Reflectance diffuse

There are quite a few cases where these two types of reflectance appear in combination. 

The quantitative description of diffuse reflectance measurements is known from thin-layer chromatography. Taking a powdery sample with such a large thickness (d = oo) that no reflection at the support material can be observed, the reflectivity of the sample is connected to the stray coefficients as well as with the absorption coefficient k. Kubelka and Munk [97] 

The equation given above allows a quantitative determination of the concentrations of the particles in such a layer. It can be used to follow a photoreaction in powdery medium. This type of layer is schematically represented in Fig. 4.24. The light path for the incident and diffuse reflected radiation are included in the figure. 

Problems with quantification are well known from the application of thin- 

Various models have been proposed that seek, with varying degrees of success, to quantify the reflectance and the concentration. The best known is the Kubelka-Munk model (Kubelka and Munk, 1931) which is sometimes called the 

This relationship works well for many different types of scatterers and for low concentrations of the absorber. The best results have been obtained for mixtures of absorbing and nonabsorbing powders (Fig. 9.15) and for absorbers adsorbed on a colorless solid. A fair agreement has been obtained also for evaluation of colored zones on paper chromatograms. A better result for this type of sample has been obtained using the modified formula (Hecht, 1983) 

In this case, the value of reflectance for a pure scatterer Ro is used to normalize the measurement. Parameters J3 and Qr are defined in terms of empirical parameters related to reflection (r), transmission (t), and absorption (/i) 

for a highly reflecting and minimally transmitting sample, Qr = 1, and (9.33) simplifies to 

The empirical parameters r, t, and jj. are used to adjust the equation to the morphology of the sample. 

Kubelka and Munk developed a theory describing the diffuse reflectance process for powdered samples, which relates the sample concentration to the scattered radiation intensity. The Kubelka-Munk equation is as follows  

An alternative relationship between the concentration and the reflected intensity is now widely used in near-infrared diffuse reflectance spectroscopy. The relationship is analogous to the Beer-Lambert law, which is discussed in Chapter 5  

Unlike densitometric determinations where absorption measurements are made by transmission through the surface of the thin layer, measurements of densitometry by reflectance are based on the diffusely reflected light from the surface of the layer. Thus, the light source and phototube are mounted on the same side of the absorbing surface. 

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

If relation 2.26 is introduced into eqn.2.25 the following function is obtained  

When applied to a spot on a chromatogram where the reflectance of the spot is measured relative to the adsorbent background, the term K in function 2.27 may be replaced by the product 2.3 e c, where e is the molar extinction coefficient and c is the molar concentration. The Kulbeka-Munk function then becomes 

A comparison of reflectance and transmission in absorption measurements is of interest 

The DR experiment reqnires that the incident beam penetrate into the sample, bnt the path length is not well defined. The path length varies inversely with the sample absorptivity. The resnlt-ing spectrum is distorted from a fixed path absorbance spectrum and is not nsefnl for qnantitative analysis. Application of the Kubelka-Mnnk eqnation is a common way of making the spectral response linear with concentration. 

R is the ratio of the sample reflectance spectrum at infinite sample depth to that of a nonabsorbing matrix such as KBr K is a proportionality constant C is the concentration of absorbing species 

The Kubelka-Munk equation gives absorbance-like results for DR measurements, as can be seen by comparing it to Beer s law, A = abc = Kc for a fixed path length. In Beer s law, is a proportionality constant based on the absorption coefficient and the path length. K is also a proportionality constant, but based on the ratio of absorption coefficient to scattering coefficient. The term/(R J can be considered a pseudoabsorbance.  

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Enloe, Noise-like structure in the image of diffusely reflecting objets in coherent illumination . Bell Syst. Tech. I., vol. 46, p.1479(1967). 

DRIFTS Diffuse reflectance infrared Fourier-transform Same as IR Same as IR... 

Vibrational Spectroscopy. Infrared absorption spectra may be obtained using convention IR or FTIR instrumentation the catalyst may be present as a compressed disk, allowing transmission spectroscopy. If the surface area is high, there can be enough chemisorbed species for their spectra to be recorded. This approach is widely used to follow actual catalyzed reactions see, for example. Refs. 26 (metal oxide catalysts) and 27 (zeolitic catalysts). Diffuse reflectance infrared reflection spectroscopy (DRIFT S) may be used on films [e.g.. Ref. 28—Si02 films on Mo(llO)]. Laser Raman spectroscopy (e.g.. Refs. 29, 30) and infrared emission spectroscopy may give greater detail [31]. 

Willey R R 1976 Fourier transform infrared spectrophotometer for transmittance and diffuse reflectance measurements Appl. Spectrosc. 30 593-601... 

Vreugdenhil A J and Butler I S 1998 Investigation of MMT adsorption on soils by diffuse reflectance infrared spectroscopy DRIFTS and headspace analysis gas-phase infrared spectroscopy HAGIS Appl. Organomet. Chem. 

