Correlation of counterions with rodlike macroions as assessed by anomalous small-angle X-ray scattering

We consider the analysis of a rodlike synthetic polyelectrolyte in solution by anomalous small-angle X-ray scattering (ASAXS) in order to elucidate the correlation of the counterions with the highly charged macroion. ASAXS can be applied to these systems because the absorption edge of typical counterions, for example, bromine or iodine ions can be attained by synchrotron radiation. Model calculations using the Poisson-Boltzmann cell model show that ASAXS furnishes two terms caused by the anomalous dispersion of the counterions. The leading terms is a cross-term between the ordinary scattering amplitude of the polyelectrolyte and the real part of the scattering length f ' of the counterions. A second term refers solely to the anomalous contribution of the counterions, i.e., to f ' and f " (f ": imaginary part of scattering length). Preliminary data obtained from rodlike synthetic macroions having iodine counterions corroborate the theoretical deductions. They demonstrate that ASAXS is capable of furnishing information that is not available by the ordinary SAXS experiment.