$M$中的$[η]$线性不隐含Rouse动力学
An $[η]$ Linear in $M$ Does Not Imply Rouse Dynamics
摘要：
与某些预期相反，聚合物的溶液特性粘度$[η]$或熔体粘度与聚合物分子量$M$成线性关系的实验发现并不表明聚合物动力学是类Rouselike的。为什么？为什么？另一个主要的聚合物动力学模型是由Kirkwood和Riseman [ \emph{J. Chem.\ Phys.\ } \textbf{16}，565-573（1948）]提出的，它以自由排水的形式导致预测$[η] \sim M$，尽管该模型中的聚合物运动与Rouse模型中的聚合物运动完全不同。在Rouse模型中，链运动是线性平移和内部（“Rouse”）模式。在柯克伍德-里斯曼模型（以及这里推导出的自由排水形式）中，链条运动是平移和全身旋转。产生这种差异是因为Rouse的计算隐含地仅涉及受到零外部剪力的链（并且，顺便说一句，Rouse对$[η]$的构造是无效的，因为它得出的结论是，在Rouse隐含地假设没有施加剪力的系统中存在粘性耗散）。
英文摘要：
Contrary to some expectations, an experimental finding for a polymer that the solution intrinsic viscosity $[η]$ or the melt viscosity is linear in the polymer molecular weight $M$ does not indicate that polymer dynamics are Rouselike. Why? The other major polymer dynamic model, due to Kirkwood and Riseman [\emph{J. Chem.\ Phys.\ } \textbf{16}, 565-573 (1948)], leads in its free-draining form to a prediction $[η] \sim M$, even though the polymer motions in this model are totally unlike the polymer motions in the Rouse model. In the Rouse model, the chain motions are linear translation and internal ('Rouse') modes. In the Kirkwood-Riseman model (and its free-draining form, derived here), the chain motions are translation and whole-body rotation. The difference arises because Rouse's calculation implicitly refers only to chains subject to zero external shear force (And, as an aside, Rouse's construction of $[η]$ is invalid, because it concludes that there is viscous dissipation in a system that Rouse implicitly assumed to have no applied shear).
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