Rayleigh-Debye-approximation

Figure 3. The scattering intensity, Cj, per particle as a function of particle diameter according to the exact Mie theory (solid line) and the Rayleigh Debye approximation (dotted line).

Light scattering by a dipole in a plane is considered. Colloidal scattering is discussed using the Rayleigh-Debye approximation, which holds for optically-soft any-form particles comparable with the wavelength. 

A master table is presented containing the formulae of colloidal scattering for the characteristic quantities r, Rgo, Re, and /Zgox in terms of polarizability a, permittivity t and refractive index p of the components in the Rayleigh and Rayleigh-Debye approximations is given. 

Light scattering in liquids within the critical region is described with the Rayleigh-Debye approximation including the correlation functions formalism. 

For time-averaged light-scattering in the Rayleigh-Debye approximation, equation (18) reduces to ... 

Rayleigh ratio Ro(K), is given in the Rayleigh-Debye approximation by ... 

In the Rayleigh-Debye-approximation the argument of the scattering function is the product of the size parameter and the length of the scattering vector h h = 4nX sin 0/2). Therefore the size dependence can be represented by one scattering curve. 

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. 

G. H. Meeten, Conservative dichroism in the Rayleigh-Gans-Debye approximation, J. Coll. Inter. Sci., 84,235 (1981). 

For small colloidal particles (a < 1 /mi), with spherically symmetric distribution of scattering material inside its volume, the field amplitude is given by the Rayleigh-Gans-Debye approximation [38]... 

T. L. Farias, M. G. Carvalho, U. 0. Koylii, and G. M. Faeth, Computational Evaluation of Approximate Rayleigh-Debye-Gans/Fractal Aggregate Theory for the Absorption and Scattering Properties of Soot, ASME Journal of Heat Transfer, 117, pp. 152-159,1995. 

In summary, the diflBculties in determining aggregate form factors, particle form factors, phase shifts, and distribution functions combine to make the Rayleigh-Debye approach too complicated for practical application. On the other hand, the coalesced-sphere approach using the Jobst approximations to the Mie scattering eflBciencies allows rapid correlation of turbidity with particle size distributions. Consequently, a coalesced-sphere approach was adopted for experimentation in the E. coli-PEI system. 

Figure 2.9. Efficiency factor K a,in) in Rayleigh-Debye s approximation (the upper curves of each couple) and from Mie s rigorous theory (the lower curves) (Mie, 1908 Klenin et al., 1977a)...

In Rayleigh-Debye s approximation, light scattering has been studied on... 

Hy some estimates (Shifrin, 1951 van de Hulst, 1957 Heller, 1963 Kerker and Farone, 1963 Moore et al., 1968 Kerker, 1969), the results of the soft pajticle approximation are qualitatively true within, at le.a,st, 0.8 < m < 1.5 if Q 1 when m < 1.15 they are valid quantitatively with a slight error. Hence, Rayleigh-Debye and van de Hulst s approximations are very fruitful in studying the heterogeneous structures of polymer and biological origin. 

According to Equations 68 and 96, in Rayleigh-Debye s approximation (KhlebUsov and Shchyogolev, 1977a Khlebtsov et aJ., 1977)... 

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