Scattering and Interference

Superficially, the attenuation is related to the random projected areas of the particles. The relationship is more complex than this however, due to the breakdown in the laws of geometric optics so that complex diffraction, scattering, interference and absorption effects have to be considered. For small particles, an amount of light flux, equal in magnitude to that incident upon the particle, is diffracted away from the forward direction (Figure 7.10), making their effective obscuration area twice their projected... 

New XAFS data analysis protocols, including wavelet analysis, principle component analysis, and explicit treatment of multi-electronic excitations, multiple scattering interferences, and anharmonic effects are improving the accuracy of EXAFS analysis of environmental, biological, and geochemical samples (Wasserman 1997 Wasserman et al. 1999 Ressler et al. 2000 Beauchemin et al. 2002 Farges 2002 Farges et al. 2002 Frenkel et al. 2002 Isaure et al. 2002 Munoz et al. 2002). 

Figure Bl.17.4. Visualization of image contrast fomiation methods (a) scattering contrast and (b) interference contrast (weak phase/weak amplitude contrast).

Accuracy Under normal conditions relative errors of 1-5% are easily obtained with UV/Vis absorption. Accuracy is usually limited by the quality of the blank. Examples of the type of problems that may be encountered include the presence of particulates in a sample that scatter radiation and interferents that react with analytical reagents. In the latter case the interferant may react to form an absorbing species, giving rise to a positive determinate error. Interferents also may prevent the analyte from reacting, leading to a negative determinate error. With care, it maybe possible to improve the accuracy of an analysis by as much as an order of magnitude. 

At a fundamental level, it has been shown that PECD stems from interference between electric dipole operator matrix elements of adjacent continuum f values, and that consequently the chiral parameters depend on the sine rather than the cosine of the relative scattering phases. Generally, this provides a unique probe of the photoionization dynamics in chiral species. More than that, this sine dependence invests the hj parameter with a greatly enhanced response to small changes in scattering phase, and it is believed that this accounts for an extraordinary sensitivity to small conformational changes, or indeed to molecular substitutions, that have only a minimal impact on the other photoionization parameters. 

Before scattering intensity measurements can be converted to molecular weights, the two corrections previously discussed—the dissymmetry correction for intraparticle interference and the extrapolation to zero concentration—must be introduced, or established to be negligible. The relationships given in the preceding sections unfortunately account rigorously for either only in the absence of the other. The theory of the concentration dependence of the scattered intensity applies to the turbidity corrected for dissymmetry, and the treatment of dissymmetry is strictly valid only at zero concentration (where interference of radiation scattered by different polymer molecules vanishes). 

Practically all classical methods of atomic spectroscopy are strongly influenced by interferences and matrix effects. Actually, very few analytical techniques are completely free of interferences. However, with atomic spectroscopy techniques, most of the common interferences have been studied and documented. Interferences are classified conveniently into four categories chemical, physical, background (scattering, absorption) and spectral. There are virtually no spectral interferences in FAAS some form of background correction is required. Matrix effects are more serious. Also GFAAS shows virtually no spectral interferences, but... 

The excitation maximum for BODIPY 493/503 C3 hydrazide occurs at 498 nm and its emission at 506 nm. Since this is an extremely small Stoke s shift, it may be difficult to avoid completely problems of excitation-light scattering interference in critical emission measurements unless sub-optimal excitation wavelengths are used. The molecule has an extinction coefficient in methanol of about 92,000M-1cm 1 at 493 nm. 

Total reflection x-ray fluorescence (TXRF) has become very popular for the conduct of microanalysis and trace elemental analysis [77-79]. TXRF relies on scatter properties near and below the Bragg angle to reduce background interference, and to improve limits of detection that can amount to an order of magnitude or moreover more traditional XRF measurements. As illustrated in Fig. 7.18, if x-rays are directed at a smooth surface at a very small angle, virtually all of the radiation will be reflected at an equally small angle. However, a few x-rays will excite atoms immediately at the surface, and those atoms will emit their characteristic radiation in all directions. One obtains very clean... 

Similar work was performed by Shaw et al.3 in 1999 when they used FT-Raman, equipped with a charge coupled device (CCD) detector (for rapid measurements) as an on-line monitor for the yeast biotransformation of glucose to ethanol. An ATR (attenuated total reflectance) cell was used to interface the instrument to the fermentation tank. An Nd YAG laser (1064 nm) was used to lower fluorescence interference and a holographic notch filter was employed to reduce Rayleigh scatter interference. Various chemometric approaches were explored and are explained in detail in their paper. The solution was pumped continuously through a bypass, used as a window in which measurements were taken. 

After cleaning with a phosphate-free detergent, labware should be rinsed extensively with deionized water and finally rinsed at least twice with doubly distilled water before drying. Avoid using paper towels, because lint and microscopic paper fibers often contain metal ions as well as acids/bases used in commercial treatment of paper products. Paper fibers also scatter light and interfere with spectrophotometric assays. 

The effect of averaging over one or more particle parameters—size, shape, orientation—is to efface details extinction fine structure, particularly ripple structure, to a lesser extent interference structure (Chapter 11) and undulations in scattering diagrams. If the details disappear upon averaging over an ensemble perhaps the best strategy in this instance would be to avoid the details of individual-particle scattering altogether and reformulate the problem statistically. 

The next question we must consider is how this result may be applied to a particle that consists of N, not just two, scattering centers. If the composition of the particle is such that the scattering from one part of the particle has no effect (other than interference) on the scattering from another part, then the particle may be subdivided into N scattering elements, and Equation (58) can be applied to all possible pairs. If we define rtJ as the distance between the /th andy th members of the set of N scattering elements, then this argument leads to the result (given without proof)... 

The facts that we have explicitly included the intraparticle interference function P[Q) in the analysis of scattering intensities and that it is accessible experimentally allow us to characterize colloidal dispersions structurally in more detail than we have been able to so far. In order to understand this, we need to understand clearly what we mean by small or large values of 6 or s and how they affect the behavior of P(6). This will also help us to understand how (and why) it is possible to combine light scattering with x-ray or neutron scattering to study structures of particles and their aggregates. 

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