链刚度对线形和环形聚合物熔体中Cox-Merz规则失效的影响
Effects of chain stiffness on the breakdown of the Cox-Merz rule in linear and ring polymer melts
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中文总结 AI 辅助
本研究通过分子动力学模拟发现，Cox-Merz规则在线形聚合物熔体中的失效随链长和链刚度增加而加剧，而环形聚合物保持较好一致性，表明其适用性依赖链长、刚度和分子拓扑。
中文摘要 AI 辅助
Cox-Merz规则是线性黏弹性中获得的复数黏度大小$|\eta^*(\omega)|$与稳态剪切黏度$\eta(\dot{\gamma})$之间的经验关系。在本研究中，我们使用Kremer-Grest模型对粗粒化聚合物熔体进行了分子动力学模拟，并系统地考察了Cox-Merz规则对线形和环形聚合物的链长和链刚度的有效性。对于短链，更普遍地，对于柔性链，$|\eta^*(\omega)|$和$\eta(\dot{\gamma})$在对应的角频率$\omega$和剪切速率$\dot{\gamma}$下表现出良好的一致性。然而，对于线形聚合物，随着链长和链刚度的增加，两种黏度之间的差异变得越来越明显，在高对应的$\omega$和$\dot{\gamma}$值下，$|\eta^*(\omega)|$超过$\eta(\dot{\gamma})$。这种偏差与强稳态剪切下的显著非线性响应有关，此时流动诱导的链伸展和取向可以改变控制近平衡松弛的缠结约束。相比之下，环形聚合物在所考察的范围内，随着链长和刚度的增加，$|\eta^*(\omega)|$和$\eta(\dot{\gamma})$之间保持明显更好的一致性，表明Cox-Merz规则的失效较弱。这些结果表明，Cox-Merz规则的适用性强烈依赖于链长、链刚度和分子拓扑结构。当稳态剪切下的分子响应与近平衡线性黏弹性所表征的松弛行为显著偏离时，复数黏度不再能准确预测稳态剪切黏度，导致Cox-Merz规则的显著失效。
英文摘要
The Cox-Merz rule is an empirical relation between the magnitude of the complex viscosity, $\lvertη^*(ω)\rvert$, obtained from linear viscoelasticity, and the steady-shear viscosity, $η(\dotγ)$. In this study, we performed molecular dynamics simulations of coarse-grained polymer melts using the Kremer-Grest model and systematically examined the validity of the Cox-Merz rule as a function of chain length and chain stiffness for linear and ring polymers. For short chains and, more generally, for flexible chains, $\lvertη^*(ω)\rvert$ and $η(\dotγ)$ show good agreement at corresponding values of angular frequency $ω$ and shear rate $\dotγ$. For linear polymers, however, the discrepancy between the two viscosities becomes increasingly pronounced with increasing chain length and chain stiffness, with $\lvertη^*(ω)\rvert$ exceeding $η(\dotγ)$ at high corresponding values of $ω$ and $\dotγ$. This deviation is associated with the pronounced nonlinear response under strong steady shear, where flow-induced chain extension and alignment can modify the entanglement constraints that govern relaxation near equilibrium. In contrast, ring polymers retain substantially better agreement between $\lvertη^*(ω)\rvert$ and $η(\dotγ)$ with increasing chain length and stiffness within the range examined here, indicating a weaker breakdown of the Cox-Merz rule. These results demonstrate that the applicability of the Cox-Merz rule depends strongly on chain length, chain stiffness, and molecular architecture. When the molecular response under steady shear deviates substantially from the relaxation behavior characterized by linear viscoelasticity near equilibrium, the complex viscosity can no longer accurately predict the steady-shear viscosity, resulting in a pronounced breakdown of the Cox-Merz rule.
发表机构
- The University of Osaka（大阪大学）
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