Modeling orthogonal superposition rheometry to probe nonequilibrium dynamics of entangled polymers

Abstract

Understanding changes to microstructural dynamics under nonlinear deformations is critical for designing flow processes of entangled polymeric fluids, motivating the development of experimental methods to probe strain- and rate- dependent modifications to relaxation mechanisms. Although orthogonal superposition rheometry (OSR) holds promise as such a probe, the ability to interpret the superposition moduli accessible by OSR in the context of entangled polymer dynamics remains an open question. To fill this gap, we report model OSR predictions using detailed microstructural models for both monodisperse and polydisperse entangled polymers, i.e., the Rolie-Poly and the Rolie-Double-Poly models, respectively, which account for reptation, chain retraction, and convective constraint release. By combining numerical calculations with a perturbation analysis, we demonstrate that for polymers that can be described by a single-mode model, the OSR superposition moduli at different shear rates and frequencies can generally be collapsed onto a single master curve, with rate-dependent shift factors that depend on the nonlinear rate-dependent modification of polymer conformation and relaxation rates without changing the dominant relaxation mechanisms. We systematically study how the OSR moduli are sensitive to the shape and dispersity of the molecular weight distribution. We discuss the generality of our results for a broad class of constitutive models and suggest an analogy to Laun’s rule to relate OSR moduli to the first normal stress difference. Our results provide a foundation to guide the design and interpretation of future experiments and demonstrate that orthogonal superposition rheometry often probes features in nonlinear dynamics more directly than conventional rheometry techniques.