Salt Effect on the Viscosity of Semidilute Polyelectrolyte Solutions: Sodium Polystyrenesulfonate

Abstract

We studied the viscosity of semidilute aqueous solutions of sodium polystyrenesulfonate as a function of polymer and salt concentrations. The viscosity data were quantified by applying a scaling relationship between solution correlation length ξ = lg ν /B and number of monomers g per correlation volume for chains with monomer projection length l. The specific values B pe ,B g, and B th of the B-parameter corresponding to exponents ν = 1, 0.588, and 0.5 were determined by the fraction of charged monomers and their degree of ionization, the effective solvent quality for the polymer backbone, the chain Kuhn length, and the type and strength of monomer–solvent interactions. The values of the B-parameters were obtained from the plateaus of normalized specific viscosity η sp (c)/N w (cl 3)1/(3ν–1) as a function of the monomer concentration c for polyelectrolytes with weight-average degree of polymerization N w . The extension of this approach to the entangled solution regime allowed us to determine the packing number of a chain of correlation blobs, P̃ e , which completes the set of parameters {B pe , B g , B th , P̃ e } uniquely describing static and dynamic properties of polyelectrolyte solutions. This information was used to construct a diagram of states, calculate the fraction of free counterions and the energy of the electrostatic blobs, and establish a crossover concentration to the entangled solution regime.

Dilute polyelectrolyte solutions: recent progress and open questions

“…This scaling has also been reported for other systems. 286,406 For N ≳ 3000, the data from Gulati et al , 100 Han et al , 301 Boris and Colby, 285 and Ganter et al 298 deviated to a power-law of N −0.78 , as expected in eqn (1) in the 2 c s ≫ fc region. These datasets follow eqn (1) with c s ≃ 10 −5 M, shown by the dashed line.…”

“…11. Other strong departures from the trend are observed by Boris and Colby, 285 Ganter et al 298 and Gulati et al 100 in DI water. A common feature of these datasets is the high molar mass of the polymers, all of which have N > 5000.…”

“…The estimation method of the residual salt concentration can be found in ref. 100, 285 and 301. In Fig.…”

“…Here, δ denotes the fraction of monomers that contain an ionic group. Some experimental evidence 100 suggests that the Coulomb energy inside an electrostatic blob may significantly exceed k B T , thus adding a pre-factor to eqn (5) and making the size of electrostatic blobs larger than expected by eqn (6). This would mean that the electrostatic blob concept may apply even when there are more than one dissociated charge per bare Kuhn segment, see further discussions in Section 3.10.…”

“…This is consistent with estimates for the residual salt in NaPSS solutions, which arise due to carbonic acid dissolved from the air, of ∼10 −5 –10 −4 M, see ref. 100, 285, 297 and 301. Vink, 318 Yamanaka et al 322,323 and Batzill et al 320 measured the viscosities of NaPSS in a nitrogen atmosphere to avoid contamination from carbonic acid.…”