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A multiscale approach is pursued to develop a modified shear-lag model for capturing size-scale effects on electrostatic potential generated by a zinc oxide (ZnO) nanowire (NW) in a nanocomposite electrical generator (NCEG). The size-scale effect on elastic modulus of ZnO NWs is captured using a core-surface model. Closed form of governing equations are derived considering linear elasticity for axisymmetric problem and cylindrical coordinate system. Two different configurations based on parallel and series connecting of NCEGs for application in NEMS/MEMS devices are also studied. Parametric studies are performed for sample cases to demonstrate application of the developed model. It is shown that aspect ratio and diameter of NWs are crucial controlling parameters for determining the performance of nanocomposite electrical generators. Numerical results disclose that there is an optimum aspect ratio for each NW of specific diameter. It was also shown that despite the symmetry of loading with respect to mid-plane normal to the NW's axis, the electric potential is not symmetric.

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... Differently, after the external electric field E 1 was applied, we recorded the axial polarization change P 1 rather than the axial stress generated in the wurtzite materials. Here, considering the fact that the influence of polarization between nucleus and electrons usually can be neglected in the wurtzite materials [17,58,69,70], the axial polarization change P 1 can be approximately defined as ...

... / [17,58,69,70], where x i and V are the axial coordinate of atom i and the volume of simulated structures, respectively. Since the axial dielectric constant is defined as [58] k 11 =ε 0 +∂P 1 /∂E 1 , k 11 thus can be easily achieved after giving a linear curve fitting to the recorded P 1 -E 1 curves. ...

The piezotronic behaviours of wurtzite core-shell nanowires (NWs) are studied in this paper by using a multiscale modelling technique. A difference between piezopotentials obtained from molecular dynamics simulations and finite element calculations indicates that due to the influence of small-scale effects the widely used conventional electromechanical theory is not accurate in describing the piezopotential properties of the present core-shell NWs. Although the residual strains intrinsically existing in core-shell NWs and the structural reconstruction at their surface and interface both account for these small-scale effects, the latter is found to play the dominate role, which makes the material properties of core-shell NWs significantly depend on their geometric size. A novel core-interface-shell-surface model is proposed here to analytically describe the size dependence of the material properties and thus the small-scale effects on the piezopotential of core-shell NWs. Besides possessing a good piezoelectric performance, our density functional theory calculations also show that the core-shell NWs under external loading can retain the semiconducting properties, which confirms the existence of piezotronic effects in them. However, owing to the intrinsic asymmetric Schottky barriers at the source and drain contacts induced by residual piezopotentials in core-shell NWs, the piezotronic effects of core-shell NWs are different to those of their conventional single-component counterparts. The superb piezopotential properties and unique piezotronic behaviours observed in wurtzite core-shell NWs make them good candidates for high performance components in novel piezotronic nanodevices.

... In comparison with other smart materials, piezoelectric reveals some important advantages such as high accuracy, generation of large forces and very fast response. Hence, piezoelectric characteristics have been of great interest and a lot of works have been devoted to investigate its different properties in different size scales [8][9][10][11][12][13]. ...

... (8)), these highly coupled partial differential equations are reduced to ordinary differential equations with variable coefficients by means of trigonometric function expansion in circumferential and longitudinal directions satisfying mechanical and electrical boundary conditions [27,51]. The solution satisfying the boundary conditions may be assumed as (17) Applying the boundary conditions (9) and (10) ...

In the present study, a layerwise finite element method is utilized to solve the coupled elasticity and piezoelectricity equations to study a functionally graded shell panel integrated w i t h piezoelectric layers under electromechanical loading. The system of equations is reduced to ordinary differential equations w i t h variable coefficients by means of trigonometric function expansion in circumferential and longitudinal directions satisfying mechanical and electrical boundary conditions. These equations are solved using the Galerkin F E M and Newmark method. The results of stress, displacement, and electrical potential are presented and the effect of panel thickness and applied voltage on the structural behavior is investigated.

... Efficient computational tools have been developed to perform simulations within timespans not accessible to experimental studies [22,23]. We may refer to large-scale continuum simulations , phase-field simulations for capturing the microstructure [48][49][50][51][52][53][54][55], MD simulations to capture the atomistic mechanisms [2,47,[56][57][58][59][60][61][62][63][64][65][66][67], and multiscale simulations to capture the broad spectrum of materials and processes response [24,25,46,[68][69][70][71][72][73]. Out of several computational methods, molecular dynamics simulation allows the capturing of materials evolution with atomistic accuracy, including the radiation damage mechanism. ...

Ferritic-martensitic steels, such as T91, are candidate materials for high-temperature applications, including superheaters, heat exchangers, and advanced nuclear reactors. Considering these alloys’ wide applications, an atomistic understanding of the underlying mechanisms responsible for their excellent mechano-chemical properties is crucial. Here, we developed a modified embedded-atom method (MEAM) potential for the Fe-Cr-Si-Mo quaternary alloy system—i.e., four major elements of T91—using a multi-objective optimization approach to fit thermomechanical properties reported using density functional theory (DFT) calculations and experimental measurements. Elastic constants calculated using the proposed potential for binary interactions agreed well with ab initio calculations. Furthermore, the computed thermal expansion and self-diffusion coefficients employing this potential are in good agreement with other studies. This potential will offer insightful atomistic knowledge to design alloys for use in harsh environments.

... Hence, the mixture of nanoscale ZnOs and a passive/active polymer are examined to be substituted for conventional brittle and lead-based piezoceramics. The resulting piezoelectric nanocomposite brings some other benefits to the final electronic device, including structural weight reduction and biocompatibility [15,16]. However, the broader application of such piezoelectric nanocomposites needs extensive knowledge of their electromechanical behaviours [17,18]. ...

