Statistical mechanical constitutive theory of polymer networks: The inextricable links between distribution, behavior, and ensemble
Statistical mechanical constitutive theory of polymer networks: The inextricable links between distribution, behavior, and ensemble
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DOI：
10.1103/physreve.102.012501
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发表时间：
2020-07-02
影响因子：
2.4
通讯作者：
Silberstein, Meredith N.
中科院分区：
文献类型：
--
作者：
Buche, Michael R.;Silberstein, Meredith N.
提出了一种将统计力学原理与宏观热力学本构理论无缝结合起来的大变形下聚合物网络力学响应的基本理论。我们的配方允许考虑任意的聚合物链的行为时，链之间的相互作用可以忽略不计。这种细致的处理突出了单链力学行为与网络中链的平衡分布之间自然发生的对应关系，以及不同单链热力学系综之间的对应关系。我们证明了这些重要的区别与可扩展的自由连接链模型。这种统计力学理论，然后扩展到连续体尺度，在那里我们利用传统的宏观本构理论，最终检索柯西应力的变形和聚合物网络统计。再次使用可扩展的自由连接链模型，我们说明了自然发生的统计对应的重要性，通过它们对网络的应力-拉伸响应的影响。我们还表明，这些差异消失时，链中的链接的数量变得足够大，并讨论为什么某些方法比其他人更好地达到这个限制之前。
A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation permits the consideration of arbitrary polymer chain behaviors when interactions among chains may be neglected. This careful treatment highlights the naturally occurring correspondence between single-chain mechanical behavior and the equilibrium distribution of chains in the network, as well as the correspondences between different single-chain thermodynamic ensembles. We demonstrate these important distinctions with the extensible freely jointed chain model. This statistical mechanical theory is then extended to the continuum scale, where we utilize traditional macroscopic constitutive theory to ultimately retrieve the Cauchy stress in terms of the deformation and polymer network statistics. Once again using the extensible freely jointed chain model, we illustrate the importance of the naturally occurring statistical correspondences through their effects on the stress-stretch response of the network. We additionally show that these differences vanish when the number of links in the chain becomes sufficiently large enough, and discuss why certain methods perform better than others before this limit is reached.