Intensity Decay Between SAXS and WAXS Porods Law

2 Intensity Decay Between SAXS and WAXS Porod s Law 

The ideas of the classical evaluation of Porod s law have been developed by Vonk [134], Ruland [132,134], and Stein [135]. 

Basic Equations. Scattering according to Porod s law [18,137] is a consequence of phase separation in materials. In a two-phase system (e.g., a semicrystalline polymer) every point of the irradiated volume belongs to one of two distinct phases (in the example to the crystalline phase or to the amorphous phase). In a multiphase system there are more than two distinct phases. 

Frequently at least one of the phases forms particles (e.g., crystalline lamellae). The shape and position of the tth particle from the irradiated volume is described by a shape function 7 (r). It is obvious that the scattering intensity of an ideal multiphase system can be expressed in terms of autocorrelations Y (r) and cross-correlations of the shape functions and the average electron densities of each phase (cf. Sect. 2.5). 

The scattering patterns from any materials that are made from a finite number of discrete phases conform to Porod s law. In most of the practical applications it is sufficient to consider the most simple case of a two-phase system. In-depth considerations concerning the interpretation of scattering data from multiphase systems have been published by Janosi [138]. 

---