Rayleigh-Debye scattering

The time-independent Maxwell s equations to be solved in this case are 

Employing the potential function, b, we are led to an inhomogeneous form of Laplace s equation with the solution, 

Comparing equations (4.24) and (4.28) along with the definition of the polarizability in equation (4.10) gives 

In general, the polarizability is related to the volume of an object and the magnitude of the scattered light will be proportional to the contrast in the dielectric constants of the scattering object and its supporting matrix. 

When a particle becomes comparable in size or larger than the wavelength, several complications may arise. If the index of refraction of the particle is different from its surroundings (np/ns 1), refraction can occur at the interface that will contribute an angular 

It is known from electrostatics that the polarization vector V is related to E by means of 

the polarization vector difference in a particle and in the dispersion medium is 

As the polarization vector reflects the polarization of a unit space of the dielectric, then 

The field of the light scattered by a particle at the point of observation is the sum of the fields of all the elementary scatters with due account of their phase shift (see Equation 3). 

The phase shift of the beams scattered by this space element and by any other one (A) is expressed as 

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This technique is reliant upon the following expression (Eq. 3.1), which, for classical Rayleigh-Debye scattering, relates the intensity of the scattered light (Is) to the particle concentration (c) and the scattering coefficient (cj). 

Smoluchowski, Rayleigh, Cans and Debye. Scattering by independent particles is... 

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).

The Zimm-plot technique, like q.l.s., also involves a difficult extrapolation to zero angle. Another difficulty is that its qiplication assumes that the particles are Rayleigh-Cans-Debye scatterers (namely, that there is no change of phase or other distortions of the incident radiation by the particle). For the larger mucins in particular, this may not be the case. 

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. 

The conditions for Rayleigh-Debye-Gans scattering are as follows ... 

The Rayleigh-Debye-Gans differential scattering cross section in the scattering plane for vertically polarized light (Eigure 14.1) is... 

In Equation 14.22 the subscripts RDG and R denote Rayleigh-Debye-Gans and Rayleigh. In Equation 14.23b q is the scattering wave vector to be discussed below. 

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

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. 

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