Influence of counterion valency on the scattering properties of highly charged polyelectrolyte solutions revisited

In light of recent simulations showing the importance of hydration in the thermodynamic properties and structural organization of polyelectrolytes in solution, we revisit small-angle neutron scattering measurements examining the influence of charge valence, along with polymer concentration and mass, on the structure of model salt-free polystyrene sulfonate (PSS) solutions and basic scattering features, such as the polyelectrolyte peak and the radius of gyration and persistence length lp of the PSS molecules. In previous companion work, we showed that the replacement of monovalent by divalent counterions leads to a reduced low-angle scattering intensity related to a reduction of chain association, while the interchain correlation length within the clusters becomes larger, indicating that the divalent counterions give rise to a weakening of the interchain attractive interactions and a reduction in the slow mode relaxation time arising from ion solvation rather than enhanced molecular association. In the present work, we show that the scaling exponent describing the polymer concentration dependence of the polyelectrolyte peak position q* correspondingly changes from a magnitude near 1/2 to a value near 1/3 over a wide polymer concentration range below 1M. This change of scaling behavior with counterion valence raises questions about the hypothesis that salt-free long polyelectrolyte chains exhibit a rod-like conformation in the dilute limit. Direct contrast-matching neutron scattering measurements indicate that the polyelectrolyte chains exhibit substantially enhanced chain flexibility with the replacement of monovalent by divalent counterions. Moreover, lp was found correspondingly to scale with the salt concentration with exponents 1/2 to a value near 1/3, providing further evidence of the sensitivity of the polyelectrolyte properties to counterion valence. Collectively, these properties generally point to the importance of counterion valence and ion and polymer hydration in the properties of polyelectrolyte solutions.