Regular Article

Curling behavior of free-standing nanofilms driven by surface stress: core–shell model

¹ School of Physics and Electronic Science, Shanxi Datong University & Shanxi Province Key Laboratory of Microstructure Electromagnetic Functional Materials, Shanxi Datong University, Datong 037009, P.R. China
² College of Science, Inner Mongolia University of Science and Technology, Baotou 014010, P.R. China
³ Key Laboratory of Interface Science and Engineering in Advanced Materials, Taiyuan University of Technology, Ministry of Education, Taiyuan 030024, P.R. China

^* e-mail: jhding2019@163.com;wanghua001@tyut.edu.cn

Received: 26 June 2022
Received in final form: 7 September 2022
Accepted: 28 September 2022
Published online: 2 December 2022

Abstract

A continuum theoretical model for describing curling behavior of free-standing nanofilms was given in this paper. Surface stress, surface elasticity (surface Young's modulus), surface slice thickness and anisotropic deformation were considered. For a nanofilm with only several nanometers, curling behavior is apt to be more common than isotropic bending behavior. The curling behavior is an anisotropic problem and is different from isotropic bending behavior as Stoney formula interprets. The isotropic bending behavior makes nanofilm to become a ball-like object while curling behavior makes nanofilm to become a tube-like object. If surface elasticity is imbalance, surface stress sum will bend nanofilms and surface stress difference expands nanofilms. For the balance surface elasticity, surface stress sum induces isotropic elongation deformation despite the anisotropic shape of nanotubes. If surface elasticity is imbalance, the anisotropic elongation deformation in tangential and cylindrical directions appears.