Diffusely reflecting particles

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. 

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). 

Particles are moved along their current velocity vectors without undergoing interactions for a time At which is chosen smaller than the mean collision time. If a particle hits the domain boundary, its velocity vector is modified according to the corresponding boundary condition (for example specular or diffuse reflection if a particle hits a wall) ... 

For some applications, especially such involving solid samples or fluids containing suspended particles, reflection spectroscopic systems are better suitable than transmission sensors. Apart from specular reflection, which provides comparatively little information and is of hardly any practical importance for IR sensing, two reflectrometric methods can be used to gain spectroscopic information about a sample diffuse reflection and transflection, a combination of transmission and diffuse reflection. 

The light reflected by a powdered solid will consist of a specular reflection component and of a diffuse reflection component. The specular component represents reflection of the incident light by the surfaces of the component particles, and it is characterized by a complete absence of light transmission through the interiors of the particles. By contrast, diffuse reflectance is associated with the radiation that penetrates into the particles to some extent and that then emerges from the bulk solid. This light will exhibit spectral characteristics that are modified from those of the incident beam by the electronic transitions that took place within the solid phase and at the boundaries of the component particles. 

Fig. 2 Reflectance spectra of pure KMn04 samples of differing particle sizes, illustrating the effect of particle size on the intensity of diffuse reflectance. Spectra are reported for particle-size ranges of (A) 1-2 jam, (B) 42-50 y.m, (C) 60-75 /urn, and (D) 100-150 /urn. (Data adapted from Ref. 12.)...

Depth profiling of a solid sample may be performed by varying the interferometer moving-mirror velocity (modulated IR radiation). By increasing the mirror velocity, the sampling depth varies, and surface studies may be performed. Limitations do exist, but the technique has proven to be quite effective for solid samples [21]. In addition, unlike diffuse reflectance sampling techniques, particle size has a minimal effect upon the photoacoustic measurement. 

In each of the aforementioned studies, qualitative IR spectroscopy was used. It is important to realize that IR is also quantitative in nature, and several quantitative IR assays for polymorphism have appeared in the literature. Sulfamethoxazole [35] exists in at least two polymorphic forms, which have been fully characterized. Distinctly different diffuse reflectance mid-IR spectra exist, permitting quantitation of one form within the other. When working with the diffuse reflectance IR technique, two critical factors must be kept in mind when developing a quantitative assay (1) the production of homogeneous calibration and validation samples, and (2) consistent particle size for all components, including subsequent samples for analysis. During the assay development for... 

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 ... 

The solids analysis described above can be taken to yet another level by correlating the color measurement to chemical properties. An excellent model system is vanadium pyrophosphate (VPO), which is a well-known catalyst for butane oxidation to maleic anhydride. During the synthesis of the catalyst precursor, solid V2O5 particles are dispersed in a mixture of benzyl alcohol and i-butanol. In this slurry phase, the vanadium is partly reduced. Addition of phosphoric acid leads to a further reduction and the formation of the VPO structure. With a diffuse reflectance (DR) UV-vis probe by Fiberguide Ind., the surface of the suspended solid particles could be monitored during this slurry reaction. Four points can be noted from Figure 4.4 ... 

In diffuse reflection spectroscopy, the spectrometer beam is reflected from, scattered by, or transmitted through the sample, whereas the diffusely scattered light is reflected back and directed to the detector. The other part of the electromagnetic radiation is absorbed or scattered by the sample [124,125]. Changes in band shapes or intensity as well as signal shifts can be affected by morphological and physicochemical properties of the sample or combinations thereof (e.g., chemical absorptions, particle size, refractive index, surface area, crystallinity, porosity, pore size, hardness, and packing density [126]). Therefore, NIR diffuse reflection spectra can be interpreted in dependence of various physical parameters [127]. 

Diffuse reflectance is an excellent sampling tool for powdered or crystalline materials in the mid-IR and near-IR spectral ranges. Heated reaction chambers for diffuse reflectance allow the study of catalysis and oxidation reactions in situ, and can evaluate the effects of temperature and catalyst behavior. Scratching sample surfaces with abrasive paper and then measuring the spectra of the particles adhering to the paper allows for analysis of intractable solids. Perhaps one of the greatest additional benefits is that this system is amenable to automation. 

In the creeping flow range, C is equal to the ratio of the terminal velocity to the terminal velocity in continuum flow. The value of C is sensitive to the nature of molecular reflections from the surface of the particle (E5). The accommodation coefficient, o-r, may be interpreted as the fraction of molecules undergoing diffuse reflection, the balance being specularly reflected. Typical values for lie between 0.8 and unity. For near-continuum flow. Basset (B9) showed that... 

The dielectric function of a metal can be decomposed into a free-electron term and an interband, or bound-electron term, as was done for silver in Fig. 9.12. This separation of terms is important in the mean free path limitation because only the free-electron term is modified. For metals such as gold and copper there is a large interband contribution near the Frohlich mode frequency, but for metals such as silver and aluminum the free-electron term dominates. A good discussion of the mean free path limitation has been given by Kreibig (1974), who applied his results to interpreting absorption by small silver particles. The basic idea is simple the damping constant in the Drude theory, which is the inverse of the collision time for conduction electrons, is increased because of additional collisions with the boundary of the particle. Under the assumption that the electrons are diffusely reflected at the boundary, y can be written... 

In the diffuse reflectance technique (Fig. 14.2d), light scattered by a thick layer of particles is directed by the integrating sphere to a detector. Absorption... 

Geiger H. Marsden, E. On a diffuse reflection of the a-particles. Proa R. Soa London, Ser. A 1909, 82, 495-500 http //www.chemteam.info/Chem-History/GM-1909.html. 

---