Power-law scattering

By measuring the scattered intensity as a function of q over multiple decades in q, information from multiple structural levels can be obtained. Two distinct scattering feamres distinguish each stmctural level, a power-law region and a knee region in a log-log plot of I q) versus q. An example of power-law scattering is shown in Figure 17.2. For particles with a smooth surface the... 

Power-law scattering features will be discussed in relation to mass-fractal scaling laws. Fractal scaling concepts used to interpret the power-law decay are well published in the literature. 

P. W. Schmidt, D. Avnir, D. Levy, A. Hohr, M. Steiner and A. Roll, Small-angle x-ray scattering from the surfaces of reversed-phase silicas Power-law scattering exponents of magnitudes greater than four, J. Chem. Phys., 1991, 94, 1474. 

Figure 5.23. Light scattering data from aggregates of colloidal silica demonstrate convergence to power-law scattering behaviort J.

Another type of morphology that can be studied with SAXS is the case when a system exhibits fractal properties. In this case one finds over a certain range a power law scattering behavior I < q. The parameter x is correlated with the fractal dimension. " In some cases the fractal dimension can be linked to certain types of growth processes. However, care should be taken before analyzing data in a fractal context since there are conditions which the scattering data has to satisfy and there are several... 

Fig. 16. (a) Selective examples of SANS patterns collected at several temperatures where typical structures are revealed in decane solution of 1% tetra-block copolymer (Radulescu et al., 2011) the power-law scattering behaviour characteristic of different structures is indicated the arrow denotes the peak arising from intra-particle correlation as concluded following the observation of the constant peak-position for different o/ in solution, which is illustrated in (b) for the case of the tri-block copolymer in decane the red curve represents the description of data with the density-modulated rod model. 

Sedimentary rocks are often porous and can be studied by SAS techniques. Early work by Mildner, Hall and co-workers [13] has shown that these structures can be represented by a fractal formalism. We have extended some of their work by using a combination of SAXS and USAXS techniques. The results are given in Fig.6. The (U)SAXS intensity shows a power law scattering with an exponent of -3.49 suggesting a surface fractal dimensionality of Dg = 2.51 whereas the SANS value is Dg 2.61. 

We can attribute the power-law scattering having s2 = 1 for the swollen pellide to the scattering from the ribbons that build the bundles and that are randomly placed in the direction perpendicular to the bundles as shown in Figure 12 (b-2). The bundles form the percolated network as shown in... 

---