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Enhanced mechanical properties of ZnO nanowire-reinforced nanocomposites: A size-scale effect
Abstract
A multiscale approach is pursued to develop a shear-lag model in combination with core-surface and core-shell models for capturing size-scale effect on mechanical properties of ZnO nanowire (NW)-reinforced nanocomposites. Surface effects are represented by a zero-thickness (finite-thickness) surface with different elastic modulus from the central part of NW. The molecular dynamics technique is utilized for calculating thickness of the shell in the core-shell model. Linear elasticity for an axisymmetric problem and the cylindrical coordinate system is used to find the closed form of governing equations. The effect of different parameters, including diameter and aspect ratio of NWs, is studied to demonstrate the application of the developed model. Numerical results disclose that NWs with a larger aspect ratio and a smaller diameter can carry a larger portion of applied stress and are preferable in designing high-performance nanocomposites. This result is in agreement with the reported computational and experimental data.
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Ultrathin resonant cantilevers are promising for ultrasensitive detection. A technique is developed for high-yield fabrication of single-crystalline-silicon cantilevers as thin as 12 nm. The formed cantilever resonators are characterized by resonance testing in high vacuum. Significant specimen size effect on Young’s modulus of ultrathin (12–170 nm) silicon is detected. The Young’s modulus decreases monotonously as the cantilevers become thinner. The size effect is consistent with the published simulation results of direct-atomistic model, in which surface effects are taken into consideration.
Molecular dynamics simulations of carbon nanotube (NT) pull-out from a polymer matrix are carried out. As the NT pull-out develops, variations in the displacement and velocities of the NT are monitored. The existence of a carbon-ring-based period in NT sliding during pull-out is identified. Linear trends in the NT velocity–force relation are observed and used to estimate an effective viscosity coefficient for interfacial sliding at the NT/polymer interface. As a result, the entire process of NT pull-out is characterized by an interfacial friction model that is based on a critical pull-out force, and an analog of Newton’s friction law used to describe the NT/polymer interfacial sliding.
Based on a recent result showing that the net Coulomb potential in condensed ionic systems is rather short ranged, an exact and physically transparent method permitting the evaluation of the Coulomb potential by direct summation over the r−1 Coulomb pair potential is presented. The key observation is that the problems encountered in determining the Coulomb energy by pairwise, spherically truncated r−1 summation are a direct consequence of the fact that the system summed over is practically never neutral. A simple method is developed that achieves charge neutralization wherever the r−1 pair potential is truncated. This enables the extraction of the Coulomb energy, forces, and stresses from a spherically truncated, usually charged environment in a manner that is independent of the grouping of the pair terms. The close connection of our approach with the Ewald method is demonstrated and exploited, providing an efficient method for the simulation of even highly disordered ionic systems by direct, pairwise r−1 summation with spherical truncation at rather short range, i.e., a method which fully exploits the short-ranged nature of the interactions in ionic systems. The method is validated by simulations of crystals, liquids, and interfacial systems, such as free surfaces and grain boundaries. © 1999 American Institute of Physics.
The arrays of piezoelectric, semiconducting ZnO nanowires (NW) grown on flexible plastic substrates can be used to convert mechanical energy into electrical energy using a conductive atomic force microscope. The estimated piezoelectric induced electrical power density of the NW array upon deflection of an AFM tip was on the order of milliwatts per centimeter squared, which is large enough to power a variety of MEMS, NEMS, and other nanoscale devices. The piezoelectric power generators that use ZnO NW arrays on flexible plastic substrates may be able to harvest energy from their environment for powering nanodevices and nanosystems. This flexible power source can find potential applications in implantable biosensors and biodetection, wireless self-powered sensors, and self-powering electronic devices.
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.
Surface and interface stresses in solids are defined and their role in the thermodynamics of solids is presented. A discussion concerning the physical meaning of these quantities is given, along with a review of selected theoretical calculations and experimental measurements. It is shown that for a solid phase with one or more of its dimensions smaller than about 10 nm, the surface and interface stresses can be principal factors in determining the equilibrium structure and behavior of the solid. In particular, the effects of surface and interface stresses on thin films are reviered along with the related topic of surface reconstructions in metals.
