Steenbakkers Rudi J A, Andreev Marat, Schieber Jay D
Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 3440 South Dearborn Street, Chicago, Illinois 60616, USA.
Department of Chemical and Biological Engineering, Illinois Institute of Technology, 10 West 35th Street, Chicago, Illinois 60616, USA.
Phys Rev E. 2021 Feb;103(2-1):022501. doi: 10.1103/PhysRevE.103.022501.
We evaluate the thermodynamic consistency of the anisotropic mobile slip-link model for entangled flexible polymers. The level of description is that of a single chain, whose interactions with other chains are coarse grained to discrete entanglements. The dynamics of the model consist of the motion of entanglements through space and of the chain through the entanglements, as well as the creation and destruction of entanglements, which are implemented in a mean-field way. Entanglements are modeled as discrete slip links, whose spatial positions are confined by quadratic potentials. The confinement potentials move with the macroscopic velocity field, hence the entanglements fluctuate around purely affine motion. We allow for anisotropy of these fluctuations, described by a set of shape tensors. By casting the model in the form of the general equation for the nonequilibrium reversible-irreversible coupling from nonequilibrium thermodynamics, we show that (i) since the confinement potentials contribute to the chain free energy, they must also contribute to the stress tensor, (ii) these stress contributions are of two kinds: one related to the virtual springs connecting the slip links to the centers of the confinement potentials and the other related to the shape tensors, and (iii) these two kinds of stress contributions cancel each other if the confinement potentials become anisotropic in flow, according to a lower-convected evolution of the confinement strength or, equivalently, an upper-convected evolution of the shape tensors of the entanglement spatial fluctuations. In previous publications, we have shown that this cancellation is necessary for the model to obey the stress-optical rule and the Green-Kubo relation, and simultaneously to agree with plateau modulus predictions of multichain models and simulations.
我们评估了用于缠结柔性聚合物的各向异性移动滑移链模型的热力学一致性。描述的层次是单链层次，其与其他链的相互作用被粗粒化为离散缠结。该模型的动力学包括缠结在空间中的运动、链通过缠结的运动，以及缠结的产生和破坏，这些都是以平均场的方式实现的。缠结被建模为离散的滑移链，其空间位置由二次势限制。限制势随宏观速度场移动，因此缠结围绕纯仿射运动波动。我们考虑了这些波动的各向异性，由一组形状张量描述。通过将该模型以非平衡热力学中关于非平衡可逆-不可逆耦合的一般方程的形式表示，我们表明：（i）由于限制势对链的自由能有贡献，它们也必须对应力张量有贡献；（ii）这些应力贡献有两种：一种与将滑移链连接到限制势中心的虚拟弹簧有关，另一种与形状张量有关；（iii）如果根据限制强度的下随体演化，或者等效地，根据缠结空间波动的形状张量的上随体演化，限制势在流动中变得各向异性，那么这两种应力贡献会相互抵消。在之前的出版物中，我们已经表明，这种抵消对于模型遵守应力-光学规则和格林-库博关系，同时与多链模型和模拟的平台模量预测一致是必要的。