In conventional piezoelectric ceramics, their brittle nature and containing lead are two crucial issues that significantly restrict their uses in many applications such as biomedical devices. In this work, we suggest the use of an eco-friendly piezoelectric nanocomposite material to piezoelectrically activate a cantilever meta-structure plate to be used as a novel actuator/sensor or even energy harvester; this cantilever plate is formed of several polymeric links to create an auxetic core plate that structurally shows a negative Poisson’s ratio. Moreover, the active nanocomposite materials are used as the face sheets on the auxetic plate; these active layers are made of nanowires of zinc oxide (ZnO) that are placed into an epoxy matrix in different forms of functionally graded (FG) patterns. For such active sandwich plates (ASPs) with potential electromechanical applications, a coupled electromechanical analysis has been performed to numerically investigate their natural frequencies as a crucial design parameter in such electromechanical devices. By developing a meshless method based on a higher plate theory, the effects of nanowire volume fraction, nanowire distribution, auxetic parameters, layer dimensions, and electrical terminal set-up have been studied; this in-depth study reveals that ASPs with an auxetic core have much lower natural frequencies than ASPs with honeycomb cores which would be very helpful in designing actuators or energy harvesters using the proposed cantilever sandwich plates.

... Due to its outstanding electro-mechanical properties, ZnO has received growing attention in comparison with other compound materials with the same crystal structures, such as GaN, InN, and CdS, because of its ecofriendly nature and low-cost [23]. The outstanding properties of ZnO are more enticing at the nano-scale, where ZnO has a diversity of morphologies, such as nanowire, nanocage, nanobelt, nanocube, nanohelix/nanospring, nanoring or nanoplate [24][25][26]. Recently, ZnO NWs have mostly been synthesized using solid-vapor phase thermal sublimation technique [27] and extensively utilized in studies for their physical properties and reliability in new devices such as nanogenerators [28,29]. ...

This paper is concerned with the thermo-electro-dynamic modeling of a novel micro fuel delivery system (MFDS) that is accurate, low cost and ecofriendly. To avoid the use of brittle piezoelectric materials, we propose to use a two-chamber micro-device with a bimorph piezoelectric nanocomposite diaphragm containing Zinc Oxide Nanowires (ZnO NWs). The numerical study of our dynamic model is facilitated by mesh-free method and higher order shear deformation theory (HSDT) for varied temperatures and applied electro-mechanical loads. The elasticity modulus of the polymeric matrix is taken to be temperature-dependent. The static behavior and the natural frequency of the proposed smart nanocomposite diaphragm are analyzed for different volume fraction of ZnO NWs, diaphragm thickness, and operating temperature. We further examined the effect of the aforementioned parameters as well as the exciting electrical potential on the delivered flowrate and backpressure of the newly proposed MFDS. The results show that the dynamic behavior of the nanocomposite piezoelectric diaphragm is governed by the volume fraction of ZnO NWs. It also demonstrates the potential use of piezoelectric ZnO NWs nanocomposite in the diaphragm of a MFDS.

... Ethylene-vinyl acetate incorporated with organically modified nanofiller clay showed worsened electrical properties owing to moisture absorption dependent on the aspect ratio of the nanofiller, and it was found that a higher aspect ratio led to greater moisture absorption [3]. Moreover, the aspect ratio of the nanoparticles strongly affects the stress distribution within the matrix reinforcement, and this stress can further affect the diffusion rate of absorbed moisture [7][8][9]. ...

The use of nanocomposites as dielectric materials is expected to lead to improved electrical performance. However, recent research has shown that moisture absorption can cause a deterioration in the electrical performance of nanocomposites. Although it is generally accepted that hydroxyl groups attached to nanoparticle surfaces are the main cause of moisture absorption, the impact of this absorption on the electrical properties of nanocomposites is still not fully understand. In this paper, a series of measurements, including thermogravimetric analysis, DC breakdown, surface potential decay and space charge, are conducted with the aim of determining the impact of moisture absorption on the electrical properties of polyethylene/silica nanocomposites. The results show that the loading ratio of nanosilica and the humidity of the conditioning environment determine the amount of absorbed moisture. According to the Zhuravlev model, the main contribution to the deterioration in electrical properties of nanocomposites comes from the large amount of moisture absorbed in multilayer form. It is found that the loading ratio of nanosilica is the most significant factor in reducing DC breakdown strength.

... Parallel aligned fibers are used for the flexible power generators, which are more likely to produce larger voltages [52]. Besides, the high aspect ratio and the diameter are crucial in determining the performance of nanocomposite electrical generators [52][53][54][55]. Among the four nanocomposites, CNT/ PMMA/PVDF has the lowest average diameter (figure 4), which also contributes to its high output voltage. ...

Piezoelectric nanofibers are of great importance in their potential applications as smart fibers and textiles to bring changes to daily lives. By employing the technique of electrospinning, polyvinylidene fluoride (PVDF) nanofibers modified with polymethyl methacrylate (PMMA) and single-wall carbon nanotubes (CNTs) (referred to as CNT/PMMA/PVDF) are prepared. The electric field induced displacement of the as-prepared nanofibers is characterized by piezoresponse force microscopy. Compared with the pure PVDF nanofibers, the CNT/PMMA/PVDF nanofibers exhibit a great enhancement of about 196% for the electric field induced displacement, while increments of about 104% and 78% are obtained for the PMMA/PVDF and CNT/PVDF nanofibers, respectively. A structural analysis indicates that the hydrogen bonding between the O atom in the carbonyl group of PMMA and the hydrogen atom in the CH2 groups of PVDF, the promotion of the nucleation of crystallites by CNTs, work synergistically to produce the high electroactive response of the CNT/PMMA/PVDF nanofibers. Based on the high-performance nanofibers, a prototype of a flexible nanofiber generator is fabricated, which exhibits a typical electrical output of 3.11 V upon a repeated impact-release loading at a frequency of 50 Hz.

