Lin Y-H, Das A K
Department of Applied Chemistry, National Chiao Tung University, Hsinchu 30050, Taiwan.
J Chem Phys. 2007 Feb 21;126(7):074902. doi: 10.1063/1.2431648.
Shear stress relaxation modulus GS(t) curves of entanglement-free Fraenkel chains have been calculated using Monte Carlo simulations based on the Langevin equation, carrying out both in the equilibrium state and following the application of a step shear deformation. While the fluctuation-dissipation theorem is perfectly demonstrated in the Rouse-chain model, a quasiversion of the fluctuation-dissipation theorem is observed in the Fraenkel-chain model. In both types of simulations on the Fraenkel-chain model, two distinct modes of dynamics emerge in GS(t), giving a line shape similar to that typically observed experimentally. Analyses show that the fast mode arises from the segment-tension fluctuations or reflects the relaxation of the segment tension created by segments being stretched by the applied step strain-an energetic-interactions-driven process-while the slow mode arises from the fluctuations in segmental orientation or represents the randomization of the segmental-orientation anisotropy induced by the step deformation-an entropy-driven process. Furthermore, it is demonstrated that the slow mode is well described by the Rouse theory in all aspects: the magnitude of modulus, the line shape of the relaxation curve, and the number-of-beads (N) dependence of the relaxation times. In other words, one Fraenkel segment substituting for one Rouse segment, it has been shown that the entropic-force constant on each segment is not a required element to give rise to the Rouse modes of motion, which describe the relaxation modulus of an entanglement-free polymer over the long-time region very well. This conclusion provides an explanation resolving a long-standing fundamental paradox in the success of Rouse-segment-based molecular theories for polymer viscoelasticity-namely, the paradox between the Rouse segment size being of the same order of magnitude as that of the Kuhn segment (each Fraenkel segment with a large force constant HF can be regarded as basically equivalent to a Kuhn segment) and the meaning of the Rouse segment as defined in the Rouse-chain model. The general agreement observed in the comparison of the simulation and experimental results indicates that the Fraenkel-chain model, while being still relatively simple, has captured the key element in energetic interactions--the rigidity on the segment--in a polymer system.
基于朗之万方程，通过蒙特卡罗模拟计算了无缠结弗伦克尔链的剪切应力松弛模量GS(t)曲线，模拟在平衡状态下以及施加阶跃剪切变形后进行。虽然涨落耗散定理在劳斯链模型中得到了完美证明，但在弗伦克尔链模型中观察到了涨落耗散定理的一个准版本。在弗伦克尔链模型的两种模拟类型中，GS(t)中出现了两种不同的动力学模式，给出了与实验中通常观察到的相似的线形。分析表明，快速模式源于链段张力涨落，或反映了由施加的阶跃应变拉伸链段所产生的链段张力的松弛——这是一个能量相互作用驱动的过程，而慢速模式源于链段取向的涨落，或代表了阶跃变形引起的链段取向各向异性的随机化——这是一个熵驱动的过程。此外，研究表明，慢速模式在所有方面都能被劳斯理论很好地描述：模量大小、松弛曲线的线形以及松弛时间对珠子数（N）的依赖性。换句话说，用一个弗伦克尔链段替代一个劳斯链段，已经表明每个链段上的熵力常数不是产生描述无缠结聚合物在长时间区域松弛模量的劳斯运动模式的必要元素。这一结论为解决基于劳斯链段的聚合物粘弹性分子理论成功中一个长期存在的基本悖论提供了解释——即劳斯链段尺寸与库恩链段尺寸处于同一数量级（每个具有大力常数HF的弗伦克尔链段基本上可视为等同于一个库恩链段）与劳斯链段在劳斯链模型中定义的含义之间的悖论。模拟结果与实验结果比较中观察到的总体一致性表明，弗伦克尔链模型虽然仍然相对简单，但已经捕捉到了聚合物体系中能量相互作用的关键要素——链段的刚性。
