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上海交通大学自然科学研究院最新成果:长程静电力的几何效应

近期,物理学顶级学术期刊物理评论快报 ( Physical Review Letters) 发表了上海交通大学自然科学研究院及物理与天文系姚振威和美国西北大学材料科学和工程系 Monica Olvera de la Cruz完成的题为“Electrostatics-driven hierarchical buckling of charged flexible ribbons”的论文(PRL 116, 148101, 2016), 报道了他们关于通过长程静电相互作用改变带状二维弹性体表面的度规从而产生丰富构型的工作。

带电弹性带在生物和材料系统中普遍存在。人们直觉上相信,带电弹性体在长程静电排斥势作用下,会倾向于采取伸展的姿态以降低静电能。然而,由于静电力本身的长程属性,带电体任何部分的位移都将对剩余部分产生影响。另一方面,静电力和带电体形状之间存在着复杂的耦合。这种耦合以及静电力的长程性,给理论上研究带电弹性体的构型变化带来挑战, 但同时为非平凡构型的产生创造了可能性。

数值模拟成为探索带电弹性体可能构型的有力工具。作者在这项工作中采用数值模拟的方法获得带电弹性带丰富的构型。这些构型可分为两类:波纹状和螺旋状,分别如图中所示。本文作者同时运用经典微分几何的数学工具,阐明了这些构型的物理起源。简而言之,带电弹性带表面的度规在静电力作用下被重新定义。而重新定义的度规正好对应正的曲率。因此采取弯曲塌缩的构型对系统能量的降低反而更为有利。这项基础研究清楚地表明可以从几何效应的角度来把握复杂的长程物理相互作用。相关结果期待可以为我们理解和最终充分利用生物和材料系统中普遍存在的静电力提供新思路。

参考文献: Zhenwei Yao* and Monica Olvera de la Cruz, “Electrostatics-driven hierarchical buckling of charged flexible ribbons”, Physical Review Letters, 116, 148101, 2016.

We investigate the rich morphologies of an electrically charged flexible ribbon, which is a prototype for many belt-like structures in biology and nanomaterials. Long-range electrostatic repulsion is found to govern the hierarchical buckling of the ribbon from its initially flat shape to its undulated and then to its out-of-plane twisted conformations. In this process, the screening length is the key controlling parameter, suggesting a convenient way to manipulate the ribbon morphology is simply to change the salt concentration. We find that these shapes originate from the geometric effect of the electrostatic interaction that fundamentally changes the metric over the ribbon surface. We also identify the basic modes by which the ribbon reshapes itself for lowering the energy. The geometric effect of the physical interaction revealed in this work has implications to the shape design of extensive ribbons-like objects in nano- and biomaterials.

带电弹性带在长程静电作用下产生的两类基本构型