Analysis of the correlation of counterions to rod-like macroions by anomalous small-angle X-ray scattering

We present a study of a rod-like polyelectrolyte by anomalous small-angle X-ray scattering (ASAXS). The polyelectrolyte consists of a stiff polyp-phenylene) backbone with attached positive charged groups that are balanced by bromine counterions. The scattering data are taken far below the absorption edge (13 473.7 eV) and in its immediate neighborhood. The decrease of the measured intensity predicted by theory is directly observed. A new analysis of these ASAXS-data leads to three partial intensities in a numerically self-consistent fashion. In particular, the scattering intensity that is solely due to the cloud of the counterions could be determined and compared to the prediction of the Poisson-Boltzmann cell model. Quantitative agreement is found. ASAXS is thus shown to be a new and highly effective tool for the analysis of polyelectrolytes.