Scattering from Large Particles

When polymer dimensions are greatCT than A.720, intraparticle interferraice causes the scattered light from two or more craitCTs to arrive considerably out of phase at the observation point, and the scattoing raivelope becomes dependent on the molecular shape. This attenuation, produced by destructive interference, is zcto in the direction 

Guinier showed that a characteristic shape-independent geometric function called the radius of gyration can be measured from large particle scattering. It is defined 

The function P(6) is size dependent and can be related to the polymer coil size by the well-known Debye equation 

One of the most common methods used to determine the shape-independent parameter uses the double extrapolation method proposed by Zimm (1948a). 

This method is based on the knowledge that, as the scattering at zero angle is independent of size, P(0) is unity when 0 = 0. Scattering at zero angle is difficult to measure experimentally, and an extrapolation procedure has been devised that makes use of a modified form of Equation 9.18 for large particles, 

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Diagrammatic representation of data on scattering from large particles, corresponding to the equation... 

We seek here a description of the scattering from large particles compared with the wavelength of light. In this limit the dominant scattering occurs at small angles. Furthermore, the major contribution to the scattering field arises from interactions with the particle boundary. 

For some typical modes of scattering from large spherical particles (f >5), simple formulations of phase functions can be obtained. These modes include scattering from a specularly reflecting sphere, scattering from a diffuse reflection sphere, and scattering by diffraction from a sphere. 

Fraunhofer diffraction theory combines the above results to compute the light scattered at small angles from large particles. Such a particle is pictured in Figure 4.15. 

The measurement does not require particles to pass through the laser beam one at a time. In fact, there are normally large numbers of particles in the beam at any point in time. Each particle forms its own diffraction pattern, and the system sums the results from these patterns over the total measurement period. It is important that the particulate concentration be low enough so that multiple scattering does not occur. This happens when light which is scattered from one particle strikes another particle and is scattered further before it is collected. This phenomenon is easily detected, and the loading range is usually quite broad. 

From Rayleigh theory, the intensity of light scattered from each particle depends largely on its size and shape and on the difference in refractive index between the particle and the medium. For a suspension, each spherical particle scatters light at an intensity Id at a distance x from the particle, according to the following relationship ... 

S.R. Aragon, R. Pecora, Theory of dynamic light scattering from large anisotropic particles. 

S.R. Aragon, R. Pecora, Theory of dynamic light scattering from large anisotropic particles. J. Chem. Phys. 66(6), 2506-2516 (1977). doi 10.1063/1.434246... 

As shown above, the nature of scattering from a particle approaching the wavelength of laser is substantially different from that of large particles. However, smaller particles also yield phase signals which contain information about their size as well as material. Some aspects of the application of phase/Doppler systems to small particles are considered here through a few examples. 

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