not much less than R 30%. The case of low diffuse reflection the deviations from linearity should be taken into account. We have R is near 1%. So, we should be careful The case of strongly absorbing samples it is possible to dilute them in nonabsorbent powder, for example in KBr powder. We have not used this traditional method because were afraid of possible chemical reactions at nigh temperature treatment of the mixture of the hydrogenated SWNTs with KBr. 

Argyle et al. (2003, 2004) introduced a method to determine the average valence of Al203-supported VOx species under the conditions of propane ODH catalysis. First, calibration measurements were made the catalyst was reduced for various periods of time in H2 at 603 K, and then the amount of 02 required to fully restore the UV-vis spectra was measured by mass spectrometry. Spectra of the fully oxidized sample were recorded to generate the background. These relative reflectance spectra were converted by applying the Kubelka-Munk function and then the intensity in the range 1.5-1.9 eV was related to the extent of... 

Calibration is necessary for in-situ spectrometry in TLC. Either the peak height or the peak area data are measured, and used for calculation. Although the nonlinear calibration curve with an external standard method is used, however, it shows only a small deviation from linearity at small concentrations [94.95 and fulfils the requirement of routine pharmaceutical analysis 96,97J. One problem may be the saturation function of the calibration curve. Several linearisation equations have been constructed, which serve to calculate the point of determination on the basis of the calibration line and these linearisation equations are used in the software of some scanners. A more general problem is the saturation function of the calibration curve. It is a characteristic of a wide variety of adsorption-type phenomena, such as the Langmuir and the Michaelis-Menten law for enzyme kinetics as detailed in the literature [98. Saturation is also evident for the hyperbolic shape of the Kubelka-Munk equation that has to be taken into consideration when a large load is applied and has to be determined. 

Hecht, H.G. A comparison of the kubelka-munk, rozen-berg, and pitts-giovanelli methods of analysis of diffuse reflectance for several model systems. Appl. Spectrosc. 1983, 37, 348-354. 

In absorption photometry the pathlength of the cuvette is usually fixed. In conventional clinical chemical methods a dilution of the sample is necessary both to run the assay under optimized conditions and to make sure that the developed color of the reaction product is within the measurable absorbance range of a spectrophotometer. The thickness of the reagent carrier in reflec-tometry which is calculated by means of the Kubelka-Munk theory, is assumed to be infinite and hence of negligible significance. Hence, the linear range in reflection spectroscopy may be expected to exceed that of absorption spectroscopy with a consequential reduction in the frequency of sample dilution prior to measurement. 

The reflection of light from opaqne and translncent materials depends on the ratio of absorption to scatter as affected by pigmentation, refractive index and the light-scattering properties of the material. The Kubelka-Munk (KM) method... 

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. 

The Kubelka-Munk two flux model predicted significantly different magnitudes of photon flux within the layers of a coating than a model based on the Lambert-Beer law. Equations and calculation methods are described and results are given that illustrate the effect of substrate reflectance, layer thickness and the absorption and scattering of the layer components on the photon flux and the light absorbed at various levels within the coating. 

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. 

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