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In this paper, the effect of van der Waals (vdW) force on the pull-in behavior of electrostatically actuated nano/micromirrors is investigated. First, the minimum potential energy principle is utilized to find the equation governing the static behavior of nano/micromirror under electrostatic and vdW forces. Then, the stability of static equilibrium points is analyzed using the energy method. It is found that when there exist two equilibrium points, the smaller one is stable and the larger one is unstable. The effects of different design parameters on the mirror’s pull-in angle and pull-in voltage are studied and it is found that vdW force can considerably reduce the stability limit of the mirror. At the end, the nonlinear equilibrium equation is solved numerically and analytically using homotopy perturbation method (HPM). It is observed that a sixth order perturbation approximation can precisely model the mirror’s behavior. The results of this paper can be used for stable operation design and safe fabrication of torsional nano/micro actuators.

Graphene sheets are extremely flexible, and thus small forces, such as van der Waals interaction, can induce significant out-of-plane deformation, such as folding. Folded graphene sheets show racket shaped edges, which can significantly affect the electrical properties of graphene. In this paper, we present combined theoretical and computational studies to reveal the folding behavior of multi-layer graphene sheets. A nonlinear theoretical model is established to determine the critical length of multilayer graphene sheets for metastable and stable folding, and to accurately predict the shapes of folded edges. These results all show good agreement with those obtained by molecular dynamics simulations.

Electromechanical carbon nanothermometers are devices that work based on the interactions and relative motions of double-walled carbon nanotubes (DWCNTs). In this paper, the mechanics of carbon nanotubes (CNTs) constituting two well-known configurations for nanothermometer, namely shuttle configuration and telescope configuration are fully investigated. Lennard-Jones (LJ) potential function along with the continuum approximation is employed to investigate van derWaals (vdW) interactions between the interacting entities. Accordingly, semi-analytical expressions in terms of single integrals are obtained for vdW interactions. Acceptance condition and suction energy are studied for the shuttle configuration. In addition, a universal potential energy is presented for the shuttle configuration consisting of two finite CNTs. Also, for the telescope configuration, extensive studies are performed on the distributions of potential energy and interaction force for various radii and lengths of CNTs. It is found that these geometrical parameters have a considerable effect on the potential energy.

In this paper the effects of temperature on the radial breathing modes (RBMs) and radial wave propagation in multiwall carbon nanotubes (MWCNTs) are investigated using a continuum model of multiple elastic isotropic shells. The van der Waals forces between tubes are simulated as a nonlinear function of interlayer spacing of MWCNTs. The governing equations are solved using a finite element method. A wide range of innermost radius-to-thickness ratio of MWCNTs is considered to enhance the investigation. The presented solution is verified by comparing the results with those reported in the literature. The effects of temperature on the van der Waals interaction coefficient between layers of MWCNTs are examined. It is found that the variation of the van der Waals interaction coefficient at high temperature is sensible. Subsequently, variations of RBM frequencies and radial wave propagation in MWCNTs with temperatures up to 1 600 K are illustrated. It is shown that the thick MWCNTs are more sensible to temperature than the thin ones.

In this paper the dynamic torsional buckling of multi-walled carbon nanotubes (MWNTs) embedded in an elastic medium is studied by using a continuum mechanics model. By introducing initial imperfections for MWNTs and applying the preferred mode analytical method, a buckling condition is derived for the buckling load and associated buckling mode. In particular, explicit expressions are obtained for embedded double-walled carbon nanotubes (DWNTs). Numerical results show that, for both the DWNTs and embedded DWNTs, the buckling form shifts from the lower buckling mode to the higher buckling mode with increasing the buckling load, but the buckling mode is invariable for a certain domain of the buckling load. It is also indicated that, the surrounding elastic medium generally has effect on the lower buckling mode of DWNTs only when compared with the corresponding one for individual DWNTs.

Surface microstructures of solid materials play a significant role in various wetting and dewetting phenomena. In the present paper, the effect of micro- and nano-structures of a substrate surface on the morphology and evolution of liquid droplets and thin films is examined. The governing equations satisfied by droplets and films on a sinusoidal surface are derived by considering van der Waals force, surface tension, gravity and hydrostatic pressure. The morphologies of both liquid droplets and thin films are numerically simulated under various characteristic sizes of roughness. It is found that the droplet shapes show a significant dependence upon the characteristic sizes of substrate microstructures. A thin liquid film on a hydrophilic substrate may have a horizontal surface or replicate the substrate morphology, depending on the wavelength of roughness.