Sharif Digital Repository

The influence of Casimir and van der Waals forces on the instability of vibratory micro and nano-bridge gyroscopes with proof mass attached to its midpoint is studied. The gyroscope subjected to the base rotation, Casimir and van der Waals attractions is actuated and detected by electrostatic methods. The system has two coupled bending motions actuated by the electrostatic and Coriolis forces. First a system of nonlinear equations for the flexural-flexural deflection of beam gyroscopes is derived using the extended Hamilton's principle. In modeling, the nonlinearities due to mid-plane stretching, electrostatic forces, including fringing field, Casimir and van der Waals attractions, are... 

The operational range of microcantilever beams under electrostatic force can be extended beyond pull-in in the presence of an intermediate dielectric layer. In this paper, a systematic method for deriving dynamic equation of microcantilevers under electrostatic force is presented. This model covers the behavior of the microcantilevers before and after the pull-in including the effects of van der Waals force, squeeze-film damping, and contact bounce. First, a polynomial approximate shape function with a time-dependent variable for each configuration is defined. Using Hamilton's principle, dynamic equations of microcantilever in all configurations have been derived. Comparison between modeling... 

In this paper, the effects of van der Waals and Casimir forces on the static deflection and pull-in instability of a micro/nano cantilever gyroscope with proof mass at its end are investigated. The micro/nano gyroscope is subjected to coupled bending motions which are related by base rotation and nonlinearities due to the geometry and the inertial terms. It is actuated and detected by capacitance plates which are placed on the proof mass. The extended Hamilton principle is used to find the equations governing the static behavior of the clamp-free micro/nano gyroscopes under electrostatic, Casimir and van der Waals forces. The equations of static motion are discritized by Galerkin's... 

Various models have been applied composed of the Peng-Robinson equation of state (PR-EoS) and the Soave-Redlich-Kwong equation of state (SRK-EoS) associated with three mixing rules including the following: Wong-Sandler (WS), van der Waals one (vdW1), and van der Waals two (vdW2) for phase behavior modeling of mixtures of supercritical CO2+different ionic liquids in vapor-liquid equilibrium (VLE) region. It has been found that the PR EoS implying the WS mixing rule can be used as a reliable thermodynamic model to perform a thermodynamic consistency test on the experimental data of phase behaviors of the supercritical CO2+ionic liquid systems (19 commonly-used ionic liquids have been studied).... 

In the current paper, a coupled two degree of freedom model which considers both bending and torsion of the supporting torsion beams is presented for electrostatically actuated torsional nano/micro-actuators under the effect of van der Waals (vdW) force. Newton's second law is utilized for finding the normalized equations governing the static behavior of the actuator. The implict function theorem is then utilized for finding the equations governing the pull-in state of the actuator. The related results show that torsion model considerably overestimates the pull-in parameters of the nano/micro-actuator. The concept of the instability mode is introduced, and it is shown that when the ratio of... 

A simple equation of state (EoS) has recently been introduced (J. Phys. Chem. B2009, 113, 11977-11987) as (Z - 1)v2 = e + f/ρ + gρ2, where Z ≡ pv/RT is the compressibility factor, v = 1/ρ is molar volume, and e, f, and g are temperature dependent parameters. This EoS has been found to be accurate for all types of nano and bulk solids and bulk fluids, in the entire temperature and pressure ranges for which experimental data are reported, except for the isotherms within 1 ≤ T r = T/Tc ≤ 1.1 for the spherical and near spherical species and for a wider temperature range for the cylindrical molecules. The aim of this work is to investigate the validity of a three-term expression similar to the... 

Finesmigration is a noticeable problem in petroleum-production engineering. Plugging of throats in porous media occurs because of detachment of fine particles from sand surfaces. Thus, the study of interactions between fines and pore surfaces and the investigation of governing forces are important factors to consider when describing the mechanism of the fines-release process. The main types of these forces are electric double-layer repulsion (DLR) and London-van der Waals attraction (LVA). It may be possible to alter these forces with nanoparticles (NPs) as surface coatings. In comparison with repulsion forces, NPs increase the effect of attraction forces. In this paper, we present new... 

This paper deals with investigation of deformations and pull-in charges of the cantilever and doubly clamped carbon nanotubes (CNTs) with different geometries using molecular dynamics simulation technique. The well-known AIREBO potential for the covalent bonds between carbon atoms, Lennar-Jones potential for the vdW interaction and the Coulomb potential for electrostatic actuation are employed to model the nano electromechanical system. The results reveal that longer CNTs with smaller diameters have smaller pull-in charges in comparison with shorter CNTs possessing larger diameters. Furthermore, the pull-in charges of the doubly clamped CNTs are higher than the pull-in charges of the... 

In this paper, the molecular structural mechanics method is employed to calculate the mechanical properties of a double-layered carbon graphene sheet more accurately. For this purpose, covalent bonds are modeled using nonlinear beam elements and van der Waals interactions are replaced by nonlinear truss elements. Morse potential and Lennard-Jones potential equations are used to simulate the covalent bonds and van der Waals interactions, respectively. For each atom, van der Waals forces are considered with respect to all the other atoms located in its cut-off radius. In addition to in-plane mechanical properties of single and double-layered graphene sheets some out-of-plane properties like... 

