Particle scattering Subject

For isotropic spherical particles of given refractive index in a medium of known refractive index, the exact form of C can be found by matching the incident, internal and scattered electromagnetic waves at the particle surface, subject to certain boundary conditions7. The solution comes in the form of an infii te series ... 

When a particle is subject to Brownian motion and irradiated, two frequencies of equal intensity are generated in addition to the frequency that would normally be scattered, inducing a positive and a negative Doppler shift proportional to the particle velocity. The interference between the nonshifted wave (photon reemission) and the two waves due to Brownian motion yields infinitesimal variations in intensity. Detection of these is the basic principle of DLS, which is therefore particularly suited to the study of properties of solutions. The scattered intensity is acquired as a function of time and is then self-correlated. This yields the relaxation time due to the Brownian motion and leads to the characterization of the particle size through hydrodynamic models of the diffusion coefficients. 

The induction time is a subject of some controversy. It in turn is made up of two components. Firstly, there is the true induction time of nucleation, the time to the appearance of the nucleus secondly, there is the time of growth until a detectable fraction has been produced. This latter time is technique dependent, with TA methods being deemed, in general, to be insensitive. If a more sensitive technique such as microscopy or particle scattering is used then this latter time is less. There is some debate as to whether a true induction time of nucleation really exists, with some authors proposing that a sufficiently sensitive technique would detect nuclei perhaps of only a few molecules at a very early stage. The overall time is referred to as the induction time of crystallisation. 

Water drops condensed in the atmosphere have much larger dimensions than gas molecules hence they are subject to the interference phenomena mentioned at the end of the last section. This alters the color of the scattered light. Smoke and dust particles are also larger and may absorb as well. 

It is sometimes convenient to use a properly chosen scattered line in the background for comparison to avoid having to add an internal standard to the sample.37 The experience of the Applied Research Laboratories shows that the effects of variations or fluctuations in the equipment and of particle size in powdered samples can be eliminated satisfactorily in this way. In some cases, absorption and enhancement effects are also adequately compensated. We have already mentioned (7.8) that scattered reference line and the analytical line will be subject to considerably different absorption effects if the two lines differ appreciably in wavelength. Everything depends upon the selection of a satisfactory scattered reference line, and this is done empirically. 

Measurements at low angles are subject to considerable error, and for this reason it is often preferred to apply appropriate corrections to scattering intensities measured at larger angles. The observed intensity ie in a direction 0 will be reduced on account of intraparticle interference by a factor cusomarily designated by P(0), which depends on the size and shape of the particle as well as on the angle 0. Thus, by definition... 

The phase relations among the scattered wavelets depend on geometrical factors scattering direction, size, and shape. But the amplitude and phase of the induced dipole moment for a given frequency depend on the material of which the particle js composed. Thus, for a full understanding of scattering und absorption by small particles, we need to know how bulk matter responds to oscillatory electromagnetic fields this is the subject of Chapters 9 and 10. 

We shall assume, in addition to single scattering, that the particles are many and their separations random, which implies incoherent scattering. That is, there is no systematic relation among the phases of the waves scattered by the individual particles thus, the total irradiance scattered by the collection is just the sum of the irradiances scattered by the individual particles. Even, however, in a collection of randomly separated particles, the scattering is coherent in the forward direction, a subject to which we shall return in Chapter 3. 

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