... The well-crystalline and alignment wurtzite ZnO nanorods with diameter and height around 90 nm and 2 μm (figure 2(a)) are synthesized on a GaN substrate by our developed CVD method [32]. As reported by Momeni et al [33,34], the optimum aspect ratio of ZnO nanowire was defined as the difference between the maximum generated electric potential at which the difference becomes less than 1%, which results in an aspect ratio higher than 16. The aspect ratio of the fabricated ZnO nanowires is around 22, higher than 16, leading to the maximum generated voltage. ...

A single-layer zinc oxide (ZnO) nanorod array-based micro energy harvester was designed and integrated with a piezoelectric metacapacitor. The device presents outstanding low-frequency (1-10 Hz) mechanical energy harvesting capabilities. When compared with conventional pristine ZnO nanostructured piezoelectric harvesters or generators, both open-circuit potential and short-circuit current are significantly enhanced (up to 3.1 V and 124 nA cm⁻²) for a single mechanical knock (∼34 kPa). Higher electromechanical conversion efficiency (1.3 pC/Pa) is also observed. The results indicate that the integration of the piezoelectric metacapacitor is a crucial factor for improving the low-frequency energy harvesting performance. A double piezoelectric-driven mechanism is proposed to explain current higher output power, in which the metacapacitor plays the multiple roles of charge pumping, storing and transferring. An as-fabricated prototype device for lighting an LED demonstrates high power transference capability, with over 95% transference efficiency to the external load.

Fragility and the presence of a poisonous substance (lead) are the two major issues with traditional piezoceramics and structures that include them. This work suggests an active structure that is lightweight, flexible, and eco-friendly such that a polymeric foam plate is sandwiched between two piezoelectrically activated nanocomposite layers. A combination of a polymer and piezoelectric nanowires (NWs) of zinc oxide (ZnO) is used in the nanocomposite layers. For the proposed active structure, two types of void distributions and functionally graded (FG) distributions of the NWs have been assumed in each corresponding layer. The buckling characterization of the proposed eco-friendly active sandwich plate (EFASP) under biaxial mechanical loads has been conducted using an extended meshless solution based on a third-order theory. An in-depth parametric study on the EFASPs’ biaxial buckling resistance revealed that increasing NW content considerably enhances buckling resistance, with this enhancement strongly reliant on the distribution profile of the NWs. Moreover, it was observed that embedding voids in the substrate layer can lead to a large structural weight reduction while only marginally lowering the buckling performance of suggested EFASPs.

Self-sustained devices, which can harvest energy from the environment, have the potential to overcome the limitations of battery-powered systems and, thus, are suitable for powering flexible or wearable electronics based on embedded microsensors. Compared with other materials used for energy harvesting, piezoelectric polymers exhibit significant advantages, such as high flexibility and durability as well as excellent stability. However, their low electricity-generating capability limits practical applications. In this work, the energy-harvesting performance of poly(vinylidene trifluoroethylene) [P(VDF-TrFE)] films with various chemical compositions and thicknesses is explored. The test circuit is connected to a picoammeter instead of an oscilloscope to maximize the energy output performance. A new self-powered sensing system is designed by switching off the microcontroller unit (MCU) to minimize power consumption rather than switching to the sleep mode. The results show that piezoelectric P(VDF-TrFE) generators meet the power consumption level of 1.1
$\mu \text{A}$
standby current and sustain the intermittent monitoring system. In addition, the system parameters, such as the generator size or the storage capacitance, are tunable, indicating the great potential of P(VDF-TrFE) to be applied to lightweight or flexible self-powered sensors.

Piezoelectric nanomaterials (PNs) are attractive for applications including sensing, actuating, energy harvesting, among others in nano-electro-mechanical-systems (NEMS) because of their excellent electromechanical coupling, mechanical and physical properties. However, the properties of PNs do not coincide with their bulk counterparts and depend on the particular size. A large amount of efforts have been devoted to studying the size-dependent properties of PNs by using experimental characterization, atomistic simulation and continuum mechanics modeling with the consideration of the scale features of the nanomaterials. This paper reviews the recent progresses and achievements in the research on the continuum mechanics modeling of the size-dependent mechanical and physical properties of PNs. We start from the fundamentals of the modified continuum mechanics models for PNs, including the theories of surface piezoelectricity, flexoelectricity and non-local piezoelectricity, with the introduction of the modified piezoelectric beam and plate models particularly for nanostructured piezoelectric materials with certain configurations. Then, we give a review on the investigation of the size-dependent properties of PNs by using the modified continuum mechanics models, such as the electromechanical coupling, bending, vibration, buckling, wave propagation and dynamic characteristics. Finally, analytical modeling and analysis of nanoscale actuators and energy harvesters based on piezoelectric nanostructures are presented.

Reducing the dimensions of materials to atomic scales results in a large portion of atoms being at or near the surface, with lower bond order and thus higher energy. At such scales, reduction of the surface energy and surface stresses can be the driving force for the formation of new low-dimensional nanostructures, and may be exhibited through surface relaxation and/or surface reconstruction, which can be utilized for tailoring the properties and phase transformation of nanomaterials without applying any external load. Here we used atomistic simulations and revealed an intrinsic structural transformation in monolayer materials that lowers their dimension from 2D nanosheets to 1D nanostructures to reduce their surface and elastic energies. Experimental evidence of such transformation has also been revealed for one of the predicted nanostructures. Such transformation plays an important role in bi-/multi-layer 2D materials.

