Dielectric relaxations in aqueous polyelectrolyte solutions: A scaling approach and the role of the solvent quality parameter

The radiowave dielectric behavior of sodium polyacrylate (NaPAA) aqueous solutions, in an extended concentration range and at various degrees of polymerization, was analyzed in the light of the scaling approach for polyelectrolyte solutions recently proposed by Dobrynin et al. [Macromolecules 1995, 28, 1859]. In the frequency range from 1 MHz to 1 GHz, the observed dielectric relaxation is attributed to the fluctuation of loosely bound counterions over a characteristic correlation length which depends on the polymer concentration. Assuming that free counterions fluctuate on a length scale that is proportional to the correlation length xi(0) of the semidilute solution, we derived power laws for the dielectric strength Deltaepsilon and the relaxation frequency nu(0). In agreement with our recently published data on conductivity, the dielectric data indicate that the effective charge on the NaPAA chains increases as concentration is raised, until the correlation length reaches the size of the electrostatic blob. By comparing the dielectric behavior of a series of polymers exhibiting different affinities for water as a solvent, we showed that the scaling behavior furnishes a very good description of the observed concentration dependence of the dielectric parameters. These findings suggest a method for evaluating, from simple dielectric measurements, the solvent quality parameter tau for the uncharged polyelectrolyte chain, a parameter which up to now eluded a precise determination by means of other experimental techniques. Finally, a correlation between the fraction f of free counterions and the solvent quality parameter tau, in poor solvent conditions, was evidenced. This gives further, support to the hypothesis that the effective polyelectrolyte-solvent entropic interaction is primarily dictated by the effective charge on the chain.