We present a comprehensive experimental rheological dataset for purified entangled ring polystyrenes and their blends with linear chains in nonlinear shear and elongation. In particular, data for the shear stress growth coefficient, steady-state shear viscosity, and first and second normal stress differences are obtained and discussed as functions of the shear rate, as well as molecular parameters (molar mass, blend composition, and decreasing molar mass of linear component in the blend). Over the extended parameter range investigated, rings do not exhibit clear transient undershoot in shear, in contrast to their linear counterparts and ring-linear blends. For the latter, the size of the undershoot and respective strain appear to increase with the shear rate. The universal scaling of the strain at overshoot and fractional overshoot (the ratio of the maximum to the steady-state shear stress growth coefficient) indicates subtle differences in the shear-rate dependence between rings and linear polymers or their blends. The shear thinning behavior of pure rings yields a slope nearly identical to predictions (−4/7) of a recent shear slit model and molecular dynamics simulations. Data for the second normal stress difference are reported for rings and ring-linear blends. While N₂ is negative and its absolute value stays below that of N₁, as for linear polymers, the ratio –N₂/N₁ is unambiguously larger for rings compared to linear polymer solutions with the same number of entanglements (almost by a factor of 2), in agreement with recent nonequilibrium molecular dynamics simulations. Furthermore, –N₂ exhibits slightly weaker shear rate dependence compared to N₁ at high rates, and the respective power-law exponents can be rationalized in view of the slit model (3/7) and simulations (0.6), although further work is needed to unravel the molecular original of the observed behavior. The comparison of shear and elongational stress growth coefficients for blends reflects the effect of ring-linear threading, which leads to significant viscosity enhancement in elongation. Along the same lines, the elongational stress is much larger than the first normal stress in shear, and their ratio is much larger for rings and ring-linear blends compared to linear polymers. This confirms the interlocking scenario of rings and their important role in mechanically reinforcing linear matrices.

中文翻译：

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缠结聚合物环和线性环共混物的非线性流变测量

我们提出了一个综合的实验流变数据集，用于纯化纠缠环聚苯乙烯及其与线性链在非线性剪切和伸长率中的共混物。特别是，获得了剪切应力增长系数、稳态剪切粘度、第一和第二法向应力差的数据，并将其作为剪切速率的函数以及分子参数（摩尔质量、共混物组成和递减摩尔数）进行了讨论。混合物中线性组分的质量）。在所研究的扩展参数范围内，与它们的线性对应物和环-线性混合相比，环在剪切中没有表现出明显的瞬态下冲。对于后者，下冲的大小和相应的应变似乎随着剪切速率的增加而增加。过冲和分数过冲处的应变的通用标度（最大值与稳态剪切应力增长系数的比率）表明环和线性聚合物或其混合物之间的剪切速率依赖性存在细微差异。纯环的剪切变薄行为产生的斜率几乎与最近剪切狭缝模型和分子动力学模拟的预测（-4/7）相同。报告了环和环线混合的第二法向应力差的数据。尽管 报告了环和环线混合的第二法向应力差的数据。尽管 报告了环和环线混合的第二法向应力差的数据。尽管N ₂为负，其绝对值低于N ₁，对于线型聚合物，与具有相同缠结数的线型聚合物溶液相比，环的-N ₂ / N ₁比率明显更大（几乎是2），与最近的非平衡分子动力学模拟一致。此外，与N _1相比， –N ₂对剪切速率的依赖性稍弱在高速率下，根据狭缝模型（3/7）和模拟（0.6），可以合理化相应的幂律指数，尽管需要进一步的工作来解开观察到的行为的分子原点。共混物的剪切和伸长应力增长系数的比较反映了环形线性螺纹的影响，这导致伸长率的粘度显着提高。同样，拉伸应力远大于剪切中的第一法向应力，并且与线性聚合物相比，环状和环状线性共混物的比例要大得多。这证实了环的互锁方案及其在机械增强线性矩阵中的重要作用。