Understanding how polymer concentration and network structure influence nonlinear rheological response remains a fundamental challenge in polymer physics. Here, we present a comprehensive investigation of the rheology of aqueous polyacrylamide (PAAm) solutions with molecular weight Mw ≈ 5 × 106 g/mol, across a wide concentration range (0.1–12.5 wt %), normalized by the entanglement concentration (cw/ce = 0.15–19.23). Using steady shear, small-amplitude oscillatory shear (SAOS), and large-amplitude oscillatory shear (LAOS) measurements, we map the evolution from viscous-dominated to elastic-dominated behavior with increasing concentration, accompanied by progressively stronger shear thinning behavior. Nonlinear analyses are performed using Fourier transform (FT) rheology, intrinsic nonlinearity (3Q0), energy dissipation ratio (ϕ), and the sequence of physical processes (SPP) framework. At low cw/ce, solutions show viscous-dominated behavior with high ϕ values even in the linear regime, whereas higher cw/ce displays an increasingly elastic response. Beyond the moduli crossover, all samples converge to a plastic-like dissipation plateau (ϕ ≈ 0.85), independent of concentration. SPP analysis reveals a robust intracycle sequence: stiffening, thickening, relaxation, and recoil, whose location and extent depend on both cw/ce and oscillation frequency. We combine these bulk measures with rheomicroscopy, which uncovers striking differences in flow-induced microstructural behavior. At low concentrations, the flow field remains homogeneous even at high strain. In contrast, highly entangled samples (cw/ce ≳ 15) show structural disruption, banding, and apparent fracture. These findings highlight that bulk rheology can mask localized instabilities, reinforcing the value of direct imaging approaches. Overall, this study demonstrates the strength of combining normalized concentration scaling with advanced LAOS-based tools (ϕ, 3Q0, SPP) and imaging to reveal the rich nonlinear rheological behavior of polymer solutions. These insights have implications for soft material design and formulation across diverse applications in printing, flow processing, and biomedical gels.
Agrawal et al. (Tue,) studied this question.