Analytical bounds for the pull-in voltage of carbon nanotubes

Carbon nanotubes (CNTs) display a number of attractive electronic and mechanical properties that are currently exploited in a wide variety of industrial applications, such as sensors, nanoactuators, memory devices, switches, high frequncy nanoresonators and nanotweezers. Due to their tiny size they indeed display ultra-low mass and very high resonance frequency as well as the capability to carry huge electrical currents and to sustain high current densities. These properties, in conjunction with the significant progress recently made in the fabrication of carbon nanostructures, allow CNTs to become essential components in the fabrication of enhanced nano-electromechanical systems (NEMS) An accurate determination of the stable actuating range and the pull-in instability threshold is a crucial issues for designing reliable CNT based NEMS. Despite the amount of numerical or approximated investigations, analytical models and closed form expressions for pull-in instability analysis of CNT still appears to be limited. An analytical methodology for assessing accurate lower and upper bounds to the pull-in parameters of an electrostatically actuated micro- or nanocantilever has been provided in two previous works [1, 2], taking into consideration the contributions of flexible support and compressive axial load. In the present work, attention is paid to investigate the pull-in phenomenon in CNT with circular cross-section, by considering the proper expressions of the electrostatic and van der Waals forces per unit length acting on a CNT, as well as the significant reduction of the pull-in voltage induced by the charge concentration at the free end [3]. Two-side accurate analytical estimates of the pull-in parameters of a carbon nanotube switch clamped at one end under electrostatic actuation are provided by considering the effects of van der Waals interactions and charge concentration at the free end. The problem is governed by a fourth-order nonlinear boundary value problem, according to the Eulero-Bernoulli beam theory. Two-side estimates on the deflection are first derived, then very accurate lower and upper bounds to the pull-in voltage and deflection are obtained as functions of the geometrical and material parameters. The analytical predictions are then found to agree remarkably well with the numerical results provided by the shooting method

Lower and Upper Bound for the Pull-in Parameters of a Micro- or Nanocantilever Beam Immersed in Liquid Electrolytes

An analytical method is proposed to accurately estimate the pull-in parameters of a micro- or nanocantilever beam immersed in liquid electrolytes with a flexible support at one end. The system is actuated by electrochemical force, namely the sum of electric and osmotic forces, and is subject to Casimir or van der Waals forces according to the spacing between the two electrodes. The deflection of the beam is described by a fourth-order nonlinear boundary value problem that can be formulated by an equivalent nonlinear integral equation. At first, a priori upper and lower analytical estimates on the beam deflection are derived and then very accurate lower and upper bounds for the pull-in voltage and tip deflection are obtained. The analytical predictions are in excellent agreement with the numerical results provided by the shooting method. Finally, a simple closed-form relation is proposed for the pull-in voltage under the effect of bulk ion concentration

The beginning of the Neolithic era in Central Italy

This paper presents the general profile of the first farming communities of Central Italy in the Early Neolithic Era. Data shows the spread of early Neolithic cultures in the Italian peninsula at the beginning of the VI millennium B.C. The first Neolithic groups appeared in the southern regions of the peninsula and moved northwards following two trajectories along the Tyrrhenian and Adriatic coasts. The process of Neolithisation was initiated by peoples who probably came from different areas and traditions creating, over time, two distinct areas within the Italian peninsula, each with its own specific cultural features. Finally the article looks at how intensive exchanges both of complex knowledge and raw materials occurred between these two distinct cultural worlds

Time-harmonic analysis of antiplane crack in couple stress elastic materials

The time harmonic response of a rectilinear and semi-infinite crack in a couple stress (CS) elastic solid under Mode III loading conditions is investigated in the present work. The full-field solution of the dynamic crack problem obtained in [1] through Fourier integral transforms and the Wiener\u2013Hopf technique is generalized here by considering more general loading conditions, consisting in arbitrary reduced stress and couple stress tractions applied at the crack faces. The solution for quasistatic Mode III crack in indeterminate CS elastic materials was given in [2]. Later, the problem of steady-state Mode III crack propagation was investigated in [3]. In the present work, a travelling wave loading, applied in the form of generalized reduced tractions at the crack faces, is considered as the forcing term. As a result, a complex wave pattern appears, which differs significantly from the Mode III classical elastic solution. The results of the present analysis may be used as a building block to address, by means of superposition, the problem of arbitrary antiplane wave propagation in a cracked CS solid. Resonance is triggered when the applied loading is fed into the crack-tip at Rayleigh speed. Elastodynamic stress intensity factors are given, which generalize the corresponding results presented in [2] for the qusistatic framework. They incorporate the effect of the applied loading frequency and thereby account for the interplay of the diffracted waves. A remarkable wave pattern appears which consists of entrained waves extending away from the crack, reflected Rayleigh waves moving along the crack surfaces, localized waves irradiating from the crack-tip and body waves scattered around the crack-tip. Interestingly, the localized wave solution may be greatly advantageous for defect detection through acoustic emission

Pull-in Instability Analysis of a Nanocantilever Based on the ‎Two-Phase Nonlocal Theory of Elasticity

This paper deals with the pull-in instability of cantilever nano-switches subjected to electrostatic and intermolecular forces in the framework of the two-phase nonlocal theory of elasticity. The problem is governed by a nonlinear integro-differential equation accounting for the external forces and nonlocal effects. Assuming the Helmholtz kernel in the constitutive equation, we reduce the original integro-differential equation to a sixth-order differential one and derive a pair of additional boundary conditions. Aiming to obtain a closed-form solution of the boundary-value problem and to estimate the critical intermolecular forces and pull-in voltage, we approximate the resultant lateral force by a linear or quadratic function of the axial coordinate. The pull-in behavior of a freestanding nanocantilever as well as its instability under application of a critical voltage versus the local model fraction are examined within two models of the load distribution. It is shown that the critical voltages calculated in the framework of the two-phase nonlocal theory of elasticity are in very good agreement with the available data of atomistic simulation