If, instead of assuming diffuse reflection at the wall, it is postulated that a fraction f of the incident molecules is scattered diffusely and the rest suffer specular reflection, the right hand side of equation (2.8) must be multiplied by a factor (2 - f)/f. ... 

Diffuse reflectance infrared Fourier transform spectroscopy... 

Several factors affect the bandshapes observed ia drifts of bulk materials, and hence the magnitude of the diffuse reflectance response. Particle size is extremely important, siace as particle size decreases, spectral bandwidths generally decrease. Therefore, it is desirable to uniformly grind the samples to particle sizes of <50 fim. Sample homogeneity is also important as is the need for dilute concentrations ia the aoaabsorbiag matrix. 

Fig. 3. Infrared spectra of polystyrene (a) transmission of a 33-p.m thick polystyrene film (b) diffuse reflection of polystyrene powder at a concentration of...

Diffuse reflection iavolves reflecting the iafrared beam off of a soHd sample, as ia specular reflectioa, but it is the aoaspecular portioa of the reflected radiatioa that is coUected. Whea an ftir spectrometer is used, diffuse reflection is caUed DRIFTS (diffuse reflectance iafrared Fourier-transform... 

Several properties of the filler are important to the compounder (279). Properties that are frequentiy reported by fumed sihca manufacturers include the acidity of the filler, nitrogen adsorption, oil absorption, and particle size distribution (280,281). The adsorption techniques provide a measure of the surface area of the filler, whereas oil absorption is an indication of the stmcture of the filler (282). Measurement of the sdanol concentration is critical, and some techniques that are commonly used in the industry to estimate this parameter are the methyl red absorption and methanol wettabihty (273,274,277) tests. Other techniques include various spectroscopies, such as diffuse reflectance infrared spectroscopy (drift), inverse gas chromatography (igc), photoacoustic ir, nmr, Raman, and surface forces apparatus (277,283—290). 

A method for measuring the diffuse reflectance from a black paste with a black tile standard. The low numbers represent the jettest or most intense black grades. 

QUALITY CONTROL OF AGROCHEMICAL FORMULATIONS BY DIFFUSE REFLECTANCE NEAR INFRARED SPECTROMETRY... 

A solvent free, fast and environmentally friendly near infrared-based methodology was developed for the determination and quality control of 11 pesticides in commercially available formulations. This methodology was based on the direct measurement of the diffuse reflectance spectra of solid samples inside glass vials and a multivariate calibration model to determine the active principle concentration in agrochemicals. The proposed PLS model was made using 11 known commercial and 22 doped samples (11 under and 11 over dosed) for calibration and 22 different formulations as the validation set. For Buprofezin, Chlorsulfuron, Cyromazine, Daminozide, Diuron and Iprodione determination, the information in the spectral range between 1618 and 2630 nm of the reflectance spectra was employed. On the other hand, for Bensulfuron, Fenoxycarb, Metalaxyl, Procymidone and Tricyclazole determination, the first order derivative spectra in the range between 1618 and 2630 nm was used. In both cases, a linear remove correction was applied. Mean accuracy errors between 0.5 and 3.1% were obtained for the validation set. 

DETERMINATION ORGANIC COMPOUNDS BY DIFFUSE REFLECTION SPECTROSCOPY... 

Fig. 2. Diffuse reflectance FTIR spectra showing evidence of Pb-O-Si bonding at a silane/lead oxide interface (from Ref. [30]).

In all cases, broad diffuse reflections are observed in the high interface distance range of X-ray powder diffraction patterns. The presence of such diffuse reflection is related to a high-order distortion in the crystal structure. The intensity of the diffuse reflections drops, the closer the valencies of the cations contained in the compound are. Such compounds characterizing by similar type of crystal structure also have approximately the same type of IR absorption spectra [261]. Compounds with rock-salt-type structures with disordered ion distributions display a practically continuous absorption in the range of 900-400 cm 1 (see Fig. 44, curves 1 - 4). However, the transition into a tetragonal phase or cubic modification, characterized by the entry of the ions into certain positions in the compound, generates discrete bands in the IR absorption spectra (see Fig. 44, curves 5 - 8). 

Artifact removal and/or linearization. A common form of artifact removal is baseline correction of a spectrum or chromatogram. Common linearizations are the conversion of spectral transmittance into spectral absorbance and the multiplicative scatter correction for diffuse reflectance spectra. We must be very careful when attempting to remove artifacts. If we do not remove them correctly, we can actually introduce other artifacts that are worse than the ones we are trying to remove. But, for every artifact that we can correctly remove from the data, we make available additional degrees-of-freedom that the model can use to fit the relationship between the concentrations and the absorbances. This translates into greater precision and robustness of the calibration. Thus, if we can do it properly, it is always better to remove an artifact than to rely on the calibration to fit it. Similar reasoning applies to data linearization. 

As an example of the second case, we may have conformationally disordered chains, but long-range order in the positions of the chain axes (condis crystals [5]). Fiber spectrum features are the occurrence of sharp reflections on the equator only and diffuse reflections on the other layer lines. 

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