The effect of van der Waals force on the vibrational properties of low-dimensional nanostructure

Abstract

On nanoscale, van der Waals (vdW) force has a very important influence on physical, chemical, electrical and mechanics properties of low-dimensional nanostructures. vdW force is an important factor affecting constitutive relation, boundary condition of low-dimensional nanostructures, and then affecting its natural frequency and nonlinear dynamics property. The nanostructures have wide applications in fabricating the nanoresonator and nanosensor, such as mass sensing, optical sensing, signal-processing, et al. In this paper, the latest research progress about the effect of vdW force on the vibrational properties of low-dimensional nanostructures is introduced. The main contents of this paper are as follows. The vdW force is introduced in the first part of this paper. The source of vdW force and the expression to describe vdW force are presented. The research progress on the basic development history of vdW force is discussed. In the second part, the effect of vdW force on the mechanical property of nanomaterials is discussed, including buckling, stretching, fracture, et al. vdW force is weak in resisting interlayer shear or sliding. However, it can affect the buckling and fracture behavior of nanomaterials, and can especially affect the deformation of nanomaterials. The effect of vdW force on the vibrational behavior of nanomaterials is presented in the third part. Different from the macro structure, vdW force has a significant influence on the vibrational behavior of low-dimensional nanoscale structures. The experimental method, molecular dynamic simulations method and continuum mechanics method are usually used for studying the influence of vdW force on the vibrational behavior of low-dimensional nanostructure. Due to the existence of vdW force between interlayer of low-dimensional nanostructures, the vibration of double-layered low-dimensional nanostructures appear anti-phase vibration mode and in-phase vibration mode. The frequency of anti-phase vibration mode is much higher than that of in-phase vibration mode, but the vdW force cannot affect the first order natural frequency. However, the existence of the vdW force between the interlayer of multi-layered low-dimensional nanostructure can cause the interlayer shear force. The vdW force can affect the vibrational behavior of low-dimensional nanostructure, e.g., the natural frequency is affected by vdW force. Some latest researches about the interlayer shear force caused by vdW force on the vibration property are discussed in this paper. The vdW force can also affect the boundary condition of the vibrational problems for low-dimensional nanostructure. For one-dimensional nanostructures, they are usually bridged on the substrate. But for two-dimensional nanostructures, they are usually suspended on the circular hole. The vdW force between the substrate and low-dimensional nanostructure is a very important factor that can affect the boundary conditions of vibrational property of these low-dimensional nanostructures. Some open problems and future researches in the dynamic behaviors of low-dimensional nanostructure with vdW force are presented. To study the effect of vdW force on the vibration characteristics of nanoscale structures by quantum mechanics method or semi quantum mechanics method is a prodigious challenge. The effect of nonlinear vdW force and long-range nonlocal vdW force on the vibration characteristics of nanoscale structures should be an interesting problem to be solved. The influence of vdW force on the vibration characteristics of nanostructures needs to be verified by experiments.