Ramírez Jorge, Sukumaran Sathish K, Likhtman Alexei E
Applied Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom.
J Chem Phys. 2007 Jun 28;126(24):244904. doi: 10.1063/1.2746867.
According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor.
根据线性响应理论，线性区域内的所有弛豫函数都可以通过在平衡态下计算的时间关联函数得到。在本文中，我们证明了交叉关联对聚合物熔体中的部分应力弛豫函数有显著贡献。我们在聚合物流变学的背景下给出了两个例子，（1）使用缠结聚合物的单链模型——滑移弹簧模型进行布朗动力学模拟，以及（2）对多链模型进行分子动力学模拟。使用单链模型，我们分析了限制势对应力弛豫和平台模量的贡献。尽管这个想法是用一个特定的模型来说明的，但它适用于任何使用势来限制链运动的单链模型。这使我们对管模型背后的一些假设产生质疑，特别是从平台模量得到的缠结分子量的意义。为了阐明这个问题，我们使用多链模型研究了非键合排斥体积相互作用对应力弛豫的贡献。键合/非键合贡献与总应力弛豫（在与密度相关的“胶体”弛豫时间之后）的比例关系，尽管管模型使用了有问题的假设，但仍为其成功之处提供了一些见解。这种比例关系表明，使用管模型确实可以再现弛豫谱的形状，问题就简化为找到正确的前置因子。