We demonstrate the feasibility of using classical atomistic simulations, i.e. molecular dynamics and molecular statics, to study the piezoelectric properties of ZnO using core-shell interatomic potentials. We accomplish this by reporting the piezoelectric constants for ZnO as calculated using two different classical interatomic core-shell potentials: that originally proposed by Binks and Grimes (1994 Solid State Commun. 89 921-4), and that proposed by Nyberg et al (1996 J. Phys. Chem. 100 9054-63). We demonstrate that the classical core-shell potentials are able to qualitatively reproduce the piezoelectric constants as compared to benchmark ab initio calculations. We further demonstrate that while the presence of the shell is required to capture the electron polarization effects that control the clamped ion part of the piezoelectric constant, the major shortcoming of the classical potentials is a significant underprediction of the clamped ion term as compared to previous ab initio results. However, the present results suggest that overall, these classical core-shell potentials are sufficiently accurate to be utilized for large scale atomistic simulations of the piezoelectric response of ZnO nanostructures.
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.
Semiconductor nanowires are unique as functional building blocks in nanoscale electrical and electromechanical devices. Here, we report on the mechanical properties of ZnO nanowires that range in diameter from 18 to 304 nm. We demonstrate that in contrast to recent reports, Young's modulus is essentially independent of diameter and close to the bulk value, whereas the ultimate strength increases for small diameter wires, and exhibits values up to 40 times that of bulk. The mechanical behavior of ZnO nanowires is well described by a mechanical model of bending and tensile stretching.
This article examines the effect of interfacial load transfer on the stress distribution in carbon nanotube/polymer composites through a stress analysis of the nanotube/matrix system. Both isostrain and isostress loading conditions are investigated. The nanotube is modeled by the molecular structural mechanics method at the atomistic level. The matrix is modeled by the finite element method, and the nanotube/matrix interface is assumed to be bonded either perfectly or by van der Waals interactions. The fundamental issues examined include the interfacial shear stress distribution, stress concentration in the matrix in the vicinity of nanotube ends, axial stress profile in the nanotube, and the effect of nanotube aspect ratio on load transfer.
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.
One-dimensional (1D) zinc oxide nanostructures are the main components of nanogenerators and central to the emerging field of nanopiezotronics. Understanding the underlying physics and quantifying the electromechanical properties of these structures, the topic of this research study, play a major role in designing next-generation nanoelectromechanical devices. Here, atomistic simulations are utilized to study surface and size-scale effects on the electromechanical response of 1D ZnO nanostructures. It is shown that the mechanical and piezoelectric properties of these structures are controlled by their size, cross-sectional geometry, and loading configuration. The study reveals enhancement of the piezoelectric and elastic modulus of ZnO nanowires (NW) with diameter d > 1 nm, followed by a sudden drop for d < 1 nm due to transformation of NWs to nanotubes (NTs). Degradation of mechanical and piezoelectric properties of ZnO nanobelts (NBs) followed by an enhancement in piezoelectric properties occurs when their lower dimension is reduced to <1 nm. The latter enhancement can be explained in the context of surface reconfiguration and formation of hexagon-tetragon (HT) pairs at the intersection of (21[combining macron]1[combining macron]0) and (011[combining macron]0) planes in NBs. Transition from a surface-reconstructed dominant to a surface-relaxed dominant region is demonstrated for lateral dimensions <1 nm. New phase-transformation (PT) kinetics from piezoelectric wurtzite to nonpiezoelectric body-centered tetragonal (WZ → BCT) and graphite-like phase (WZ → HX) structures occurs in ZnO NWs loaded up to large strains of ∼10%.
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.
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.
DOI:https://doi.org/10.1103/PhysRevB.67.039902
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.
Elastic properties of crystal surfaces are useful in understanding mechanical properties of nanostructures. This paper presents a fully nonlinear treatment of surface stress and surface elastic constants. A method for the determination of surface elastic properties from atomistic simulations is developed. This method is illustrated with examples of several crystal faces of some fcc metals modeled with embedded atom potentials. The key finding in this study is the importance of accounting for the additional relaxations of atoms at the crystal surface due to strain. Although these relaxations do not affect the values of surface stress (as had been determined in previous works), they have a profound effect on the surface elastic constants. Failure to account for these relaxations can lead to values of elastic constants that are incorrect not only in magnitude but also in sign. A possible method for the experimental determination of the surface elastic constants is outlined.
