Mixtures of polymers of varying topologies and stiffnesses display complex emergent rheological properties that often cannot be predicted from their single-component counterparts. For example, entangled blends of ring and linear polymers have been shown to exhibit enhanced shear thinning and viscosity, as well as prolonged relaxation timescales, compared to pure solutions of rings or linear chains. These emergent properties arise in part from the synergistic threading of rings by linear polymers. Topology has also been shown to play an important role in composites of flexible (e.g., DNA) and stiff (e.g., microtubules) polymers, whereby rings promote mixing while linear polymers induce demixing and flocculation of stiff polymers, with these topology-dependent interactions giving rise to highly distinct rheological signatures. To shed light on these intriguing phenomena, we use optical tweezers microrheology to measure the linear and nonlinear rheological properties of entangled ring-linear DNA blends and their composites with rigid microtubules. We show that linear viscoelasticity is primarily dictated by microtubules at lower frequencies, but their contributions become frozen out at frequencies above the DNA entanglement rate. In the nonlinear regime, we reveal that mechanical response features, such as shear thinning and stress softening, are mediated by entropic stretching, threading, and flow alignment of entangled DNA, as well as forced dethreading, disentanglement, and clustering. The contributions of each of these mechanisms depend on the strain rate as well as the entanglement density and stiffness of the polymers, leading to nonmonotonic rate dependences of mechanical properties that are most pronounced for highly concentrated ring-linear blends rather than DNA-microtubule composites.

中文翻译：

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聚合物螺纹和刚度决定了缠绕环状线性混合物及其与刚性杆微管的复合材料的粘弹性

不同拓扑结构和刚度的聚合物混合物显示出复杂的涌现流变特性，通常无法从其单组分对应物中预测出来。例如，与环或线性链的纯溶液相比，环和线性聚合物的缠结共混物已显示出增强的剪切稀化和粘度，以及延长的松弛时间尺度。这些涌现的特性部分源于线性聚合物环的协同穿线。拓扑结构也被证明在柔性（例如 DNA）和刚性（例如微管）聚合物的复合材料中发挥着重要作用，其中环促进混合，而线性聚合物诱导刚性聚合物的分层和絮凝，这些拓扑相关的相互作用给出上升到高度不同的流变特征。为了阐明这些有趣的现象，我们使用光镊微流变学来测量缠结的环状线性 DNA 混合物及其与刚性微管的复合物的线性和非线性流变特性。我们表明线性粘弹性主要由较低频率的微管决定，但它们的贡献在高于 DNA 纠缠率的频率下被冻结。在非线性机制中，我们揭示了剪切稀化和应力软化等机械响应特征是由熵拉伸、穿线和纠缠 DNA 的流动排列以及强制脱线、解缠结和聚类介导的。这些机制中的每一个的贡献取决于应变率以及聚合物的缠结密度和刚度，