A continuum theoretical scheme for self-rolling nanotubes from bilayers by mismatch is obtained by considering surface elasticity,surface stress,and symmetry lowering effects.For an ultrathin nanofilm with only severa...A continuum theoretical scheme for self-rolling nanotubes from bilayers by mismatch is obtained by considering surface elasticity,surface stress,and symmetry lowering effects.For an ultrathin nanofilm with only several nanometers in thickness,isotropic mismatch,and isotropic surface stress usually induce anisotropic rolling behavior.The isotropic Timoshenko formula should be modified anisotropically to explain the mechanical behavior of anisotropic rolling structure of nanotubes accurately.The nanofilm rolls up in tangential direction while remaining straight in cylindrical direction theoretically.Therefore,in this paper the anisotropic shape of nanotubes is taken into consideration.Along the cylindrical direction,although it maintains straight and its residual strain is uniform,the stress varies in the radial direction due to the Poisson's effect of tangential strain.The results of the current theory applied to Si-Si nanotube,InAs-GaAs nanotube,and InGaAs-Cr nanotube systems show good agreement with the experimental data.Beside the surface elasticity effect and surface stress effect,the symmetry breaking and the anisotropic rolling structure are of great importance in theoretically describing the mechanical behavior of rolling-up of nanotubes.展开更多
基金Project supported by the Natural Science Foundation of Shanxi Province,China (Grant No.201901D111316)the National Natural Science Foundation of China (Grant No.11874245)+1 种基金the Teaching Reform and Innovation Pproject of Colleges and Universities in Shanxi Province,China (Grant No.J2021508)the Natural Science Foundation of Inner Mongolia Autonomous Region,China (Grant No.2020MS06007)。
文摘A continuum theoretical scheme for self-rolling nanotubes from bilayers by mismatch is obtained by considering surface elasticity,surface stress,and symmetry lowering effects.For an ultrathin nanofilm with only several nanometers in thickness,isotropic mismatch,and isotropic surface stress usually induce anisotropic rolling behavior.The isotropic Timoshenko formula should be modified anisotropically to explain the mechanical behavior of anisotropic rolling structure of nanotubes accurately.The nanofilm rolls up in tangential direction while remaining straight in cylindrical direction theoretically.Therefore,in this paper the anisotropic shape of nanotubes is taken into consideration.Along the cylindrical direction,although it maintains straight and its residual strain is uniform,the stress varies in the radial direction due to the Poisson's effect of tangential strain.The results of the current theory applied to Si-Si nanotube,InAs-GaAs nanotube,and InGaAs-Cr nanotube systems show good agreement with the experimental data.Beside the surface elasticity effect and surface stress effect,the symmetry breaking and the anisotropic rolling structure are of great importance in theoretically describing the mechanical behavior of rolling-up of nanotubes.
