Anomalous small-angle X-ray scattering: analyzing correlations and fluctuations in polyelectrolytes

We review recent structural investigations done by anomalous small-angle X-ray scattering (ASAXS). ASAXS uses the dependence of the scattering length of a given element if the energy of the incident X-ray beam is near the absorption edge of this element. The analysis of the ASAXS data leads to three partial intensities. We show that the comparison of these three partial intensities leads to valuable information in fluctuating systems. This has been demonstrated from data derived from recent molecular dynamics simulations of charged colloidal spheres. Moreover, it is shown that the three partial intensities can be obtained from experimental ASAXS data indeed. As an example for this analysis, we discuss recent ASAXS data referring to rod-like polyelectrolytes. These polyelectrolytes consist of a stiff poly(p-phenylene) backbone with attached charged groups that are balanced by bromine counterions. The three partial intensities can be determined experimentally and compared to the prediction of the Poisson–Boltzmann cell model. Quantitative agreement is found demonstrating the strong correlation of the counterions to the rod-like macroion. ASAXS is thus shown to furnish information not available by the conventional small-angle scattering experiment.