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Herein, a corrected theoretical model is proposed for modeling the static and dynamic behavior of electrostatically actuated narrow-width nanotweezers considering the correction due to finite dimensions, size dependency and surface energy. The Gurtin–Murdoch surface elasticity in conjunction with the modified couple stress theory is employed to consider the coupling effect of surface stresses and size phenomenon. In addition, the model accounts for the external force corrections by incorporating the impact of narrow width on the distribution of Casimir attraction, van der Waals (vdW) force and the fringing field effect. The proposed model is beneficial for the precise modeling of the narrow nanotweezers in nano-scale.

A general equation for surface stress is established based on a thermodynamic consideration of the size dependence of solid–liquid interface energy under an assumption that the solid–liquid interface of a particle immersed in surrounding liquid disappears when almost all atoms of the particle are located on its surface. The predicted surface stresses of semiconductors in terms of the model are in agreement with the first principles calculations and calculations based on forces associated with the elastic distortion of the covalent bonds.

By using established statistical thermodynamic theory of adsorbate-induced surface stress of adsorption monolayer on metal surface, the surface stress Δg in the self-assembly of alkanethiols on Au(111) surface has been calculated. The quantitative relations of the surface stress Δg with the length N of the alkyl chain of the molecule and with the coverage θ of molecules on Au(111) have been theoretically studied, respectively. The calculated results agree with Berger et al.'s experiment. The qualitative discrepancy between the theory and experiment on the sign of the surface stress has been resolved. Among various components of the adsorbate–adsorbate interaction energies in the adlayer, the substrate-mediated interaction is significant for the adsorbate-induced surface stress, which shows that indirect contribution of the adsorption energy of alkanethiols through the substrate-mediated interaction is very important.

Structural stability of a double-nanowire system with surface effects subjected to axial compressive forces is analyzed. Taking into account the Casimir force between the two nanowires, two coupled governing equations for buckling of a double-nanowire system are derived. For four typical end supports including simply-supported, clamped, cantilevered, and clamped-pinned double-nanowire systems, the characteristic equations are derived and the critical loads are determined for the out-of-phase in-plane buckling. Numerical results indicate that positive surface elasticity enhances the load-carrying capacity of the nanowires, and the reverse is also true. The Casimir force and residual surface tension always increase the critical loads.

In this paper, buckling of a nanowire column subjected to self-weight and tip load is investigated. One end of the nanowire is free, while the other end is attached to a rotational spring support. Considering the equilibrium equations together with the Euler–Bernoulli beam theory, the governing differential equation describing the behavior of the column can be obtained. Effect of surface stress is also incorporated into the formulations in terms of transverse distributed loading. The differential equation has been solved analytically and the general solution can be presented in the terms of Bessel function of the first kind. Applying the boundary conditions, the characteristic equations influenced by surface stress and stiffness of the rotational spring at the support can be expressed and then the critical load can be determined using the Newton–Raphson iterative scheme. From the results, they reveal that the positive surface stress could strengthen the nanowire against the buckling. Fixity at the base is also influenced to the critical load where the increase of the stiffness of the spring results in the increase of critical load as well.

This paper presents a novel approach to the analysis of large deflection and post-buckling behavior of cantilever nanorods under different load conditions. The proposed approach utilizes a variational method, incorporating the Gurtin–Murdoch surface elasticity theory and the consistent couple stress theory to account for size-dependency effects. By accounting for the strain energy contributions of the bulk material, surface layer, and load conditions, this approach expresses the behavior of the nanorods in terms of their intrinsic coordinates. A finite element method was used to solve this numerical problem, generating a system of non-linear equations that were iteratively solved using the Newton–Raphson method. The results obtained from the finite element method were confirmed by those from the shooting method. Also, it highlights the effectiveness of the variational model in predicting the large deflection and post-buckling behavior of cantilever nanorods while considering both surface stress and couple stress effects. Furthermore, the study investigated the influence of surface stress and couple stress on the response of the nanorods to point and uniform loads. The results showed that incorporating both effects enhanced the stiffness of the nanorods compared to scenarios in which these effects were neglected. In addition, the couple stress effect was found to have a greater influence on the stiffening of nanorods for the same value of unitless parameters compared to surface stress effects. These findings offer valuable insights into the large deflection and post-buckling behavior of cantilever nanorods and highlight the importance of surface stress and couple stress effects. The model proposed in this study has potential applications in advanced technological device designs by providing a comprehensive understanding of the mechanical response of nanorods, allowing for more accurate predictions and enhanced device performance.

