Scattering Debye theory

Equation (67) shows clearly that i should be measured as a function of both concentration and angle of observation in order to take full advantage of the Debye theory. The light scattering photometer described in Section 5.4 is designed with this capability, so this requirement introduces no new experimental difficulties. The data collected then consist of an array of i/I0 values (i needs no subscript since it now applies to small and large particles) measured... 

What is the Debye theory of light scattering What are its assumptions and limitations ... 

Figures 1-3 show the observed reciprocal excess intensities of scattered light multiplied by sin 0 (to correct for the irradiated volume observed at each angle) plotted against sin2 (0/2) at constant polymer concentration for several temperatures above the phase-separation temperature. To give a clearer presentation the intensities are expressed in relation to intensities at the scattering angle 0 = 90°, as was also done by Eskin and Nesterow (11). In accord with the Debye theory, the plots give straight lines and can be represented by...

Figure 7.6 Intensity of light scattered from an unpolarised beam by a large spherical particle at the origin, as a function of scattering angle 6 (Rayleigh-Gahs-Debye theory). The intensity of light scattered at 135° is less than that at 45°.

Lichtenbelt et al. (19) made a detailed comparison of extinction cross sections for real doublets and for hypothetical doublets coalesced into spheres. Using the Rayleigh-Debye theory for a up to three, Lichtenbelt et al. determined that the coalescence assumption leads to 10% larger values of the scattering cross section than would be found for real doublets created in coagulation. This is because a real doublet is less compact than a coalesced doublet of the same volume therefore, the interference between light waves, scattered by different parts of the real... 

Debye was responsible for theoretical treatments of a variety of subjects, including molecular dipole moments (for which the de-bye is a non-SI unit). X-ray diffraction and scattering, and light scattering. His theories relevant to thermodynamics include the temperature dependence of the heat capacity of crystals at a low temperature (Debye crystal theory), adiabatic demagnetization, and the Debye-Huckel theory of electrolyte solutions. In an interview in 1962, Debye said that he... 

A. Levi and H. Suhl, Quantum theory of atom-surface scattering Debye-Waller factor. Surface Sci. 88 221 (1979). 

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. 

Affected by multiple scattering are, in particular, porous materials with high electron density (e.g., graphite, carbon fibers). The multiple scattering of isotropic two-phase materials is treated by Luzatti [81] based on the Fourier transform theory. Perret and Ruland [31,82] generalize his theory and describe how to quantify the effect. For the simple structural model of Debye and Bueche [17], Ruland and Tompa [83] compute the effect of the inevitable multiple scattering on determined structural parameters of the studied material. 

Peter Debye in 1944 further extended the work of Rayleigh and the fluctuation theory of Smoluchowski and Einstein to include the measurement of the scattering of light by macromolecular solutions for determining molecular size. 

Mie wrote the scattering and absorption cross sections as power series in the size parameter 0, restricting the series to the first few terms. This truncation of the series restricts the Mie theory to particles with dimensions less than the wavelength of light but, unlike the Rayleigh and Debye approximations, applies to absorbing and nonabsorbing particles. 

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