Scaling Behaviorof Entanglement Dynamics in PolyelectrolyteSolutions: Insights from High-Frequency Rheometry

Entanglement dynamics in polyelectrolyte solutions remain a challenging topic, particularly in capturing the entire dynamic spectrum, from single entanglement relaxation (τ_e) to reptation time (τ_rep), and aligning these observations with scaling predictions in the semidilute entangled (SE) and fully entangled (FE) neutral regimes. Using piezo compressional and classic rotational rheometry, we investigate the scaling behaviors of key viscoelastic properties over several decades of time scales in ten million Mw cationic polyacrylamide solutions. Specific viscosity (η_sp) and τ_rep scale as predicted within Fuoss, SE, and FE regimes, defining crossover concentrations between these regimes (<i>C</i>_e and <i>C</i>_D). More importantly, τ_e, the rubbery plateau width (τ_rep/τ_e), and the high-frequency modulus (<i>G</i>_e) scale as <i>C</i>^{–1.14±0.02}, <i>C</i>^1.25±0.07, and <i>C</i>^1.32±0.05, aligning with SE prediction in the early SE regime before transitioning to neutral scaling of <i>C</i>^–2.7±0.14, <i>C</i>^3.1±0.15, and <i>C</i>^2.35±0.07 at an intermediate concentration between <i>C</i>_e and <i>C</i>_D labeled <i>C</i>_D^e. These results indicate that electrostatic interactions affect single entanglements and reptation differently, leading to a transition to neutral behavior at <i>C</i>_<i>D</i>^e for the former and at <i>C</i>_D for the latter.