Phillies George David Joseph
Department of Physics, Worcester Polytechnic Institute, Worcester, MA 01609, USA.
Polymers (Basel). 2023 Jul 28;15(15):3216. doi: 10.3390/polym15153216.
In two prior articles, I demonstrated from extensive simulational studies by myself and others that the Rouse model of polymer dynamics is invalid in polymer melts and in dilute solution. However, the Rouse model is the foundational basis for most modern theories of polymeric fluid dynamics, such as reptation/scaling models. One therefore rationally asks whether there is a replacement. There is, namely by extending the Kirkwood-Riseman model. Here, I present a comprehensive review of one such set of extensions, namely the hydrodynamic scaling model. This model assumes that polymer dynamics in dilute and concentrated solution is dominated by solvent-mediated hydrodynamic interactions; chain crossing constraints are taken to create only secondary corrections. Many other models assume, contrariwise, that in concentrated solutions, the chain crossing constraints dominate the dynamics. An extended Kirkwood-Riseman model incorporating interchain hydrodynamic interactions is developed. It yields pseudovirial series for the concentration and molecular weight dependencies of the self-diffusion coefficient Ds and the low-shear viscosity η. To extrapolate to large concentrations, rationales based on self-similarity and on the Altenberger-Dahler positive-function renormalization group are presented. The rationales correctly predict how Ds and η depend on polymer concentration and molecular weight. The renormalization group approach leads to a two-parameter ansatz that correctly predicts the functional forms of the frequency dependencies of the storage and loss moduli. A short description is given of each of the papers that led to the hydrodynamic scaling model. Experiments supporting the aspects of the model are noted.
在之前的两篇文章中，我通过自己以及他人进行的大量模拟研究证明，聚合物动力学的劳斯模型在聚合物熔体和稀溶液中是无效的。然而，劳斯模型却是大多数现代聚合物流体动力学理论（如蛇行/标度模型）的基础。因此，人们合理地会问是否有替代模型。答案是有的，即通过扩展柯克伍德-里斯曼模型。在此，我对其中一组扩展模型，即流体动力学标度模型进行全面综述。该模型假定，稀溶液和浓溶液中的聚合物动力学主要由溶剂介导的流体动力学相互作用主导；链交叉约束仅产生次要修正。相反，许多其他模型假定，在浓溶液中，链交叉约束主导动力学。本文开发了一个纳入链间流体动力学相互作用的扩展柯克伍德-里斯曼模型。它给出了自扩散系数(D_s)和低剪切粘度(\eta)对浓度和分子量依赖性的赝维里级数。为了外推到高浓度，本文提出了基于自相似性以及阿尔滕贝格尔-达勒正函数重整化群的理论依据。这些理论依据正确地预测了(D_s)和(\eta)如何依赖于聚合物浓度和分子量。重整化群方法导出了一个双参数假设，该假设正确地预测了储能模量和损耗模量频率依赖性的函数形式。本文简要介绍了每一篇促成流体动力学标度模型的论文。文中还提及了支持该模型各方面的实验。