The current paper presents a two degree of freedom model for the problem of nano/micromirrors under the effect of vdW force. Energy method, the principal of minimum potential energy is employed for finding the equilibrium equations governing the deflection and the rotation of the nano/micromirror. Then using the implicit function theorem, a coupled bending-torsion model is presented for the pull-in characteristics of nano/micromirrors under vdW force and the concept of instability mode is introduced. It is observed that with increasing the ratio of the bending stiffness to the torsion stiffness, the dominant instability mode changes from bending mode to the torsion mode. It is shown that... 

In the analysis of micro structures, due to proximity of the elements Van der Waals forces plays an important role on the dynamics of the structure. In the modeling process a similar approach should be considered for the capillary effect caused by the moisture in the environment. Microplates and microbeams are used widely in the design and manufacturing of sensors and actuators. These structures are usually made of a cantilever beam or plate along with a fixed substrate. The cantilever beam usually deflects due to applied voltage. By increasing the voltage the pull-in phenomenon takes place. It is believed that the short contact time is one the important characteristic of any micro switches.... 

A novel molecularly imprinted xerogel (MIX) based on organically modified silica (ORMOSIL) was successfully prepared for on-line capillary microextraction (CME) coupled with high-performance liquid chromatography (HPLC). The sol-gel-based xerogel was prepared using only one precursor and exhibited extensive selectivity towards triazines along with significant thermal and chemical stability. Atrazine was selected as a model template molecule and 3-(trimethoxysilyl)propylmethacrylate (TMSPMA) as a precursor in which the propylmethacrylate moiety was responsible for van der Waals, dipole-dipole, and hydrogen-bond interactions with the template. This moiety plays a key role in creation of... 

Adsorption of a methane molecule (CH 4) onto a defected and rippled graphene sheet is studied using ab initio and molecular mechanics calculations. The optimal adsorption position and orientation of this molecule on the graphene surface (motivated by the recent realization of graphene sensors to detect individual gas molecules) is determined and the adsorption energies are calculated. In light of the density of states, we used the SIESTA code. It is found that (i) classical force field yields adsorption energy comparable with experimental result and ab initio calculation; (ii) the periodic nature of the van der Waals potential energy stored between methane and perfect sheet is altered due to... 

A general regularity was found based on an effective pair potential of Lennard-Jones LJ (12, 6), for both dense, nonmetallic and nonionic fluids and solids according to which (Z-1) v2 linearly varies with respect to ρ2 for each isotherm, and this equation of state (EoS I) is known as LIR. However, despite the fact that Ne is a simple spherical species, unexpectedly, its solid and liquid phases both show a significant deviation from EoS I. In this work, we have investigated the accuracy of the EoS I for other systems, including quantum light molecules, such as D 2, H 2 and He, in both fluid and solid states at different temperatures. Like Ne, we have noticed that these systems do not well... 

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... 

In this research, the static behavior of torsional nano-/micro-actuators under van der Waals (vdW) force is studied. First, the equilibrium equation governing the static behavior of torsional nano-/micro-actuators under vdW force is obtained. Then the energy method is utilized to investigate the statical stability of nano-/micro-actuator equilibrium points and a useful equation is suggested for the successful and stable design of nano-/micro-actuators under vdW force. Then, the equilibrium angle of nano-/micro-actuators is calculated both numerically and analytically using the homotopy perturbation method (HPM). It is observed that, with increasing instability number, defined in this paper,... 

Carbon nanotubes (CNTs) have been recently taken into consideration as mechanical resonators of distinguished capabilities. This study aims at investigating the free vibration characteristics of a single-walled CNT in the vicinity of a fully constrained graphene sheet. Using a molecular structural mechanics model and considering nonlinear van-der-Waals interactions, the static deformation of the nanotube is obtained using an iterative procedure. Then, the governing equations of motion are linearized about the static equilibrium state and the natural frequencies are obtained. The molecular structural mechanics model is verified using established results in literature and then a survey is... 

The van der Walls interaction between a carbon nanotube sheet (CNTS) and a rare gas atom, is studied using both atomistic and continuum approaches. We present analytical expressions for the van der Waals energy of continuous nanotubes interacting with a rare gas atom. It is found that the continuum approach does not properly treat the effect of atomistic configurations on the energy surfaces. The energy barriers are small as compared to the thermal energy, which implies the free motion above the CNTS in heights about one nanometer. In contrast to the energy surface of a graphene sheet, the honeycomb lattice structure in the energy surface of a CNTS is imperceivable. Defects alter the energy... 

This paper is devoted to investigate the nonlinear behaviors of a V-shaped microcantilever of an atomic force microscope (AFM) operating in its two major modes: amplitude modulation and frequency modulation. The nonlinear behavior of the AFM is due to the nonlinear nature of the AFM tip-sample interaction caused by the Van der Waals attraction/repulsion force. Considering the V-shaped microcantilever as a flexible continuous system, the resonant frequencies, mode shapes, governing nonlinear partial and ordinary differential equations (PDE and ODE) of motion, boundary conditions, frequency and time responses, potential function and phase-plane of the system are obtained analytically. The... 

The coupling effect between torsion and bending in nano/micromirrors under the combined effect of capillary force and van der Waals (vdW) force is presented in this paper. At the first, the dimensionless equations governing the statical behavior of the nano/micromirror are obtained using the minimum total potential energy principle. Then the equations governing the pull-in state of the mirror are obtained using the implicit function theorem. The related results show that neglecting bending effect can lead to considerable overestimation in predicting the pull-in limits of the nano/micromirror under combined vdW and capillary forces. It is observed that vdW force reduces the pull-in angle and...