An analytical model of a compressed piezoelectric ZnO rod is presented using two approximations. In one approximation, the total volume of the model system is maintained a constant, i.e., when a compressive force is applied vertically on the ZnO system, it is allowed to be deformed in the lateral direction. In the second approximation, the top potential of the ZnO rod is used as a constant initially. Later, this is approximated as a function of the radius after obtaining the first solution to observe the radial effects on the ZnO system potential. In the model used in this study, a ZnO rod of 880 nm in diameter and 700 nm in length was compressed by a tensile force of 107 N/m2. The scaled magnitude of the potential (a two-dimensional contour map) shows a radial distribution of the potential. The radial effects are directly reflected on the piezoelectric potential and the device design is required to minimize such a potential variation to achieve better uniform device performance and efficiency

The development of the Teflon® coated thread-shaped contact electrification fibre (CEF) is presented. This fibre has a simple structure, with a thin conductive core and a thin insulating coating. Contact electrification of the fibres has been characterised using both touch mode and drag mode. The output peak voltages generated from contact between the fibre and test rods were ®6 V for both modes. Owing to a very simple design, the CEF has a wide range of applications. In the future, these CEFs can be directly incorporated into the fabric to harvest energy from the surrounding environment and human activities.

A high-performance flexible piezoelectric hybrid nanogenerator (HNG) based on lead-free
perovskite zinc stannate (ZnSnO3) nanocubes and polydimethylsiloxane (PDMS) composite
with multiwall carbon nanotubes (MWCNTs) as supplement filling material is demonstrated.
Even without any electrical poling treatment, the HNG possesses an open-circuit voltage of 40 V
and a short-circuit current of 0.4 μA, respectively, under repeated human finger impact. It has
been demonstrated that the output volume power density of 10.8 μWcm−3 from a HNG can drive
several colour light emitting diodes (LEDs) and a charge capacitor that powers up a calculator,
indicating an effective means of energy harvesting power source with high energy conversion
efficiency (∼1.17%) for portable electronic devices.

The piezoelectric potential of strained intrinsic gallium nitride (GaN) nanotubes (NTs) has been studied analytically and numerically. The material properties used are obtained from molecular dynamics simulations (MDSs) and found to depend on the temperature and the NT׳s wall thickness. A novel core-surface (CS) model is developed to explain the size-dependent phenomenon and also used to predict the material properties for large-scale structures, where MDSs are not feasible. The obtained results show that GaN NTs can generate a much higher piezoelectric potential than their nanowire (NW) counterparts due to distinct material and geometric properties of NTs. This observation is not only limit for the present intrinsic structures but also can be expected for the as-grown structures. The influence of material and geometric properties becomes more significant for NTs with smaller radius or wall thickness-to-radius ratio and may enhance the piezoelectric potential by up to ten times for intrinsic NTs. However, the temperature is found to have no significant influence on the improvement of the piezoelectric potential of NTs. The observed improved piezoelectric potential in GaN NTs together with some other advantages of NTs, such as more efficient surface functionalization, suggests that the GaN NT can be a better candidate for the building blocks in piezotronic nanodevices compared with the most commonly used NWs.

Vibrating piezoelectric nanofilms (PNFs) play an important role in developing electromechanical nanodevices. To accurately characterize their dynamic behavior a sandwich-plate model is developed by integrating the surface effect and piezoelectric effect into the elastic plate theory. It is then used to analyze the vibration of PNFs with an emphasis on the effect of piezoelectricity and the surface layers. Analytic formulae are derived to identify the key factors that determine the structural responses of PNFs. Their influence on the vibration of PNFs is then evaluated qualitatively in a numerical study. It is found that the surface effect is significant and originates primarily from the residual surface stresses and the equivalent pre-stresses induced by an electrical voltage via the surface piezoelectricity.

The force required to separate a carbon nanotube from a solid polymer matrix has been measured by performing reproducible nanopullout experiments using atomic force microscopy. The separation stress is found to be remarkably high, indicating that carbon nanotubes are effective at reinforcing a polymer. These results imply that the polymer matrix in close vicinity of the carbon nanotube is able to withstand stresses that would otherwise cause considerable yield in a bulk polymer specimen. (C) 2003 American Institute of Physics.

The bending of a nonconducting piezoelectric ZnO nanowire is simulated by finite element method calculations. The top part is bent by a lateral force, which could be applied by an atomic force microscope tip. The generated electrical potential is ±0.3 V. This relatively high signal is, however, difficult to measure due to the low capacitance of the ZnO nanowire ( ∼ 4×10−5 pF) as compared to the capacitance of most preamplifiers ( ∼ 5 pF). A further problem arises from the semiconducting properties of experimentally fabricated ZnO nanowires which causes the disappearance of the voltage signal within picoseconds.

A mathematical framework is developed to study the mechanical behavior of material surfaces. The tensorial nature of surface stress is established using the force and moment balance laws. Bodies whose boundaries are material surfaces are discussed and the relation between surface and body stress examined. Elastic surfaces are defined and a linear theory with non-vanishing residual stress derived. The free-surface problem is posed within the linear theory and uniqueness of solution demonstrated. Predictions of the linear theory are noted and compared with the corresponding classical results. A note on frame-indifference and symmetry for material surfaces is appended.

A systematic experimental and theoretical investigation of the elastic and failure properties of ZnO nanowires (NWs) under
different loading modes has been carried out. In situ scanning electron microscopy (SEM) tension and buckling tests on single ZnO NWs along the polar direction [0001] were conducted.
Both tensile modulus (from tension) and bending modulus (from buckling) were found to increase as the NW diameter decreased
from 80 to 20 nm. The bending modulus increased more rapidly than the tensile modulus, which demonstrates that the elasticity
size effects in ZnO NWs are mainly due to surface stiffening. Two models based on continuum mechanics were able to fit the
experimental data very well. The tension experiments showed that fracture strain and strength of ZnO NWs increased as the
NW diameter decreased. The excellent resilience of ZnO NWs is advantageous for their applications in nanoscale actuation,
sensing, and energy conversion.
KeywordsZnO nanowire-mechanical property-size effect-Young’s modulus-fracture

The performance of a composite material system is critically controlled by the interfacial characteristics of the reinforcement and the matrix material. Here we report a study on the interfacial characteristics of a carbon nanotube (CNT)-reinforced polystyrene (PS) composite system through molecular mechanics simulations and elasticity calculations. In the absence of atomic bonding between the reinforcement and the matrix material, it is found that the nonbond interactions consists of electrostatic and van der Waals interaction, deformation induced by these forces, as well as stress/deformation arising from mismatch in the coefficients of thermal expansion. All of these contribute to the interfacial stress transfer ability, the critical parameter controlling material performance. Results of a CNT pullout simulation suggests that the interfacial shear stress of the CNT–PS system is about 160 MPa, significantly higher than most carbon fiber reinforced polymer composite systems. © 2001 American Institute of Physics.

