朱林利^1，， 郑晓静^2，*

（  1、西部灾害与环境力学教育部重点实验室, 兰州大学土木工程与力学学院力学与工程科学系；       2、西部灾害与环境力学教育部重点实验室,兰州大学土木工程与力学学院力学与工程科学系；  ）

摘要： 纳机电系统中的纳米结构，如纳米线、纳米薄膜和纳米管等，通常都将处于外加电场环境，由此导致这些纳米结构的表面带电. 实验和理论研究均表明：电解液内电极表面的剩余电荷将引起电极的表面应力发生变化，并且电极的表面原子在其垂直表面的方向会发生可逆驰豫. 本文认为：这些纳米结构的表面带电将影响这些纳米结构的力学性能. 为此，本文通过考虑纳米结构的表面能效应，在将表面电荷以及由此引起的负压作用产生的表面应变能引入到纳米结构的总表面能中后，推导给出了纳米结构等效弹性模量的解析表达式. 计算结果表明：带电纳米线材和纳米薄膜的等效杨氏模量与表面电荷密度以及电荷正负性有关；表面电荷对纳米结构弹性模量的影响程度取决于结构的几何尺寸如线材的直径或膜材的厚度，即：表现出显著的尺寸效应.
关键词： 纳米结构；弹性模量；电荷引起表面应力；负压作用；表面能效应.

Zhu, Linli^1,2,， Zheng，Xiaojing^1,2,*

（  1、Key Laboratory of Mechanics on Western Disaster and Environment, Ministry of Education；       2、Department of Mechanics and Engineering Science, College of Civil Engineering and Mechanics, Lanzhou University；  ）

Abstract： The nanostructures such as nanowires, naofilms and nanotubes in nanoelectromechanical systems (NEMS) are easy to be charged when they are working in an applied voltage or driven by an electric field. It has been revealed in experiment and theory that the excess surface charges resulted in the change of the in-plane surface stress and the normal surface relaxation for the metal electrode in an electrolyte. In this paper, we will discuss the influence of the charged surfaces on the elastic properties of the nanostructures based on the continuum mechanical theory. Incorporating the excess surface energy stemmed from the charge-induced surface stress and the negative pressure into the total surface strain energy, the effective elastic modulus of the nanostructures will be derived by considering the surface energy effects. The theoretical calculations show that the effective Young’s modulus of the charged nanowire and nanofilm are significantly dependent on the surface charges density and the sign of the surface charges. In addition, the effects of the surface charges on the modulus are associated with the structural geometric dimensions such as the thickness of the film and the diameter of the wire.

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