Small contrast

In many cases the consideration of only two phases is sufficient, because according to Eq. (8.53) the scattering power is a function of the square of the contrast between two phases. This means that the scattering from a small contrast between a second and a third phase is frequently negligible. For those cases in which three or more phases have to be considered, the corresponding equations have been reported by JAnosi [138,149]. 

In the presence of size polydispersity, there is an additional incoherent contribution to C(, t) decaying through the self-diffusion coefficient Ds((/)) [42,43,91]. The latter can also be measured for monodisperse hard sphere suspensions at finite concentrations at qR corresponding to the first minimum of S( ), i.e., when the interactions can be ignored [91]. These three different diffusion coefficients exhibit distinctly different dependence on q and 0. From these three transport quantities, Z>cou( ) is absent in monodisperse homopolymers, whereas Ds can hardly be measured in polydisperse homopolymers due to the vanishingly small contrast. 

Alternatively, Fleischmann and Hittmair [71] modeled aortic enhancement by treating the entire body as a black box, where the input function was defined by the administration of a small contrast test bolus, and the output function was simply the resulting measured time-attenuation curve. The patient function was the black box, which substitutes for the multiple compartment... 

FIGURE 26.27 Threshold of detection for small contrasting object. 

Thus, small contrasts lead to less pronounced oscillations. Similarly, a bilayer system should show two significant oscillation periods in the reflectivity depending on the thicknesses d and d,2 of each layer. The visibility of the resulting beating of the intensity depends on the contrast Ki between layer 1 and 2 (see Fig. 4, lower rows). If Ki is very small, the reflectivity of a bilayer system may be almost identical to a monolayer system. Therefore, usually neutron scattering methods are used to investigate polymer layer systems because Ki can be increased dramatically by deuterating one compound as mentioned above [5]. 

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