Semiconducting and piezoelectric nanowires and nanobelts have exciting applications in electronics, optoelectronics, sensors, and the biological sciences. We review the use of ZnO nanowires and nanobelts in electromechanical coupled devices. A nanogenerator that uses aligned ZnO nanowires for converting nanoscale mechanical energy into electric energy is described. The mechanism of the nanogenerator relies on the unique coupling of ZnO's piezoelectric and semiconducting properties. The approach has the potential to convert biological mechanical energy, acoustic/ultrasonic vibration energy, and biofluid hydraulic energy into electricity, demonstrating a new pathway for harvesting energy for self-powered wireless nanodevices and nanosystems. Based on the nanogenerator mechanism, we also describe piezoelectric field-effect transistors, diodes, force/pressure sensors, and resonators. These devices form the fundamental components of nanopiezotronics, a new field in nanotechnology.

The harvesting of mechanical energy from ambient sources could power electrical devices without the need for batteries. However, although the efficiency and durability of harvesting materials such as piezoelectric nanowires have steadily improved, the voltage and power produced by a single nanowire are insufficient for real devices. The integration of large numbers of nanowire energy harvesters into a single power source is therefore necessary, requiring alignment of the nanowires as well as synchronization of their charging and discharging processes. Here, we demonstrate the vertical and lateral integration of ZnO nanowires into arrays that are capable of producing sufficient power to operate real devices. A lateral integration of 700 rows of ZnO nanowires produces a peak voltage of 1.26 V at a low strain of 0.19%, which is potentially sufficient to recharge an AA battery. In a separate device, a vertical integration of three layers of ZnO nanowire arrays produces a peak power density of 2.7 mW cm(-3). We use the vertically integrated nanogenerator to power a nanowire pH sensor and a nanowire UV sensor, thus demonstrating a self-powered system composed entirely of nanowires.

We have converted nanoscale mechanical energy into electrical energy by means of piezoelectric zinc oxide nanowire (NW) arrays. The aligned NWs are deflected with a conductive atomic force microscope tip in contact mode. The coupling of piezoelectric and semiconducting properties in zinc oxide creates a strain field and charge separation across the NW as a result of its bending. The rectifying characteristic of the Schottky barrier formed between the metal tip and the NW leads to electrical current generation. The efficiency of the NW-based piezoelectric power generator is estimated to be 17 to 30%. This approach has the potential of converting mechanical, vibrational, and/or hydraulic energy into electricity for powering nanodevices.

We have developed a nanowire nanogenerator that is driven by an ultrasonic wave to produce continuous direct-current output.
The nanogenerator was fabricated with vertically aligned zinc oxide nanowire arrays that were placed beneath a zigzag metal
electrode with a small gap. The wave drives the electrode up and down to bend and/or vibrate the nanowires. A piezoelectric-semiconducting
coupling process converts mechanical energy into electricity. The zigzag electrode acts as an array of parallel integrated
metal tips that simultaneously and continuously create, collect, and output electricity from all of the nanowires. The approach
presents an adaptable, mobile, and cost-effective technology for harvesting energy from the environment, and it offers a potential
solution for powering nanodevices and nanosystems.

The mechanical resonance of a single ZnO nanobelt, induced by an alternative electric field, was studied by in situ transmission electron microscopy. Due to the rectangular cross section of the nanobelt, two fundamental resonance modes have been observed corresponding to two orthogonal transverse vibration directions, showing the versatile applications of nanobelts as nanocantilevers and nanoresonators. The bending modulus of the ZnO nanobelts was measured to be ∼52 GPa and the damping time constant of the resonance in a vacuum of 5×10-8 Torr was ∼1.2 ms and quality factor Q=500. © 2003 American Institute of Physics.

A nanocomposite electrical generator composed of Zinc oxide nanowires (ZnO NWs) was modeled using continuum mechanics and Maxwell's equations. Axial loading was considered and the optimum aspect ratio of ZnO NWs for getting to maximum electric potential was calculated. The bonding between the ZnO NWs and the polymer matrix was considered to be perfect and the linear piezoelectric behavior was assumed. It was shown that the electric potential has maximum and minimum values of opposite signs at the extreme ends along the nanowire length. The maximum generated electric potential varies from 0.01717 for a NW with an aspect ratio of one to 0.61107 for a NW with an aspect ratio of thirty. The optimum aspect ratio of ZnO NW was defined as the difference between the maximum generated electric potential at which the difference becomes less than 1%, which results in an aspect ratio of 16. The results are a major step toward producing ZnO NWs for nanocomposite electrical generators with maximum performance.

The influence of the surface and small-scale effects on electromechanical coupling behavior of a piezoelectric nanowire is studied by using the beam bending model. An explicit formula for the electromechanical coupling (EMC) coefficient of the piezoelectric nanowire is obtained based on the nonlocal electroelasticity theory. It is found that the inclusion of the nonlocal effect in the model produces a significant difference from the past model which ignores the nonlocal effect in the prediction of the EMC coefficient and the electric field in the nanowire, confirming the significance of including the surface and small-scale effects in the analysis of piezoelectric nanowires. In particular, the influence of surface effects on the electric field is dominant for smaller nonlocal parameters. If the nanowire is subjected to an applied concentrated load and without surface effect, the nonlocal effect has no effect on its bending and electric field. This study might be helpful for understanding the size-dependent electromechanical properties of piezoelectric nanowires and design of piezoelectric-beam–based nanogenerators.

