Exact theory of kinkable elastic polymers
Exact theory of kinkable elastic polymers
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DOI：
10.1103/physreve.71.021909
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发表时间：
2005-02-01
影响因子：
2.4
通讯作者：
Nelson, PC
中科院分区：
文献类型：
--
作者：
Wiggins, PA;Phillips, R;Nelson, PC
在宏观杆的连续介质力学中，材料本构关系中的非线性的重要性早已被认识到。虽然弯矩(扭矩)对弯曲的响应在小偏转角时几乎普遍是线性的，但许多杆系统表现出高曲率软化。这些杆系统的标志性行为是弯曲局部化的扭结转变。Cloutier和Widom最近的DNA环化实验证明，线弹性弯曲理论不能描述DNA的高曲率力学。在最近这项实验工作的启发下，我们发展了一个简单而精确的线弹性高分子链的统计力学理论，它可以经历扭结转变。我们用单参数表征了扭结行为，并表明所得到的理论既再现了蠕虫链模型已经很好地描述的低曲率线弹性行为，也再现了在最近的环化实验中观察到的高曲率软化。
The importance of nonlinearities in material constitutive relations has long been appreciated in the continuum mechanics of macroscopic rods. Although the moment (torque) response to bending is almost universally linear for small deflection angles, many rod systems exhibit a high-curvature softening. The signature behavior of these rod systems is a kinking transition in which the bending is localized. Recent DNA cyclization experiments by Cloutier and Widom have offered evidence that the linear-elastic bending theory fails to describe the high-curvature mechanics of DNA. Motivated by this recent experimental work, we develop a simple and exact theory of the statistical mechanics of linear-elastic polymer chains that can undergo a kinking transition. We characterize the kinking behavior with a single parameter and show that the resulting theory reproduces both the low-curvature linear-elastic behavior which is already well described by the wormlike chain model, as well as the high-curvature softening observed in recent cyclization experiments.