Experimental studies of polyelectrolyte solution properties

To test our understanding of polyelectrolyte solutions in poor solvents, we study the apparent viscosity, the osmotic pressure, and the conductivity of aqueous solutions of a well characterized synthetic polyelectrolyte, the sodium salt of polystyrene sulfonate. Using two rheometers we measure the apparent viscosity over more than five decades of shear rate to determine the Newtonian viscosity without the need for extrapolation, and the onset of shear thinning, which is inversely proportional to the longest relaxation time. We study five decades of polyelectrolyte concentration, from the dilute to the entangled regimes, and three decades of added salt (NaCl) concentration, a much broader range of salt and polyelectrolyte concentrations than has been previously studied on a single sample. Much of the viscosity data in the literature is shown to be in the shear thinning regime, and not indicative of the Newtonian viscosity. Our experimental data agree well with a recent scaling theory over roughly a two-decade span of concentrations, exhibiting both the predicted semi-dilute unentangled and entangled scaling. Outside of this concentration range, our data show systematic violations of accepted dynamical scaling laws, notably the Fuoss law, which is shown to be obeyed by the apparent viscosity only at higher shear rates.; We rederive and extend the static scaling theory and show similar results, more rigorously, by reanalyzing the analytical solutions of the Poisson-Boltzmann equation in the cylindrical cell model. We discuss counter-ion condensation and derive predictions for the correlation length and the osmotic pressure for polyelectrolyte solutions in the absence of added salt. Making use of a simple Ansatz, we extend the cylindrical cell model to include the effects of added salt upon the osmotic pressure predictions. Our new theory agrees excellently with literature data and our experimental data, as a function of both polyelectrolyte and added salt concentrations, using a constant fit level of counter-ion condensation. The osmotic pressure and conductivity measurements allow a direct consistent determination of the residual salt level in "salt-free" solutions, which is insufficient to explain the downturn observed in both the viscosity and relaxation time data at low concentrations.