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arXiv 0811.3946cond-mat.soft
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具有柔性交叉链路的刚性polymer网络的有效介质方法

Effective medium approach for stiff polymer networks with flexible cross-links

C. P. Broedersz, C. Storm, F. C. MacKintosh

摘要:

最近的实验表明,在一个灵活的交联剂,如丰富的细胞骨架蛋白细丝蛋白的存在下,在体外网络的生物聚合物肌动蛋白的非线性弹性显着改变。对这种网络的基本原则仍然知之甚少。在这里,我们描述了一个灵活的交联刚性聚合物网络的有效介质理论。我们认为,可以完全归因于熵硬化的交叉链接的响应,而软化由于域展开可以忽略不计。该网络被建模为一个集合的随机定向杆连接的灵活的交叉链接到一个弹性连续。该有效介质被处理在线性弹性限度以及在一个更一般的框架,其中介质自洽地表示非线性网络行为。该模型预测,非线性弹性响应在与交联剂长度成正比且与长丝长度成反比的应变下开始。此外,我们发现,微分模量的比例线性与应力的硬化制度。这些结果与本体流变学数据非常一致。

英文摘要:

Recent experiments have demonstrated that the nonlinear elasticity of in vitro networks of the biopolymer actin is dramatically altered in the presence of a flexible cross-linker such as the abundant cytoskeletal protein filamin. The basic principles of such networks remain poorly understood. Here we describe an effective medium theory of flexibly cross-linked stiff polymer networks. We argue that the response of the cross-links can be fully attributed to entropic stiffening, while softening due to domain unfolding can be ignored. The network is modeled as a collection of randomly oriented rods connected by flexible cross-links to an elastic continuum. This effective medium is treated in a linear elastic limit as well as in a more general framework, in which the medium self-consistently represents the nonlinear network behavior. This model predicts that the nonlinear elastic response sets in at strains proportional to cross-linker length and inversely proportional to filament length. Furthermore, we find that the differential modulus scales linearly with the stress in the stiffening regime. These results are in excellent agreement with bulk rheology data.

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