Structure factor Porod scattering

The surface area per unit volume can be also measured in scattering experiments. For the fully developed system containing the domains of size L and the interface of the intrinsic width c (c -C L), the Porod law [1] predicts the following asymptotic for the structure factor S(k)... 

The SAXS method allows measure the diameter of nano-size structural defects and pores. The small-angle scattering of the cellulose sample was recorded, and intensity was measured as a function of the diffraction angle. To correct the intensity, /, the background scattering was subtracted and the experimental intensity was corrected on instrumental factor, absorption of X-ray and other factors. Porod s law / = Kq, was used for visualization of the small-angle X-ray scattering (Porod, 1951, 1952]. Linearization of the experimental curves was performed as + kq or Y = Yg + kX (Fig. 7.13], where Y = and... 

As pointed out by Klee et al., such a system can also be modeled using Eq. (6.33). This was accomplished by approximating the dilute phase as a polydisperse system of core-shell particles [37] and assuming a hard sphere structure factor however, the effect of polydispersity on the structure factor was not accounted for [62]. As well, the GIFT analysis has also been used to verify the presence of a core-shell structure [73]. Ultimately, there is more than one single model that can accurately describe the SAXS in terms of the peak intensity, average size, and Porod scattering law. For example, a eore-shell structure can correctly account for the shell of amphiphilic molecules at the surface of the microemulsion, which Eq. (6.36) cannot. 

Here, Eq. 30 represents the mean square of the sectional curvature averaged around the normal vector. The first term in Eq. 28 is the Porod scattering [81]. The crossover from q "(n>6) to q with increasing q in the structure factor occurs at qcRm— [78, 79]. 

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