Rheology of Entangled Polyelectrolyte Solutions

Polyelectrolyte solution dynamics have been carefully studied experimentally and theoretically for unentangled solutions and thought to be reasonably well understood. While theoretical models have been proposed for entangled polyelectrolyte solutions, there have been limited experimental data published to justify any understanding of entangled polyelectrolyte solution rheology. Herein, we study entangled nearly monodisperse carefully dialyzed cesium polystyrene sulfonate (Mn = 2.83 × 106 g/mol) solutions without salt in water, anhydrous ethylene glycol (Tg =-95 °C), and anhydrous glycerol (Tg =-80 °C) using rotational rheometry and X-ray scattering to determine the correlation length. For the glycerol solutions, time-temperature superposition was found to work between 25 and-5 °C, yielding linear viscoelastic (LVE) response of polyelectrolyte solutions over a wide frequency range. At concentrations where scaling predictions expect entanglements, the LVE response appears unentangled (no rubbery plateau), suggesting an underestimation of the entanglement concentration ce. At higher concentrations in entangled solutions, the rubbery plateau width measured as the ratio of the two crossing points of storage and loss moduli (τrep/τe) in glycerol scales as c4, suggesting that polyelectrolyte solutions behave like solutions of neutral polymers in the entangled concentration regime. Four methods for evaluating entanglement concentration are compared, and their relative orderings are similar to those of neutral polymer solutions.