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.

中文翻译：

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模拟正交叠加流变测量以探测缠结聚合物的非平衡动力学

了解非线性变形下微观结构动力学的变化对于设计纠缠聚合物流体的流动过程至关重要，促进了实验方法的发展，以探测应变和速率相关的松弛机制修改。尽管正交叠加流变仪 (OSR) 有望成为这种探针，但在纠缠聚合物动力学的背景下解释 OSR 可获得的叠加模量的能力仍然是一个悬而未决的问题。为了填补这一空白，我们使用单分散和多分散缠结聚合物的详细微观结构模型报告模型 OSR 预测，即分别考虑爬行、链收缩和对流约束的 Rolie-Poly 和 Rolie-Double-Poly 模型释放。通过将数值计算与微扰分析相结合，我们证明对于可以由单模模型描述的聚合物，不同剪切速率和频率下的 OSR 叠加模量通常可以折叠到单个主曲线上，具有速率相关的位移取决于聚合物构象和松弛速率的非线性速率相关修改而不改变主要松弛机制的因素。我们系统地研究了 OSR 模量如何对分子量分布的形状和分散度敏感。我们讨论了我们对一大类本构模型的结果的普遍性，并建议类比 Laun 规则，将 OSR 模量与第一法向应力差相关联。