Multiwall carbon nanotubes have been dispersed homogeneously throughout polystyrene matrices by a simple solution-evaporation method without destroying the integrity of the nanotubes. Tensile tests on composite films show that 1 wt % nanotube additions result in 36%-42% and ~25% increases in elastic modulus and break stress, respectively, indicating significant load transfer across the nanotube-matrix interface. In situ transmission electron microscopy studies provided information regarding composite deformation mechanisms and interfacial bonding between the multiwall nanotubes and polymer matrix.

Surface and interface stresses represent the work per unit area to stretch the surface of a solid. These types of stresses
are discussed, emphasizing their relevance to thin film growth. In particular, the influence of these parameters on the critical
thickness for epitaxy and for intrinsic thin film stress generation are considered.

The size scale effect on the piezoelectric response of bulk ZnO and ZnO nanobelts has been studied using molecular dynamics simulation. Six molecular dynamics models of ZnO nanobelts are constructed and simulated with lengths of 150.97 Å and lateral dimensions ranging between 8.13 and 37.37 Å. A molecular dynamics model of bulk ZnO has also been constructed and simulated using periodic boundary conditions. The piezoelectric constants of the bulk ZnO and each of the ZnO nanobelts are predicted. The predicted piezoelectric coefficient of bulk ZnO is 1.4 C m−2, while the piezoelectric coefficient of ZnO nanobelts increases from 1.639 to 2.322 C m−2 when the lateral dimension of the ZnO NBs is reduced from 37.37 to 8.13 Å. The changes in the piezoelectric constants are explained in the context of surface charge redistribution. The results give a key insight into the field of nanopiezotronics and energy scavenging because the piezoelectric response and voltage output scale with the piezoelectric coefficient.

We utilize classical molecular dynamics to study surface effects on the piezoelectric properties of ZnO nanowires as calculated under uniaxial loading. An important point to our work is that we have utilized two types of surface treatments, those of charge compensation and surface passivation, to eliminate the polarization divergence that otherwise occurs due to the polar (0001) surfaces of ZnO. In doing so, we find that if appropriate surface treatments are utilized, the elastic modulus and the piezoelectric properties for ZnO nanowires having a variety of axial and surface orientations are all reduced as compared to the bulk value as a result of polarization reduction in the polar [0001] direction. The reduction in effective piezoelectric constant is found to be independent of the expansion or contraction of the polar (0001) surface in response to surface stresses. Instead, the surface polarization and thus effective piezoelectric constant is substantially reduced due to a reduction in the bond length of the Zn–O dimer closest to the polar (0001) surface. Furthermore, depending on the nanowire axial orientation, we find in the absence of surface treatment that the piezoelectric properties of ZnO are either effectively lost due to unphysical transformations from the wurtzite to non-piezoelectric d-BCT phases, or also become smaller with decreasing nanowire size. The overall implication of this study is that if enhancement of the piezoelectric properties of ZnO is desired, then continued miniaturization of square or nearly square cross-section ZnO wires to the nanometer scale is not likely to achieve this result.

Effective stiffness properties (D) of nanosized structural elements such as plates and beams differ from those predicted by standard continuum mechanics (Dc). These differences (D-Dc)/Dc depend on the size of the structural element. A simple model is constructed to predict this size dependence of the effective properties. The important length scale in the problem is identified to be the ratio of the surface elastic modulus to the elastic modulus of the bulk. In general, the non-dimensional difference in the elastic properties from continuum predictions (D-Dc)/Dc is found to scale as αS/Eh, where α is a constant which depends on the geometry of the structural element considered, S is a surface elastic constant, E is a bulk elastic modulus and h a length defining the size of the structural element. Thus, the quantity S/E is identified as a material length scale for elasticity of nanosized structures. The model is compared with direct atomistic simulations of nanoscale structures using the embedded atom method for FCC Al and the Stillinger-Weber model of Si. Excellent agreement between the simulations and the model is found.

The mechanical properties of individual zinc oxide (ZnO) nanowires, grown by a solid–vapour phase thermal sublimation process, were studied in situ by transmission electron microscopy (TEM) using a home-made TEM specimen holder. The mechanical resonance is electrically induced by applying an oscillating voltage, and in situ imaging has been achieved simultaneously. The results indicate that the elastic bending modulus of individual ZnO nanowires were measured to be ~58 GPa and the damping time constant of the resonance in a vacuum of 10−8 Torr was ~14 ms. A nanobalance was built and the mass of the nanoparticle attached at the tip of a nanowire was measured. The ZnO nanowires are promising in potential applications as nanocantilevers and nanoresonators.

An analysis is made of the effect of orientation of the fibres on the stiffness and strength of paper and other fibrous materials. It is shown that these effects may be represented completely by the first few coefficients of the distribution function for the fibres in respect of orientation, the first three Fourier coefficients for a planar matrix and the first fifteen spherical harmonics for a solid medium. For the planar case it is shown that all possible types of elastic behaviour may be represented by composition of four sets of parallel fibres in appropriate ratios. The means of transfer of load from fibre to fibre are considered and it is concluded that the effect of short fibres may be represented merely by use of a reduced value for their modulus of elasticity. The results of the analysis are applied to certain samples of resin bonded fibrous filled materials and moderately good agreement with experimental results is found.

