Effects of the Van der Waals Force on the Vibration of Typical Multi-layered Two-dimensional Nanostructures

Recently, two-dimensional nanostructures have caught much attention because of their magnificent physical characteristics. The vibrational behavior of typical multi-layered two-dimensional nanostructures (TMLTNs) is extraordinary significant to TMLTN-based nanoresonantors. In this investigation, the vibrational behavior of TMLTNs, taking black phosphorus (BP), graphene and BN as examples, is studied adopting molecular dynamics (MD) simulations and the sandwich plate model (SPM). The MD results show that the fundamental resonant frequency of multi-layered BP (MLBP) and multi-layered BN (MLBN) increase obviously with the number of layers. However, the fundamental resonant frequency of a multi-layered graphene sheet (MLGS) rise slightly when the number of layers increases. This phenomenon is caused by the shear modulus in the xz-plane and yz-plane resulted by the vdW force. Hence, an SPM considering the shear modulus in the xz-plane and yz-plane caused by the vdW force is used to investigate the vibration of the TMLTN. Compared with the MD results, it is shown that the SPM can better predict the vibration of the TMLTN.