Modeling pull-in instability of CNT nanotweezers under electrostatic and van der Waals attractions based on the nonlocal theory of elasticity

This work investigates the electromechanical response and pull-in instability of an electrostatically-actuated CNT tweezer taking into consideration a TPNL constitutive behavior of the CNTs as well as the intermolecular forces, both of which provide a significant contribution at the nanoscale. The nonlocal response of the material introduces two additional parameters in the formulation, which are effective in capturing the size effects observed at the nanoscale. The problem is governed by a nonlinear integrodifferential equation, which can be reduced to a sixth-order nonlinear ODE with two additional boundary conditions accounting for the nonlocal effects near to the CNT edges. A simplified model of the device is proposed based on the assumption of a linear or parabolic distribution of the loading acting on the CNTs. This assumption allows us to formulate the problem in terms of a linear ODE subject to two-point boundary conditions, which can be solved analytically. The results are interesting for MEMS and NEMS design. They show that strong coupling occurs between the intermolecular forces and the characteristic material lengths as smaller structure sizes are considered. Considering the influence of the nonlocal constitutive behavior and intermolecular forces in CNT tweezers will equip these devices with reliability and functional sensitivity, as required for modern engineering applications

Experimental characterization of pull-in parameters for an electrostatically actuated cantilever

MEMS-NEMS applications extensively use micro-nano cantilever structures as actuation system, thanks to their intrinsically simple end efficient configuration. Under the action of an electrostatic actuation voltage the can- tilever deflects, until it reaches the maximum value of the electrostatic actuation voltage, namely the pull-in voltage. This limits its operating point and is a critical issue for the switching of the actuator. The present work aims to experimentally measure the variation of the pull-in voltage and the tip deflection for different geometri- cal parameters of an electrostatically actuated cantilever. First, by relying on a nonlinear differential model from the literature, we designed and built a macro-scale cantilever switch, which can be simply adapted to different configurations. Second, we experimentally investigated the effect of the free length of the suspended electrode, and of the gap from the ground, on the pull-in response. The experimental results always showed a close agree- ment with the analytical predictions, with a maximum relative error lower that 10% for the pull-in voltage, and a relative difference lower than 18% for the pull-in deflection

On fracture criteria for dynamic crack propagation in elastic materials with couple stresses

The focus of the article is on fracture criteria for dynamic crack propagation in elastic materials with microstructures. Steady-state propagation of a Mode III semi-infinite crack subject to loading applied on the crack surfaces is considered. The micropolar behavior of the material is described by the theory of couple-stress elasticity developed by Koiter. This constitutive model includes the characteristic lengths in bending and torsion, and thus it is able to account for the underlying microstructures of the material. Both translational and micro-rotational inertial terms are included in the balance equations, and the behavior of the solution near to the crack tip is investigated by means of an asymptotic analysis. The asymptotic fields are used to evaluate the dynamic J-integral for a couple-stress material, and the energy release rate is derived by the corresponding conservation law. The propagation stability is studied according to the energy-based Griffith criterion and the obtained results are compared to those derived by the application of the maximum total shear stress criterion.Comment: 31 pages, 6 figure

Integral identities for a semi-infinite interfacial crack in anisotropic elastic bimaterials

The focus of the article is on the analysis of a semi-infinite crack at the interface between two dissimilar anisotropic elastic materials, loaded by a general asymmetrical system of forces acting on the crack faces. Recently derived symmetric and skew-symmetric weight function matrices are introduced for both plane strain and antiplane shear cracks, and used together with the fundamental reciprocal identity (Betti formula) in order to formulate the elastic fracture problem in terms of singular integral equations relating the applied loading and the resulting crack opening. The proposed compact formulation can be used to solve many problems in linear elastic fracture mechanics (for example various classic crack problems in homogeneous and heterogeneous anisotropic media, as piezoceramics or composite materials). This formulation is also fundamental in many multifield theories, where the elastic problem is coupled with other concurrent physical phenomena.Comment: 29 pages, 4 figure

Ocean warming and acidification detrimentally affect coral tissue regeneration at a Mediterranean CO2 vent

Among the main phenomena that are causing significant changes in ocean waters are warming and acidification, largely due to anthropogenic activities. Growing evidence suggests that climate change is having more substantial and rapid effects on marine communities than on terrestrial ones, triggering several physiological responses in these organisms, including in corals. Here we investigated, for first time in the field, the combined effect of increasing seawater acidification and warming on tissue regeneration rate of three Mediterranean scleractinian coral species characterized by different trophic strategies and growth modes. Balanophyllia europaea (solitary, zooxanthellate), Leptopsammia pruvoti (solitary, non-zooxanthellate) and Astroides calycularis (colonial, non-zooxanthellate) specimens were transplanted, during a cold, intermediate, and warm period, along a natural pH gradient generated by an underwater volcanic crater at Panarea Island (Mediterranean Sea, Italy), characterized by continuous and localized CO2 emissions at ambient temperature. Our results show a decrease in regenerative capacity, especially in the zooxanthellate species, with increasing seawater temperature and acidification, with demonstrated species-specific differences. This finding suggests that increasing seawater temperature and acidification could have a compounding effect on coral regeneration following injury, potentially hindering the capacity of corals to recover following physical disturbance under predicted climate change