Kubelka diffuse reflection

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 nature and the distribution of different types of Fe species in calcined (C) and steamed (S) samples were investigated by means of UV-vis spectroscopy. UV-vis spectra of Fe species were monitored on UV-vis spectrometer GBS CINTRA 303 equipped with a diffuse reflectance attachment with an integrating sphere coated with BaS04 and BaS04 as a reference. The absorption intensity was expressed using the Schuster-Kubelka-Munk equation. 

Fig-1 Absorption spectra, obtained through the Kubelka-Munk transformation of diffuse reflectance spectra, of indolinonaphthospiropyran adsorbed onto silica gel. Spectra are shown for coverages of (A) 2.35, (B) 9.49, (C) 34.2, and (D) 46.7 /ig/m2. (Data adapted from Ref. 12.)... 

The theory associated with diffuse reflectance has been developed in great detail, and its full exposition is beyond the scope of this chapter. Interested readers are referred to the texts by Kortum 1], and by Wendlandt and Hecbt [2], where the general theory is presented in sufficient detail. The most generally accepted theory concerning diffuse reflectance was developed by Kubelka and Munk [3,4],... 

The Kubelka-Munk theory treats the diffuse reflectance of infinitely thick opaque layers [4], a situation achieved in practice for UV/VIS spectroscopy through the use of powder path lengths of at least several millimeters. In this instance, the Kubelka-Munk equation has the form... 

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 ... 

Spectra of solid samples are usually recorded in the units of reflectance (R) or percent reflectance (%/ ), which is analogous to percent transmittance in that reflectance equals the ratio of the reflected radiation to the incident radiation. With diffuse reflectance, the reflected signal is attenuated by two phenomena absorption (coefficient k) and scattering (coefficient s). Lollowing the Kubelka-Munk theory, these two coefficients are related to the reflectance of an infinitely thick sample, by... 

Opaque minerals like iron oxides are frequently examined in the reflectance mode - and usually give diffuse reflectance spectra. Reflectance spectra provide information about the scattering and absorption coefficients of the samples and hence their optical properties. The parameters of reflectance spectra may be described in four different ways (1) by the tristimulus values of the CIE system (see 7.3.3) (2) by the Kubelka-Munk theory and (3) by using the derivative of the reflectance or remission function (Kosmas et al., 1984 Malengreau et ak, 1994 1996 Scheinost et al. 1998) and, (4) more precisely, by band fitting (Scheinost et al. 1999). 

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... 

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).

Diffuse reflectance R is a function of the ratio K/S and proportional to the addition of the absorbing species in the reflecting sample medium. In NIR practice, absolute reflectance R is replaced by the ratio of the intensity of radiation reflected from the sample and the intensity of that reflected from a reference material, that is, a ceramic disk. Thus, R depends on the analyte concentration. The assumption that the diffuse reflectance of an incident beam of radiation is directly proportional to the quantity of absorbing species interacting with the incident beam is based on these relationships. Like Beer s law, the Kubelka-Munk equation is limited to weak absorptions, such as those observed in the NIR range. However, in practice there is no need to assume a linear relationship between NIRS data and the constituent concentration, as data transformations or pretreatments are used to linearize the reflectance data. The most used linear transforms include log HR and Kubelka-Munk as mathemati-... 

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.

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. 

UV-VIS-NIR diffuse reflectance (DR) spectra were measured using a Perkin-Elmer UV-VIS-NIR spectrometer Lambda 19 equipped with a diffuse reflectance attachment with an integrating sphere coated by BaS04. Spectra of sample in 5 mm thick silica cell were recorded in a differential mode with the parent zeolite treated at the same conditions as a reference. For details see Ref. [5], The absorption intensity was calculated from the Schuster-Kubelka-Munk equation F(R ,) = (l-R< )2/2Roo, where R is the diffuse reflectance from a semi-infinite layer and F(R00) is proportional to the absorption coefficient. 

Diffuse reflectance FTIR spectra of the ground Mo03/Al203 catalysts were recorded on an FTIR instrument (Nicolet, Model 740, MCT detector). The microreactor in the flow system was replaced by an FTIR cell. The cell used a Harrick diffuse reflectance accessory (DRA-2CO) fitted with a controlled environmental chamber (HVC-DRP). Spectra (500 scans, 4 cm 1 resolution) were presented in Kubelka-Munk units and recorded at RT. 

The generally accepted theory of diffuse reflectance was developed originally by Kubelka and Munk [43,44] for application to infinitely thick, opaque layers. 

Fig. 9.15 Diffuse reflectance from solid mixture of KM11O4 and KCIO4. The solid line is calculated from (9.32) (adapted from Kubelka et al., 1931)...

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. 

Fig. 11.6 Absorption spectra K restored from diffuse reflection R by using the Kubelka-Munk equation. Spectra 1, 2, and 3 are initial nanostructures, hydrogenated and annealed at 700°C during 6 h, respectively, (a) Spectra of NFs, (b) SWNTs. Dashed curves are Drude approximation of the absorption spectra, K = A. v0 5...

The Kubelka-Munk theory of diffuse reflectance is a good description of the optical properties of paper. The two parameters of the theory, absorption and scattering coefficient, are purely phenomenological, but are closely related to basic properties of paper. The absorption coefficient is approximately a linear function of the chrcmgphore concentration in the paper. The scattering coefficient is related to the nonbonded fiber surface area in the paper, or the area "not in optical contact," and the Fresnel reflectivity of that surface. 

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. 

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 ... 

Figure 8A Diffuse reflectance spectra recorded following the steady-state photolysis (visible light) of Acid Orange 7 adsorbed on Ti02 nanoparticles (0.02 mmol A07/g of Ti02). The ordinate scale is expressed in Kubelka-Munk units, where R is the reflectivity measured at the corresponding wavelength. (From Ref. 258.)...

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