The objective of this paper is to study the postbuckling behaviors of an unknown-length nanobeam combined with small-scale effects. The concept of variable-arc-length elastica is firstly applied on the problem of nanobeams. The span length is not changed while the arc length is varied increasingly. The nanobeam is on a clamped support at one end, while the other end is an overhanging part through a frictionless slot subjected to axial compression. At this end, the nanobeam is movable only in a horizontal direction. The governing equation is developed by the moment–curvature relationship based on the classical Euler–Bernoulli beam theory, including the effects of nonlocal elasticity, residual surface stress, and both combined effects. The shooting–optimization technique with two-point boundary condition is employed to solve the differential equations in this problem. The results, including nonlocal elasticity, reveal that nanobeams have decreased structural stiffness; meanwhile, the residual surface tension and both combined effects have increased strength. The postbuckling loads decrease as the arc length of nanobeams is increased. The equilibrium configurations are close to an anti-loop for very large deflections. The friction force at the nanoslot is also considered.

Nanowires (NWs) play a crucial role across a wide range of disciplines such as nanoelectromechanical systems, nanoelectronics and energy applications. As NWs continue to reduce in dimensions, their mechanical properties are increasingly affected by surface attributes. This study conducts a comprehensive examination of nanomechanical models utilized for interpreting large deformations in the bending response of silicon NWs. Specifically, the Heidelberg, Hudson, Zhan, SimpZP and ExtZP nanomechanical models are explored regarding their capability to predict the elastic properties of silicon NWs with varying critical dimensions and crystal orientations. Molecular dynamics simulations are employed to model silicon NWs with unreconstructed surface states. The calculation of intrinsic stresses and the methodology for quantifying surface properties, including surface stresses and surface elasticity constants, are carried out using atomistic modeling. The findings reveal significant disparities of up to 100 GPa among nanomechanical models in interpreting a singular force-deflection response obtained for a silicon NW. Inadequate consideration of surface and intrinsic effects in nanomechanical modeling of NWs leads to substantial variability in their mechanical properties. This investigation yields valuable insights into the surface characteristics of silicon NWs, thereby enhancing our understanding of the essential role played by nanomechanical models in the intricate interpretation of mechanical properties at the nanoscale.

The biaxial and planar characteristics of surface stress produce a parabolic differential stress distribution inside the sensing zone of microcantilever biosensors, which can be used to design novel biosensors. The present work studies and compares the effect of parabolic and conventional rectangular-shaped piezoresistor placed inside this sensing zone on sensitivity of the biosensors. Two different cantilevers made of silicon and silicon dioxide with doped silicon as piezoresistor are used in five design variations. The cantilevers are characterized for their deflections, von Mises stresses, resonant frequencies and self-heating temperatures produced using ANSYS. Analytical models for predicting deflections in the cantilevers is presented and compared with numerical results obtained. Results show good compatibility between analytical and numerical values for deflection with a 4–5% average deviation and that parabolic designs have higher sensitivity.

Receptor-functionalized membranes provide a new paradigm for developing mechanical biosensors. However, the lower sensitivity of these biosensors is still a challenge. In this research, a sensitive and thin (1.5 $\mu$m) gold nanoparticles-polydimethylsiloxane (AuNPs-PDMS) membrane is fabricated by reducing HAuCl₄. Experimental results reveal that surface stress deforms the AuNPs-PDMS membrane, further increasing the resistance due to the tunneling mechanism and conductive percolation. During the functional process, the resistance change is consistent with theoretical prediction. The relative resistance change demonstrates a linear relationship with the glucose concentration. The biosensors exhibit a wider linear range for glucose from 0 to 30mM with a lower detection limit of 0.035mM. AuNPs-PDMS thin membrane-based surface stress biosensor shows promising application prospects to detect biomolecules.