Porod regime

Small-angle scattering intensity in the high angle (q) region can be analysed to provide information on interface thickness (e.g. the lamellar interface thickness block in copolymer melts or core-corona interface widths in micelles). For a perfectly sharp interface, the scattered intensity in the POrod regime falls as q A (Porod 1951). For an interface of finite width this is modified to... 

Hasmy, A., Vacher, R. and JuUien, R. (1994). Small-angle scattering by fractal aggregates-a numerical investigation of the crossover between the fractal regime and the Porod regime. Phys. Rev. B, 50, 1305-1308. 

Here, Vo is the total volume of the sample, ps is the density of the solid phase, (f) is the porosity of the sample, Apsuo is the difference in coherent scattering length density between the solid and the pore phase, and Cn, Cx are the factors to be applied in case of neutrrMi and X-ray scattering, respectively (Table 21.2). When two Porod regimes are present [as it is the case for microporous samples (see Figure 21.15)] both can be evaluated according to (21.13 a, b). Hereby care has to be taken to correctly match the Porod constants with the respective densities of the sohd phase and the surface area that can be extracted. ... 

Fig. 11.15 Left-. A schematic representation of the fully hydrated morphology of a PFSA ionomer (e.g., Nafion) under the assumptions of a cubic lattice model which fitted data from small angle X-ray scattering (SAXS) experiments. Right. SAXS spectra of hydrated Nafion and a hydrated sulfonated polyetherketone. The characteristic hydrophobic/hydrophilic separation lengths are obtained from the position of the ionomer peaks while the internal hydrophobic/hydrophilic interfaces are obtained from the intensities in the Porod regime. First reported in Ref. [66]...

Figure 11 (a) SAXS from titania nanoparticles and unified fit. fp = 34.9nm, PDI = 14.4, / g = 44.2nm. (b) Particle size distribution for titania unified analysis of Porod regime, TEM particle counting, and a scattering integral method. Adapted from Beaucage, G. Kammler, H. K. Pratsinis, S. E. J. Appl. Cryst. 2004, 37,523-535, Figures 5(a) and 5(b). ... 

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