Modelling fast mode dielectric relaxation of counterions in aqueous solutions of ionene bromides and fluorides

The parameters derived from previously published (M. Lukšičet al., Macromolecules, 2009, 42, 4337–4342) dielectric spectra of aqueous solutions of aliphatic 3,3-, 4,5-, 6,6-, and 6,9-ionene bromides and fluorides were analyzed within the existing models for the fast counterion-relaxation process. By fitting the Poisson–Boltzmann results to the experimental data for the osmotic coefficients of the ionenes in question, we were able to estimate the self diffusion coefficients of counterions. The coefficients were then used to calculate the correlation lengths as proposed by the Ito model. The corresponding correlation lengths obtained by the Mandel–Manning model were of similar magnitude. The observed trends in correlation lengths were consistent with the model-independent values derived from the experimental relaxation times. Combination of the dielectric data and Poisson–Boltzmann model analysis yields the conclusion that the fluoride counterions prefer longitudinal, whereas the bromide counterions favour transverse, fluctuation with respect to the polyelectrolyte backbone.