Semidilute solution rheology of polyelectrolytes with no added salt

We report rheological data on anionic polyelectrolyte solutions of variable chain length and concentration, specifically sodium poly(2-acrylamido-2-methylpropanesulfonate), with no added salt. Our results are consistent with literature data on the sodium salt of sulfonated polystyrene. We find a strong dependence of viscosity η on chain length: η to approximately M^2.4. This is in reasonable agreement with the scaling theory proposed by Witten and Pincus (η to approximately M²) and is much stronger than the scaling prediction of Dobrynin et al. (η to approximately M). The ratio of the viscosity and relaxation time gives the modulus at the relaxation time, which is experimentally consistent with the kT per chain expected by Dobrynin et al., and much smaller than the kT per charged monomer expected by Witten and Pincus (upon which the η to approximately M² prediction is based). Thus, we are forced to draw a conclusion for polyelectrolytes that seems to be a recurring one in polymer dynamics: The modulus is in quantitative agreement with theory, but the relaxation time is poorly understood. This exemplifies the fact that frictional and/or hydrodynamic interactions are not properly accounted for in scaling theories of polymer dynamics.