Porod region

Figure 8.9. The scattering curve of an isotropic ideal two-phase system after multiplication by i 4 (cf. Eq. (8.43)). The Porod region in which the oscillations are almost faded away is generally beginning after the 2nd order of the long period reflection... 

Classical Evaluation of Porod s Law. The practical evaluation of Porod s law in the most common case of an isotropic sample measured with point-focus is demonstrated in Fig. 8.11. By variation of the fluctuation background a long and linear Porod region can be received. Nevertheless, the line still shows a negative slope (Fig. 8.11). Ruland s theory of the systematic deviations from Porod s law [132] explains this finding. 

While the zero-dimensional projection is only a number, the ID projection is a curve which can still be evaluated after the projecting integration has been carried out. This means in practice that the evaluation of background and Porod region can be carried out later on the curve /, (si). 

Porod analysis is carried out in a plot In / j (st) I Fl)vs. sf. We find the number I Fi by trial-and-error and are satisfied when the linear region becomes longest. We determine the intercept Apx = nAp and the end of the Porod region, Smax (cf. Fig. 8.11). Now we can carry out the numerical integration, again add the remainder term (Apl /smax) from the analytical continuation, and obtain... 

Discuss some of the limiting forms of the form factor. Explain what is meant by (a) the center-of-mass region, (b) the Guinier region, (c) the fractal region, and (d) the Porod region. 

The SAXS patterns at higher k-values display asymptotic linear slopes indicating a power law relation. For a sharp interfece with a smooth geometry, the intensity is expected to foUow a k power law in this Porod region. The observed slope varies systematically with pore size, membrane orientation and thickness. In some cases, exponents more negative than 4 are observed. This may arise from either angulosity or a non-sharp interface, and is discussed in more detail elsewhere [15]. 

A test of whether one has gone to small enough angles is to see whether one is in the "Porod region" by examining the product of r )q For a valid measurement, this should be less than one. 

Estimation of contribution to background scattering from analysis of Porod region (schematic). 

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