Department of Chemical and Biological Engineering and Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 3440 S. Dearborn Street, Chicago, Illinois 60616, USA.
J Chem Phys. 2010 Feb 21;132(7):074905. doi: 10.1063/1.3314727.
We consider the spatiotemporal fluctuation of slip-link positions via the implementation of elastic slip-links. The level of description is similar to our previously proposed slip-link model, wherein we use the entanglement position in space as dynamic variables, and the number of Kuhn steps between entanglements. However, since it is a mean-field, single-chain description it has some relevance to the slip-spring simulations of Likhtman, and the phantom chain model for cross-linked networks. It might also provide a connection between slip-links and tubes. Two implementations are possible, depending on whether or not the slip-links are allowed to pass through one another. If a boundary condition on the dynamics preventing such passage is imposed, then the plateau modulus is unchanged from perfectly rigid slip-links. Only the dynamics is changed. On the other hand, for phantom slip-links the distribution of the number of entanglements changes from Poisson. Furthermore, requiring normalization of the distribution function sets a constraint on how loose the virtual springs for the elastic slip-link are. These restrictions appear to be in agreement with parameter values used for the slip-spring simulations, although nonphantom slip-links were used there. The results are completely analogous to what was found by James and Guth for ideal elastic networks, whose derivation is repeated here. Our earlier rigid slip-link model is recovered as a limiting case.
我们通过弹性滑动连接的实现来考虑滑动连接位置的时空波动。描述的水平与我们之前提出的滑动连接模型相似，其中我们使用空间中的缠结位置作为动态变量，以及缠结之间的库恩步骤数。然而，由于它是一个平均场、单链描述，因此与 Likhtman 的滑动弹簧模拟和交联网络的幻影链模型有一定的相关性。它也可能在滑动连接和管道之间建立联系。有两种可能的实现方式，具体取决于滑动连接是否允许相互穿过。如果对动力学施加防止这种通过的边界条件，那么平台模量与完全刚性的滑动连接保持不变。只有动力学发生了变化。另一方面，对于幻影滑动连接，缠结数量的分布从泊松分布变为非泊松分布。此外，分布函数的归一化要求对弹性滑动连接的虚拟弹簧的松弛程度施加了限制。这些限制似乎与用于滑动弹簧模拟的参数值一致，尽管那里使用的是非幻影滑动连接。结果与 James 和 Guth 为理想弹性网络所发现的结果完全类似，这里重复了它们的推导。我们之前的刚性滑动连接模型是作为一个极限情况被恢复的。
