Polyelectrolyte conductivity

Using the de Gennes scaling model for the configuration of a polyelectrolyte chain in semidilute solution, we construct a simple model of AC conductivity for semidilute solutions of strongly charged polyelectrolytes without added salt. We compare the predictions of this model with literature data and new data on two polyelectrolytes with very different affinities for water. The sodium salt of sulfonated polystyrene in water is a hydrophobic polyelectrolyte (the uncharged monomer does not dissolve in water), where the chain is locally collapsed. The sodium salt of poly(2-acrylamido-2-methylpropanesulfonate), is a much more hydrophilic polyelectrolyte, making the chain quite expanded locally. The model describes the conductivity of both cases reasonably for concentrations below 10^-2M (mol of monomer per liter). Deviations between experiment and theory at higher concentrations lead us to conclude that counterion condensation decreases as concentration is increased. This is qualitatively consistent with the experimental observation that the dielectric constant of the polyelectrolyte solution increases as polyelectrolyte is added.