Debye light scattering theory

Unsaturated polyesters for laminates Debye, light scattering of polymer solutions Flory, viscosity of polymer solutions Harkins, theory of emulsion polymerization Weissenberg, normal stresses in polymer flow Silicones... 

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 ... 

Tn the critical region of mixtures of two or more components some physical properties such as light scattering, ultrasonic absorption, heat capacity, and viscosity show anomalous behavior. At the critical concentration of a binary system the sound absorption (13, 26), dissymmetry ratio of scattered light (2, 4-7, II, 12, 23), temperature coefficient of the viscosity (8,14,15,18), and the heat capacity (15) show a maximum at the critical temperature, whereas the diffusion coefficient (27, 28) tends to a minimum. Starting from the fluctuation theory and the basic considerations of Omstein and Zemike (25), Debye (3) made the assumption that near the critical point, the work which is necessary to establish a composition fluctuation depends not only on the average square of the amplitude but also on the average square of the local... 

In contrast to osmotic pressure, light-scattering measurements become easier as the particle size increases. For spherical particles the upper limit of applicability of the Debye equation is a particle diameter of c. A/20 (i.e. 20-25 nm for A0 600 nm or Awater 450 nm or a relative molecular mass of the order of 10 ). For asymmetric particles this upper limit is lower. However, by modification of the theory, much larger particles can also be studied by light scattering methods. For polydispersed systems a mass-average relative molecular mass is given. 

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

In this chapter we present a simple model calculation that demonstrates how this cooperative motion affects the scattering spectrum. Our approach is based on the Debye-Onsager treatment of ion transport (see Falkenhagen, 1934 Stephen, 1971). This is our first discussion of cooperative effects in light scattering. In Chapter 13 this problem is reconsidered in the context of the general theory of nonequilibrium thermodynamics. 

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°.

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.

Light scattered from coagulating systems can be evaluated by one of three theories Rayleigh, Rayleigh-Debye, or Mie, depending on the size... 

Mie Scattering. For systems more complex than very small particles (Rayleigh) or small particles with low refractive indices (Rayleigh-Debye), the scattering from widely separated spherical particles requires solving Maxwells equations. The solution of these boundary-value problems for a plane wave incident upon a particle of arbitrary size, shape, orientation, and index of refraction has not been achieved mathematically, except for spheres via the Mie theory (12,13). Mie obtained a series expression in terms of spherical harmonics for the intensity of scattered light emergent from a sphere of arbitrary size and index of fraction. The coeflBcients of this series are functions of the relative refractive index m and the dimensionless size parameter a = ird/k. 

The theory developed by Rayleigh and Debye for coherent light scattering shows that only sub-volume elements in a sample (whose size is determined by the wave length of the incident radiation) contribute to the scattering which are different in... 

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