The dielectric increments of aqueous polyelectrolyte solutions: a scaling approach

This paper deals with dielectric dispersion curves (covering a frequency range from a few Hz to 100 MHz) of Na-poly(styrene-sulfonate) of 65,000 < or = Mw < or = 1,060,000 g mol(-1) in aqueous solutions. The values of the low frequency (dielectric increment1) and high frequency (dielectric increment2) dielectric increments, obtained from the experimental curves matched to a superposition of two Cole-Cole equations, have been analyzed in terms of their concentration and molar mass dependence. The concentrations C (g l(-1)) of the various solutions were mostly situated in the transition regime defined by Odijk [T. Odijk, Macromolecules 12 (1979) 688] between the dilute regime (C < Cg*) and the semi-dilute one (C > C**), and wherein the characteristic concentration C* marks the onset of flexibility effects on the polyion behavior. It has been shown that in the concentration range Cg* < C < C** the increments in both frequency domains satisfy a scaling relation dielectric increment(j) = Bj M(nu j) (C/C*)(mu j) with molar mass independent exponents nu j and mu j changing around C*. Their values are different for dielectric increment1 and dielectric increment2, except for mu above C* where both increments appear to become concentration-independent. Below Cg*, in the dilute regime, the two dispersion domains seem to merge. The increment dielectric increment = relative permittivity (0) - high frequency limit of relative permittivity is molar mass independent if scaled to (C/Cg*). The molar mass dependence of the increments as a function of the macromolecular concentration rhoP, dielectric increment or dielectric increment(j) approximately Mgamma (rhoP)mu, also reveals differences between the different concentration regimes. Extrapolation from above Cg* to zero concentration is thus unjustified.