Current experimental research aims to reduce the size of quartz crystal oscillators into the submicrometer range. Devices then comprise multimillion atoms and operating frequencies will be in the gigahertz regime. Such characteristics make direct atomic scale simulation feasible using large scale parallel computing. Here, we describe molecular-dynamics simulations on bulk and nanoscale device systems focusing on elastic constants and flexural frequencies. Here we find (a) in order to achieve elastic constants within 1% of those of the bulk requires approximately one million atoms; precisely the experimental regime of interest; (b) differences from continuum mechanical frequency predictions are observable for 17 nm devices; (c) devices with 1% defects exhibit dramatic anharmonicity. A subsequent paper describes the direct atomistic simulation of operating characteristics of a micrometer scale device. A PAPS cosubmission gives algorithmic details.
DOI:https://doi.org/10.1103/PhysRevB.74.149901
Uniaxial tensile experiments were performed on single crystal zinc oxide nanowires with a custom microfabricated tool. The measured Young’s modulus is about 30%—40% of the bulk value for specimens with 200–400 nm in diameter, which cannot be explained with classical elasticity formulations. We discuss this anomaly in light of the enhanced electromechanical coupling due to static mechanical and isolated electrical boundary conditions that can significantly contribute to the softening of the material, irrespective of the length scale.
Atomistic simulation methods have been used to determine the incorporation mechanisms of excess zinc and chromium in stoichiometric ZnCr2O4. It is shown that oxidising conditions aid the solution of zinc giving rise to the possibility of highly zinc excess materials. Conversely reducing conditions do not enhance chromia solution and a highly excess chromium materials is not predicted to form.
Molecular dynamics simulations are performed to characterize the response of zinc oxide (ZnO) nanobelts to tensile loading. The ultimate tensile strength (UTS) and Young's modulus are obtained as functions of size and growth orientation. Nanobelts in three growth orientations are generated by assembling the unit wurtzite cell along the [0001], , and crystalline axes. Following the geometric construction, dynamic relaxation is carried out to yield free-standing nanobelts at 300 K. Two distinct configurations are observed in the [0001] and orientations. When the lateral dimensions are above 10 Å, nanobelts with rectangular cross-sections are seen. Below this critical size, tubular structures involving two concentric shells similar to double-walled carbon nanotubes are obtained. Quasi-static deformations of belts with and orientations consist of three stages, including initial elastic stretching, wurtzite-ZnO to graphitic-ZnO structural transformation, and cleavage fracture. On the other hand, [0001] belts do not undergo any structural transformation and fail through cleavage along (0001) planes. Calculations show that the UTS and Young's modulus of the belts are size dependent and are higher than the corresponding values for bulk ZnO. Specifically, as the lateral dimensions increase from 10 to 40 Å, decreases between 38–76% and 24–63% are observed for the UTS and Young's modulus, respectively. This effect is attributed to the size-dependent compressive stress induced by tensile surface stress in the nanobelts. and nanobelts with multi-walled tubular structures are seen to have higher values of elastic moduli (~340 GPa) and UTS (~36 GPa) compared to their wurtzite counterparts, echoing a similar trend in multi-walled carbon nanotubes.
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.
A bond-order–bond-length–bond-strength (bond-OLS) correlation mechanism is presented for consistent insight into the origin of the shape-and-size dependence of a nanosolid, aiming to provide guidelines for designing nanomaterials with desired functions. It is proposed that the coordination number imperfection of an atom at a surface causes the remaining bonds of the lower-coordinated surface atom to relax spontaneously; as such, the bond energy rises (in absolute value). The bond energy rise contributes not only to the cohesive energy (ECoh) of the surface atom but also to the energy density in the relaxed region. ECoh relates to thermodynamic properties such as self-assembly, phase transition and thermal stability of a nanosolid. The binding energy density rise is responsible for the changes of the system Hamiltonian and related properties, such as the bandgap, core-level shift, phonon frequency and the dielectrics of a nanosolid of which the surface curvature and the portion of surface atoms vary with particle size. The bond-OLS premise, involving no assumptions or freely adjustable parameters, has led to consistency between predictions and experimental observations of a number of outstanding properties of nanosolids.
