Recent experiments suggest that the terminal relaxation time ${\hat{\tau }}_b$ of star-linear blends varies nonmonotonically with the weight fraction of the star polymer in the blend $w_s$ [Hall et al., Macromolecules 52, 7831 (2019)], when the linear polymer is more viscous than the star; i.e., the ratio of linear and star viscosities $r_{\eta }={\eta }_{0,l}/{\eta }_{0,s}>1$. We used a fast slip link model called ecoSLM to assess whether slip link models, unlike tube-based theories, can correctly capture this trend. Simulations were performed on around 150 different star-linear blends where the average number of entanglements per star arm was varied between 8 and 25, and the viscosity ratio $r_{\eta }$ was varied between 0.1 and 1000. Results agree with experiments: nonmonotonic variation of ${\hat{\tau }}_b$ with $w_s$ is observed only when $r_{\eta }>1$ due to partial suppression of constraint release on the star polymers in the blend. In this regime, for a given star polymer, we found that the star weight fraction $w_s^{\ast }$ corresponding to the blend with the longest terminal relaxation time ${\hat{\tau }}_b^{\ast }$ decreased with increasing $r_{\eta }$. By extrapolating plots of $w_s^{\ast }$ versus $r_{\eta }$, we estimated an upper-bound $r_{\eta }^{\mathrm{ub}}\approx 0.3\log {\eta }_{0,s}+1.23$, where the nonmonotonic variation of ${\hat{\tau }}_b$ with $w_s$ is expected to subside. This prediction is directly confirmed in ecoSLM simulations with $r_{\eta }\approx 100-1000$. Thus, we find that $r_{\eta }>1$ is a necessary, but not sufficient, condition for nonmonotonic variation of terminal relaxation of a star-linear blend with composition.

中文翻译：

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用快速滑移连接模型探测星形线性混合中终端松弛的非单调变化

最近的实验表明，终端弛豫时间 ${\hat{\tau }}_{乙}$ 星形线性共混物的数量随共混物中星形聚合物的重量分数非单调变化 ${瓦}_{秒}$[霍尔等人。, Macromolecules 52 , 7831 (2019)]，当线性聚合物比星形聚合物更粘稠时；即线性和星形粘度的比率$r_{\eta }={\eta }_{0,升}/{\eta }_{0,秒}>1$. 我们使用称为ecoSLM 的快速滑动链接模型来评估滑动链接模型是否与基于管的理论不同，可以正确捕捉这种趋势。对大约 150 种不同的星形-线性共混物进行了模拟，其中每个星形臂的平均缠结数在 8 到 25 之间变化，粘度比$r_{\eta }$ 在 0.1 和 1000 之间变化。结果与实验一致：非单调变化 ${\hat{\tau }}_{乙}$ 和 ${瓦}_{秒}$ 仅当 $r_{\eta }>1$由于部分抑制了共混物中星形聚合物的约束释放。在这种情况下，对于给定的星形聚合物，我们发现星形重量分数${瓦}_{秒}^{＊}$ 对应于终端弛豫时间最长的混合物 ${\hat{\tau }}_{乙}^{＊}$ 随着增加而减少 $r_{\eta }$. 通过外推图${瓦}_{秒}^{＊}$ 相对 $r_{\eta }$，我们估计了一个上限 $r_{\eta }^{\mathrm{乌布}}\approx 0.3\mathrm{日志}{\eta }_{0,秒}+1.23$，其中非单调变化 ${\hat{\tau }}_{乙}$ 和 ${瓦}_{秒}$预计会消退。这种预测在ecoSLM 模拟中得到了直接证实$r_{\eta }\approx 100-1000$. 于是，我们发现$r_{\eta }>1$ 是星形-线性混合物与成分的终弛豫非单调变化的必要条件，但不是充分条件。