Scattering intensity function

The scattering of electrons by an atom pair separated by a rigid distance, r, averaged over all possible orientations in space, gives rise to a molecular scattering intensity function which can be represented in the following way1 ... 

According to the Borue and Erukhimovich theory for polyelectrolyte solutions [84], the scattered intensity function for ionic gels may be given by the... 

Fig. 12. Observed (symbols) and calculated (solid Ones) scattered intensity functions for the NIPA/AAc gels having = 0.107...

In the case of well-ordered crystals, It Is possible to deduce their atomic structures by appropriate manipulation of diffraction Intensities. In the case of x-ray scattering by liquids, direct use of measured intensities yields, at best, very limited structural Information (radial distribution functions). For ordered liquids, however, it is possible to posit structural models and to calculate what their scattering Intensities would be so that it is more productive to conduct the comparisons in diffraction space. To this end, it is possible to devise a point model to represent the spatial repetition of the constituent units in the ordered array and to compare its scattering maxima to the observed ones (6,9). More sophisticated analyses (10-12) make use of the complete electron densities (or projections onto the chain axis z), usually by calculating their Patterson functions P(z) since the scattering intensity function is its Fourier transform. 

When a binary mixture is quenched in the unstable coexistence region, by thermal treatment or pressure changes or simply by mixing the two macromolecules, fluctuations in density grow with time, and finally result in a complete phase separation. The dynamics of phase separation are generally divided into early, intermediate and late stages. The different stages can be described by means of the temporal evolution of the scattered intensity function.20-22... 

Figure 2 Temporal evolution of scattered intensity functions [1(0 vs Q] as determined by SALS on BLGjAG dispersions at 0.1 wt% total biopolymer concentration, pH 4.2 and Pr.Ps weight ratio of 2 1...

As the shape of the different scattered intensity functions and the power-law growth of structural domains suggested that the system was located in the late... 

Figure 5.3 The Debye function, Equation (5.31), for a random coil chain is plotted and compared with the independent scattering intensity function for a thin rod and a thin circular disk.

Figure 2.22. A semi-logarithmic plot of the scattering intensity function vs. time for PBD blends with PS at wave-vector q = 2750 nm filled circles are for SD and open circles are for ND [Hashimoto, 1987],...

Mitchell and Windle have used this approach to evaluate the orientation parameters for a random thermotropic co-polyester. Figure 16 shows the recorded X-ray scattering intensity function I(s, a), and... 

The above treatment assumes a single atomic component system whereas the rare earth transition metal amorphous materials (R-T) are two component and thus three pair correlation functions, G(r), exist, one each for the possible R-R, R-T, and T-T combinations. These are lumped together to produce the observed scattered intensity function, but may be separated by experiments on isotopically substituted alloys which have different neutron scattering amplitudes, or as in the case of Co-P by separating the magnetic components using polarized neutrons (Bletry and Sadoc, 1975). 

The function y(r)—named correlation function (Debye, 1949)— is the volume average of the product of Ap(r) in two volume elements dv, located at i and 2, connected by a vector r. The function y(f) can directly be determined from an experimental scattering intensity function I( ) by a Fourier transformation ... 

The scattering intensity function related to a dilute set of A spherical nano-objects with a radius distribution defined by N R)—schematically illustrated in Figure 8-4 (b)—is calculated by solving the equation... 

Several scattering intensity functions defined by equation (8-34) for different structural parameters are plotted in log-log scale in Figure 8-9(c) and (d). If the condition ro is fulfilled, the scattering intensity exhibits three distinct and simple q dependences over different q ranges (Fig. 8-9(c)). The main features of the scattering curves are directly... 

Figure 21.1 A scheme illustrating the rela- correlation function, (c) Pair (distance) distri-tionships between the relevant functions In button function, (d) Amplitude function, the analysis of SAXS data, using an isolated (e) Scattering intensity function. Note that...

Fig, 3. The fiilly corrected and normalized (scaled to electron units) x-ray scattering intensity function I (j) for poly(/i-butyl methacrylate), derived from the scattering of Fig. 2. The dashed curve indicates the independent component of the scattering, which includes the incoherent scattering. 

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