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.
Crystalline piezoelectric dielectrics electrically polarize upon application of uniform mechanical strain. Inhomogeneous strain, however, locally breaks inversion symmetry and can potentially polarize even nonpi-ezoelectric centrosymmetric dielectrics. Flexoelectricity—the coupling of strain gradient to polarization—is expected to show a strong size dependency due to the scaling of strain gradients with structural feature size. In this study, using a combination of atomistic and theoretical approaches, we investigate the "effective" size-dependent piezoelectric and elastic behavior of inhomogeneously strained nonpiezoelectric and piezoelectric nanostructures. In particular, to obtain analytical results and tease out physical insights, we analyze a paradig-matic nanoscale cantilever beam. We find that in materials that are intrinsically piezoelectric, the flexoelec-tricity and piezoelectricity effects do not add linearly and exhibit a nonlinear interaction. The latter leads to a strong size-dependent enhancement of the apparent piezoelectric coefficient resulting in, for example, a "giant" 500% enhancement over bulk properties in BaTiO 3 for a beam thickness of 5 nm. Correspondingly, for nonpiezoelectric materials also, the enhancement is nontrivial e.g., 80% for 5 nm size in paraelectric BaTiO 3 phase. Flexoelectricity also modifies the apparent elastic modulus of nanostructures, exhibiting an asymptotic scaling of 1 / h 2 , where h is the characteristic feature size. Our major predictions are verified by quantum mechanically derived force-field-based molecular dynamics for two phases cubic and tetragonal of BaTiO 3 .
We studied the elastic properties of ZnO nanofilms (NFs) and nanowires (NWs) terminated by either (10 1 0) or (11 2 0) surfaces, based on the empirical Buckingham-type potential. It is found that the Young’s moduli of ZnO NFs increase as the thicknesses decrease and that of (10 1 0) -surface terminated NFs are systematically larger than that of (11 2 0) -surface terminated ones. In these NFs, the surface atomic layers of both types of NFs are stiffened significantly with respect to the bulk ZnO, and the (10 1 0) -surface layer is much stiffer than the (11 2 0) -surface layer. In contrast, all the interior atomic layers are only slightly stiffer than the bulk ZnO, and are independent on the orientations. The ZnO NWs show similar size- and orientation-dependent mechanical behaviors which also originate from the significant stiffening of the surface atomic layers. Through this study, we predict that the mechanical properties of ZnO nanostructures can be manipulated through controlling the size and orientations of these materials.
Integropartial differential equations of the linear theory of nonlocal elasticity are reduced to singular partial differential equations for a special class of physically admissible kernels. Solutions are obtained for the screw dislocation and surface waves. Experimental observations and atomic lattice dynamics appear to support the theoretical results very nicely.
A semicontinuum model is presented for nanostructured materials that possess a platelike geometry, such as ultra-thin films. In contrast to the classical continuum theory, the current model accounts for the discrete nature in the thickness direction. In-plane Young’s modulus, and in-plane and out-plane Poisson’s ratios are investigated with this model. It is found that the values of the Young’s modulus and Poisson’s ratios depend on the number of atom layers in the thickness direction and approach the respective bulk values as the number of atom layers increases. © 2003 American Institute of Physics.
Thin chromium cantilevers with sub- 100 nm thickness have been characterized by an atomic force microscope operating in contact mode. A continuous determination of the local mechanical properties at all lengths was accomplished by applying force along the length of the cantilevers. The result show a decrease of the Young’s modulus as the cantilevers get thinner.
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.
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.