In this paper, an atomistic-based representative volume element (RVE) is developed to characterize the behavior of carbon nanotube (CNT) reinforced amorphous epoxies. The RVE consists of the carbon nanotube, the surrounding epoxy matrix, and the CNT/epoxy interface. An atomistic-based continuum representation is adopted throughout all the components of the RVE. By equating the associated strain energies under identical loading conditions, we were able to homogenize the RVE into a representative fiber. The homogenized RVE was then employed in a micromechanical analysis to predict the effective properties of the newly developed CNT-reinforced amorphous epoxy. Numerical examples show that the effect of volume fraction, orientation, and aspect ratio of the continuous fibres on the properties of the CNT-reinforced epoxy adhesives can be significant. These results have a direct bearing on the design and development of nano-tailored adhesives for use in structural adhesive bonds.

The shear yield strength and the shear strength of a resin matrix increase almost linearly as the logarithm of the strain rate increases. This increasing tendency is almost the same at various temperatures. The strain rate temperature superposition held and an experimental equation was found to estimate the strain rate and temperature dependence of these shear properties. The strain rate and temperature dependence of the shear yield strength at the fibre-matrix interphase can be also estimated by the same equation. A strong quantitative relation was observed between the strain rate and temperature dependence of the shear properties of a resin matrix and that of the shear yield strength at the fibre-matrix interphase.

The elastic constants of ZnO nanostructures control their elastic energy and thereby are important to their function in converting strain energy to electricity. This letter presents the size dependence of Young’s moduli of ZnO nanoplates, according to density-functional-theory-based ab initio calculations. Our results show that Young’s moduli of (0001)/(000 1 ) , (1 1 00) , and (11 2 0) nanoplates increase as size decreases. For (0001)/(000 1 ) nanoplate, Young’s moduli vary discontinuously with size, due to a phase transformation from wurtzite to graphitic structure. Further, our analyses show that the increase of moduli is due to surface stiffening and bulk nonlinear elasticity.

Relation between the elastic modulus and the diameter (D) of ZnO nanowires was elucidated using a model with the calculated ZnO surface stresses as input. We predict for ZnO nanowires due to surface stress effect: (1) when D≫20 nm , the elastic modulus would be lower than the bulk modulus and decrease with the decreasing diameter, (2) when 20 nm ≫D≫2 nm , the nanowires with a longer length and a wurtzite crystal structure could be mechanically unstable, and (3) when D≪2 nm , the elastic modulus would be higher than that of the bulk value and increase with a decrease in nanowire diameter.

A shear-lag model is developed for carbon nanotube-reinforced polymer composites using a multiscale approach. The main morphological features of the nanocomposites are captured by utilizing a composite cylinder embedded with a capped nanotube as the representative volume element. The molecular structural mechanics is employed to determine the effective Young’s modulus of the capped carbon nanotube based on its atomistic structure. The capped nanotube is equivalently represented by an effective (solid) fiber having the same diameter and length but different Young’s modulus, which is determined from that of the nanotube under an isostrain condition. The shear-lag analysis is performed in the context of linear elasticity for axisymmetric problems, and the resulting formulas are derived in closed forms. To demonstrate applications of the newly developed model, parametric studies of sample cases are conducted. The numerical results reveal that the nanotube aspect ratio is a critical controlling parameter for nanotube-reinforced composites. The predictions by the current analytical model compare favorably with the existing computational and experimental data.

The interfacial shear strength in single-wall nanotube–polymer composites is calculated using a traditional force balance approach, modified for a hollow tube, and the effect of varying some of the model parameters is examined and discussed. It is shown that high values of the interfacial shear strength (compared to those in current advanced fiber-based polymer composites) are in principle attainable. Defects in the hexagonal structure of a nanotube, which technically is a `perfect' material, are expected to strongly reduce its strength and the model predicts that, as a consequence, a large variability should be experimentally observed in either the interfacial strength or the critical length of apparently identical nanotubes.

One-dimensional solids like nanowires and nanotubes are potential materials for future nanoscale sensors and actuators. Due to their unique length scale, they exhibit superior mechanical properties and other length scale dependent phenomena. In this paper, we report experimental investigations on the mechanical properties of ZnO nanowires. We have designed a MEMS test-bed for mechanical characterization of nanowires. The MEMS device exploits the mechanics of post-buckling deformation of slender columns to achieve very high force and displacement resolution. The small size of the test-bed allows for in situ experimentation inside analytical chambers, such as SEM and TEM. We present microscale version of pick-and-place as a generic specimen preparation and manipulation technique for experimentation on individual nanostructures. We performed experiments on ZnO nanowires inside a scanning electron microscope (SEM) and estimated the Young's modulus to be about 21 GPa and the fracture strain to vary from 5% to 15%.

Scanning conductance microscopy (SCM) is used to measure the dielectric constant of a single pencil-like zinc oxide (ZnO) nanowire with the diameters ranging from 85 to 285 nm. As the diameter decreases, the dielectric constant of ZnO nanowire is found to decrease from 6.4 to 2.7, which is much smaller than that of the bulk ZnO of 8.66. A core-shell composite nanowire model in terms of the surface dielectric weakening effect is proposed to explore the origin of the size dependence of dielectric constant, and the experimental results are well explained.

A nanocomposite electrical generator composed of an array of zinc oxide nanowires is considered. The electric potential distribution along zinc oxide nanowires is modeled using continuum mechanics and Maxwell's equations for the case of axial loading. A perturbation technique is used for decoupling the constitutive equations. The governing differential equations are solved using a finite difference method. It is shown that a gradient of electric potential exists along the axis of the zinc oxide nanowires. Maximum and minimum values of electric potential exist at the extreme ends along the nanowire length and have opposite signs. The positive and negative voltages are separated by a zero-valued electric potential at the middle of the nanowire. It is also shown that the electric potential is a strong function of shear stress at the interface of matrix-nanowire. The proposed system and loading configuration can generate up to 160% more electric potential than the values reported for the nanowire in the bended configuration, which results in a more sustainable energy source.

