Solution Properties of Polyelectrolytes with Divalent Counterions

Abstract

Divalent ions are known to strongly influence the phase behavior, conformation, and flow properties of polyelectrolytes in solution. Here, we report small-angle neutron scattering and viscosity data for the magnesium salt of polystyrene sulfonate (MgPSS) in salt-free water and compare these results with analogous measurements for NaPSS. In a dilute solution, both salts are found to exhibit a rod-like conformation for high degrees of polymerization, but the chain dimensions of MgPSS are significantly smaller than for NaPSS, which is consistent with the lower charge density of MgPSS found from conductivity data. In the semidilute regime, the correlation length scales as ξ ≃ 3.7c −1/2 nm for NaPSS and ξ ≃ 5.4c −1/2 nm for MgPSS. At high concentrations, deviations to weaker power laws are observed for both salts. The variation of the viscosity with the degree of polymerization (η sp ∼ N) is consistent with unentangled, Rouse-like dynamics. Fuoss-law-type behavior (η sp ∼ c 1/2 ) is observed at low polymer concentrations, which turns into a stretched exponential dependence at high c, perhaps due to an increase in the local friction experienced by polymer segments.

Quantifying the Effect of Multivalent Ions in Polyelectrolyte Solutions

“…We extend the approach developed above to quantify the effect of divalent ions on solution properties of polystyrene sulfonate. − Figure shows the analysis of viscosity data for sodium polystyrene sulfonate (NaPSS) with six different molecular weights ranging from 2.9 × 10 4 to 9.7 × 10 5 g/mol. , The degrees of polymerization were determined from the molecular weights of the parent polystyrene samples divided by the molar mass of the polystyrene repeat unit, M 0 = 104 g/mol. The repeat unit projection length for a carbon backbone is l = 0.255 nm.…”

“…The same NaPSS samples were then used to prepare and study MgPSS solutions in ref . Figure a shows specific viscosity data taken from this study with the same adjusted values of N w as ones used for NaPSS.…”

“…As in the case of the CMC systems, we can overlay the calculated values of the correlation length ξ with experimental values obtained from the peak position 2π/ q *. For this plot, we use values for scattering peak positions q * given in refs , , , and . These data are shown in Figure , with arrows indicating our estimations for the locations of the electrostatic blob overlap concentration c D for NaPSS and MgPSS solutions (see Table ).…”

“…Open left black triangles correspond to scattering data of CaPSS from ref . Open black pentagons correspond to scattering data of MgPSS from ref . The inset shows original peak position data.…”

“…The method , is based on the linear dependence of the solution specific viscosity on the weight-average degree of polymerization and the concentration dependence of the solution correlation length in the unentangled solution regime. In particular, we apply this scaling approach , to obtain the fraction of ionized groups, excluded volume, and Kuhn length in salt-free solutions of carboxymethylcellulose (CMC) with Na + , Ca 2+ , Mg 2+ , Mn 2+ , Co 2+ , and Ba 2+ counterions , and polystyrene sulfonate with Na + and Mg 2+ counterions. − This information is used to elucidate the differences and similarities in the system behavior depending on the counterion valence. Furthermore, this approach , allows us to represent solution specific viscosity as a universal function of the number of repeat units per solution correlation length in a broad concentration range.…”