Determination of polyelectrolyte charge and interaction with water using dielectric spectroscopy

Using the dielectric strength and relaxation time of a high-frequency (1 MHz-1 GHz) dielectric relaxation, we estimate the effective charge on polyelectrolytes and their net thermodynamic repulsive interaction with solvent. The utility of this method is demonstrated for semidilute aqueous solutions of the sodium salt of several sulfonated polyelectrolytes of varying charge and strength of repulsive interaction with water, with no added salt. At high concentrations, as the concentration is increased, the effective charge of strongly charged polyelectrolytes always increases, as previously observed in conductivity and osmotic pressure measurements. Interestingly, we find that the effective polymer-solvent repulsion increases in direct proportion to the effective charge on the polyelectrolyte chains. This proportionality means that, although the additional charge would increase the contour length of the chain of electrostatic blobs, the increase in repulsion between solvent and polymer offsets this effect, making the contour length of the chain essentially independent of polyelectrolyte concentration. This then explains why the correlation length of semidilute polyelectrolyte solutions fortuitously agrees with simple scaling predictions.