Scattering, independent, from

The above considerations are valid only for monodisperse samples of rather low molecular weight. When characterizing polydisperse samples, all components i having different molecular weights M, and concentrations c, scatter independently from each other. Thus one obtains the following equation ... 

In addition to coherent contributions, there are incoherent contributions to light scattering In which fractons of characteristic size smaller than the optical wavelength scatter Independently from each other. In that case, the scattered intensity is the sum of the individual scattering intensities, while for... 

Thus for an ideal two-phase system the total calibrated intensity that is scattered into the reciprocal space is the product of the square of the contrast between the phases and the product of the volume fractions of the phases, Vi (1 — Vi) = V1V2. V1V2 is the composition parameter66 of a two-phase system which is accessible in SAXS experiments. The total intensity of the photons scattered into space is thus independent from the arrangement and the shapes of the particles in the material (i.e., the topology). Moreover, Eq. (8.54) shows that in the raw data the intensity is as well proportional to the irradiated volume. From this fact a technical procedure to adjust the intensity that falls on the detector is readily established. If, for example, we do not receive a number of counts that is sufficient for good counting statistics, we may open the slits or increase the thickness of a thin sample. 

Rayleigh scattered light from dense transparent media with nonuniform density. If these nonuniformities are time-independent, there will be no frequency shift of the scattered light. If, however, time-dependent density fluctuations occur, as e. g. in fluids, due to thermal or mechanical processes, the frequency of the scattered light exhibits a spectrum characteristic of this time dependence. The type of information which can be obtained by determining the spectral line profile and frequency shift is described in an article by Mountain 235). 

The radius of gyration of polymer coils can be determined independently from light scattering. Fox and Flory measured both Rg and [17] for various molecular weight fractions of polystyrene in various solvents at several temperatures. The following results were obtained ... 

For a given polymer that has variable amounts of crystallinity, the scattered intensity over a large range of reciprocal space may be integrated over a number of intervals sQ - Sp. Such intervals can be defined experimentally in such a way that the following equation be verified independently from the crystallinity of the material... 

In the coal samples, usually one of the two phases is coal, and the other is pores, which are considered to contain air. Sometimes, however, the effects of the mineral matter in the coal must be considered. The system then contains three phases. Our scattering data from the coals suggest that the pores and mineral matter scatter independently of each other, so that when the contribution of the minerals to the scattering must be considered, the coals can be taken to be two independent systems—one made up of coal and air, and the other consisting of coal and mineral matter. As we will explain below in more detail, we have estimated the contribution of the mineral matter to the scattering from several of the coals and have concluded that this scattering is small and often can be completely neglected.. ... 

In (6), F is a constant. The scattered intensity from relatively small inhomogeneities thus is independent of the scattering angle but is proportional to dC... 

The reflectance depends upon the K/S ratio and not on the absolute values of K and S. The scattering S coefficient is independent from the wavelength over wide spectral ranges and therefore the SKM function reflects the trend of the absorption K coefficient. Moreover, because SKM is a function of a(hv), a plot of (F(RJj against hv can be used to determine f g in powdered semiconductor oxides. 

This procedure has been used to determine droplet size in sprays. Oseillations in the curve relating x and D can be smoothed out by the use of an incident laser beam having a broad speetral bandwidth [83]. An accumulation of independent scattering intensities from multiple scatterers ean be used to measure the mean droplet size of a group [84]. This procedure has been applied to water sprays and the experimental data confirmed by phase Doppler anemometry [85]. The applicability of the polarization ratio technique is strongly influenced by the complex refractive index of the dispersed media and is limited to media having a relative refractive index below about 1.44 [86]. 

The particles must scatter independently otherwise the diffusion coefficient, and particle size, cannot be determined unambiguously from the decay rate of the autocorrelation function. The net effects of multiple scattering are that the instrument factor B/A decreases, and the autocorrelation factor decays faster, leading to too low an estimate for particle size. Thus, multiple scattering limits the application of the technique to low concentration dispersions (< 0.01% by volume), although techniques have been developed to overcome this condition. 

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