Debyes Scattering Theory

Higher dielectric constant Lower dielectric constant 

---

Equation (10.82) is a correct but unwieldy form of the Debye scattering theory. The result benefits considerably from some additional manipulation which converts it into a useful form. Toward this end we assume that the quantity srj, is not too large, in which case sin (srj, ) can be expanded as a power series. Retaining only the first two terms of the series, we obtain... 

Since the product srj, appears in Eq. (10.84), there is a trade-off possibility between particle size and the angle of observation. That is, the Debye scattering theory applies with the same level of accuracy to larger molecules at smaller angles and to smaller molecules at larger angles. 

The scattering center is the metal ion, the Coulomb potential of which is screened in the manner of the Debye-Huckel theory of weak electrolytes. The screened potential has the form... 

For a non-ideal (pseudo) two-phase system having interface layer, the overall scattering will show negative deviation from Porod s law (see the curve 11 in Fig.l) and Debye s theory (see the curve II in Fig.2), thence the Porod equation (1) becomes [6,9]... 

FIGURE 5.71 The Rayleigh-Debye-Gans theory is based on the assumptions that (1) the incident beam propagates without being affected by the particles, and (2) the scattered hght, received by the detector, is a superposition of the beams emitted from the induced dipoles in the different parts of the particle. 

Wang, G.M., and Sorensen, C.M., Experimental test of the Rayleigh-Debye-Gans theory for light scattering by fractal aggregates, Appl. Opt, submitted. 

While by far the greater portion of the electrochemical studies on solutions have been made using water as solvent, researches have also been carried out in which the water has been replaced by other solvents, or mixtures of non-aqueous solvents with water. Until very recently such studies yielded little of value because of their scattered nature and, usually, lack of accuracy, to which was added a lack of an adequate theory for their interpretation. It will be shown in the following chapter that some headway has been made in the, difficult field of study of the thermodynamic properties of such solutions of electrolytes. The Debye-Hiickel theory is, if anything, more valuable in the interpretation of the results in this field than in that of aqueous solutions. 

The Debye-Waller factor was originally derived during the development of Bragg X-ray scattering theory. The difference between the two effects is that X-ray scattering is fast when compared with the characteristic time for lattice vibrations whereas the mean lifetime of a Mossbauer nucleus is long when compared with the lattice time. 

Tables IV and V show the dimensions calculated from the various theories of viscosity and sedimentation, respectively, in comparison with those obtained from light-scattering. It will be seen that, in the case of the viscosity data, the agreement between the calculated and experimental values is, with the exception of the Brinkman-Debye-Bueche theory, very reasonable. The values of (ro) calculated from sedimentation data are not, in general, in such good agreement with the light-scattering results.

The absorption and elastic scattering of light by a spherical particle is a classical problem in physics, the mathematical formalism of which is called Mie theory (sometimes also Mie-Debye-Lorenz theory). It is a beautiful and elegant theory, which is the subject of entire treatises. In particular, we refer the reader to Kerker (1969) and Bohren and Huffman (1983). The key parameters that govern the scattering and absorption of light by a particle... 

The two major themes in scattering theory are the scattering properties of biological materials and the geometrical relationships between these materials within the macromolecule. These are embodied in the Debye equation. The most comprehensive account of X-ray scattering theory is given in Glatter and Kratky s compendium [7]. 

One of the advantages of this method is reasonably strong theoretical basis. The principal basis of scattering theory was given by Reyleigh [18]. Thompson [19], Debye [20], and Guinier [21] developed the scattering theory. 

While much of his reputation was based on nonpolymeric accompHshments, such as demonstrated by the Debye-Huckel theory, the Debye-Scherrer x-ray diffraction technique, the Debye-Sears effect in liquids, the Debye temperature, the Debye shielding distance, the Debye frequency and the Debye unit of electric moment, his development of the hght scattering technique for the determination of the molecular weight of polymers resulted in his also being recognized as a world class polymer scientist. 

Petrus (Peter) Josephus Wilhelmus Debye (1884-1966). .. was a Dutch physicist and physical chemist, who worked in the fields of quantum physics, X-ray analysis, microwave spectroscopy, and electrochemistry. Colloid science benefits from his contribution to X-ray and light scattering (in particular for aggregates— Eq. (4.39)— and concentrated suspensions—Eq. (2.24)), his work on electrolyte solutions (Debye-Hiickel theory), as well as his remarks to electrophoresis and his research on polymers. He was awarded the Nobel Prize in Chemistry in 1936 for his work on molecular structure through his investigations on dipole moments and the diffraction of X-rays and electrons in gases . 

---