In this investigation, the size-scale in mechanical properties of individual [0001] ZnO nanowires and the correlation with atomic-scale arrangements were explored via in situ high-resolution transmission electron microscopy (TEM) equipped with atomic force microscopy (AFM) and nanoindentation (NI) systems. The Young's modulus was determined to be size-scale-dependent for nanowires with diameter, d, in the range of 40 nm ≤ d ≤ 110 nm, and reached the maximum of ∼ 249 GPa for d = 40 nm. However, this phenomenon was not observed for nanowires in the range of 200 nm ≤ d ≤ 400 nm, where an average constant Young's modulus of ∼ 147.3 GPa was detected, close to the modulus value of bulk ZnO. A size-scale dependence in the failure of nanowires was also observed. The thick ZnO nanowires (d ≥ 200 nm) were brittle, while the thin nanowires (d ≤ 110 nm) were highly flexible. The diameter effect and enhanced Young's modulus observed in thin ZnO nanowires are due to the combined effects of surface relaxation and long-range interactions present in ionic crystals, which leads to much stiffer surfaces than bulk wires. The brittle failure in thicker ZnO wires was initiated from the outermost layer, where the maximum tensile stress operates and propagates along the (0001) planes. After a number of loading and unloading cycles, the highly compressed region of the thinner nanowires was transformed from a crystalline to an amorphous phase, and the region near the neutral zone was converted into a mixture of disordered atomic planes and bent lattice fringes as revealed by high-resolution images.

In this work, the influence of surface effects, including residual surface stress, surface elasticity and surface piezoelectricity, on the vibrational and buckling behaviors of piezoelectric nanobeams is investigated by using the Euler-Bernoulli beam theory. The surface effects are incorporated by applying the surface piezoelectricity model and the generalized Young-Laplace equations. The results demonstrate that surface effects play a significant role in predicting these behaviors. It is found that the influence of the residual surface stress and the surface piezoelectricity on the resonant frequencies and the critical electric potential for buckling is more prominent than the surface elasticity. The nanobeam boundary conditions are also found to influence the surface effects on these parameters. This study also shows that the resonant frequencies can be tuned by adjusting the applied electrical load. The present study is envisaged to provide useful insights for the design and applications of piezoelectric-beam-based nanodevices.

Nanowires made of materials with noncentrosymmetric crystal structure are under investigation for their piezoelectric properties and suitability as building blocks for next-generation self-powered nanodevices. In this work, we investigate the size dependence of piezoelectric coefficients in nanowires of two such materials - zinc oxide and gallium nitride. Nanowires, oriented along their polar axis, ranging from 0.6 to 2.4 nm in diameter were modeled quantum mechanically. A giant piezoelectric size effect is identified for both GaN and ZnO nanowires. However, GaN exhibits a larger and more extended size dependence than ZnO. The observed size effect is discussed in the context of charge redistribution near the free surfaces leading to changes in local polarization. The study reveals that local changes in polarization and reduction of unit cell volume with respect to bulk values lead to the observed size effect. These results have strong implication in the field of energy harvesting, as piezoelectric voltage output scales with the piezoelectric coefficient.

The bending Young's modulus of ZnO nanobelts was measured by performing three-point bending tests directly on individual nanobelts with an atomic force microscope (AFM). The surface-to-volume ratio has no effect on the bending Young's modulus of the ZnO nanobelts for surface-to-volume ratios ranging from 0.017 to 0.035 nm(2) nm(-3), with a belt size of 50-140 nm in thickness and 270-700 nm in width. The bending Young's modulus was measured to be 38.2 +/- 1.8 GPa, which is about 20% higher than the nanoindentation Young's modulus of 31.1 +/- 1.3 GPa. The ZnO nanobelts exhibit brittle fracture failure in bending but some plastic deformation in indentation.

Understanding the mechanical properties of nanowires made of semiconducting materials is central to their application in nano devices. This work presents an experimental and computational approach to unambiguously quantify size effects on the Young's modulus, E, of ZnO nanowires and interpret the origin of the scaling. A micromechanical system (MEMS) based nanoscale material testing system is used in situ a transmission electron microscope to measure the Young's modulus of [0001] oriented ZnO nanowires as a function of wire diameter. It is found that E increases from approximately 140 to 160 GPa as the nanowire diameter decreases from 80 to 20 nm. For larger wires, a Young's modulus of approximately 140 GPa, consistent with the modulus of bulk ZnO, is observed. Molecular dynamics simulations are carried out to model ZnO nanowires of diameters up to 20 nm. The computational results demonstrate similar size dependence, complementing the experimental findings, and reveal that the observed size effect is an outcome of surface reconstruction together with long-range ionic interactions.

We have applied the perturbation theory for calculating the piezoelectric potential distribution in a nanowire (NW) as pushed by a lateral force at the tip. The analytical solution given under the first-order approximation produces a result that is within 6% from the full numerically calculated result using the finite element method. The calculation shows that the piezoelectric potential in the NW almost does not depend on the z-coordinate along the NW unless very close to the two ends, meaning that the NW can be approximately taken as a "parallel plated capacitor". This is entirely consistent to the model established for nanopiezotronics, in which the potential drop across the nanowire serves as the gate voltage for the piezoelectric field effect transistor. The maximum potential at the surface of the NW is directly proportional to the lateral displacement of the NW and inversely proportional to the cube of its length-to-diameter aspect ratio. The magnitude of piezoelectric potential for a NW of diameter 50 nm and length 600 nm is approximately 0.3 V. This voltage is much larger than the thermal voltage ( approximately 25 mV) and is high enough to drive the metal-semiconductor Schottky diode at the interface between atomic force microscope tip and the ZnO NW, as assumed in our original mechanism for the nanogenerators.

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