纳米薄膜尺度依赖的杨氏模量及表面应力导致的弯曲  

Size-dependent Young's modulus and surface stress-induced bending of nanofilms

作　　者：李建刚[1] 白那日苏[2] 云国宏[1,2] 

机构地区：[1]内蒙古大学物理科学与技术学院内蒙古自治区纳米科学与技术重点实验室,呼和浩特010021 [2]内蒙古师范大学物理与电子学院内蒙古自治区功能材料物理与化学重点实验室,呼和浩特010022

出　　处：《中国科学：物理学、力学、天文学》2015年第8期78-88,共11页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(批准号:11072104,50901039,11464037);内蒙古自治区高校青年科技英才计划(编号:NJYT-12-B07)资助项目

摘　　要：考虑纳米薄膜表面弹性及其作用厚度得到了纳米薄膜尺度依赖的杨氏模量的表达式.通过考虑表面层厚度,引入了表面效应的二级和三级修正,这有助于对纳米薄膜弹性性质进行更深入的研究.针对纳米薄膜上、下两个表面上表面应力不平衡的情况,由能量极小原理得到了表面应力导致的单层纳米薄膜的弯曲公式.通过将本文弹性(及弯曲)理论同前人工作进行比较,研究了表面层厚度对薄膜弹性性质影响的规律,揭示了本文理论与前人理论的内在联系.A formula for size-dependent Young’s modulus was obtained by including surface elasticity effect and by considering the thickness of surface slice. By considering surface slice thickness, the second and third surface modification were introduced. This is helpful for the further research of the elasticity of nanofilms. Considering the imbalance of surface stresses at top and bottom surfaces, the bending curvature of nanofilms was obtained by using the principle of minimal total free energy. The law of surface slice thickness effect on elastic properties was pointed by comparing current elasticity（as well as bending） theory in this paper with former works. The relationship between the elasticity theory with and without the thickness of surface slice was discovered.

关 键 词：纳米薄膜 表面效应 杨氏模量 弯曲 

分 类 号：O484[理学—固体物理]