This Letter describes the production of single-wall carbon nanotube (SWNT) – polymer composites with enhanced mechanical and electrical properties and exceptional nanotube alignment. A combination of solvent casting and melt mixing was used to disperse SWNT materials in poly(methyl methacrylate) (PMMA). Composite films showed higher conductivity along the flow direction than perpendicular to it. Composite fibers were melt spun to achieve draw ratios between 20 and 3600. The elastic modulus and yield strength of SWNT–PMMA composite fibers increased with nanotube loading and draw ratio. Polarized resonant Raman spectroscopy indicates that the nanotubes in the fibers are well aligned, with mosaic distribution FWHMs as small as 4°.
The ‘shear-lag’ analysis method is frequently used for analysis of stress transfer between the fiber and the matrix in composites. The accuracy of shear-lag methods has not been critically assessed, in part because the assumptions have not been fully understood. This paper starts from the exact equations of elasticity for axisymmetric stress states in transversely isotropic materials and introduces the minimum assumptions required to derive the most commonly used shear-lag equations. These assumptions can now be checked to study the accuracy of shear-lag analysis on any problem. Some sample calculations were done for stress transfer from a matrix into a broken fiber. The shear-lag method did a reasonable job (within 20%) of predicting average axial stress in the fiber and total strain energy in the specimen provided the shear-lag parameter most commonly used in the literature is replaced by a new one derived from the approximate elasticity analysis. The shear-lag method does a much worse job of predicting shear stresses and energy release rates. Furthermore, the shear-lag method does not work for low fiber volume fractions.
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%.
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.
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.
We demonstrate a mechanical-electrical trigger using a ZnO piezoelectric fine-wire (PFW) (microwire, nanowire). Once subjected to mechanical impact, a bent PFW creates a voltage drop across its width, with the tensile and compressive surfaces showing positive and negative voltages, respectively. The voltage and current created by the piezoelectric effect could trigger an external electronic system, thus, the impact force/pressure can be detected. The response time of the trigger/sensor is approximately 10 ms. The piezoelectric potential across the PFW has a lifetime of approximately 100 s, which is long enough for effectively "gating" the transport current along the wire; thus a piezoelectric field effect transistor is possible based on the piezotronic effect.
Piezoelectricity in pyroelectrics and the linear response of polarization to a strain gradient?lexoelectricity) are discussed in the framework of the unified approach. It was pointed out by Born and Huang and by Martin, that there was a difference between the piezoelectric response for the cases of a sound wave and of a uniform strain in a finite crystal, and that only the ‘‘proper’’ parts of piezoelectric constants coincided for these cases. It is shown in this paper that there is no such difference if an accurate definition of piezoelectricity is applied. The theory of flexoelectricity in solid crystalline dielectrics is developed. It is shown that the general properties of flexoelectric response strongly differ from those of piezoelectric response: (1) there is an appreciable surface contribution to the flexoelectric response and (2) the bulk flexoelectric responses for the case of a propagating sound wave and for that of a static uniform strain gradient are considerably different. It is proposed to use flexoelectric effect as a method of crystal surface investigation.
An atomic force microscopy (AFM) based technique is demonstrated for measuring the elastic modulus of individual nanowires/nanotubes aligned on a solid substrate without destructing or manipulating the sample. By simultaneously acquiring the topography and lateral force image of the aligned nanowires in the AFM contacting mode, the elastic modulus of the individual nanowires in the image has been derived. The measurement is based on quantifying the lateral force required to induce the maximal deflection of the nanowire where the AFM tip was scanning over the surface in contact mode. For the [0001] ZnO nanowires/nanorods grown on a sapphire surface with an average diameter of 45 nm, the elastic modulus is measured to be 29 +/- 8 GPa.
We report a size dependence of Young's modulus in [0001] oriented ZnO nanowires (NWs) with diameters ranging from 17 to 550 nm for the first time. The measured modulus for NWs with diameters smaller than about 120 nm is increasing dramatically with the decreasing diameters, and is significantly higher than that of the larger ones whose modulus tends to that of bulk ZnO. A core-shell composite NW model in terms of the surface stiffening effect correlated with significant bond length contractions occurred near the {1010} free surfaces (which extend several layers deep into the bulk and fade off slowly) is proposed to explore the origin of the size dependence, and present experimental result is well explained. Furthermore, it is possible to estimate the size-related elastic properties of GaN nanotubes and relative nanostructures by using this model.
A thermodynamic diffuse interface analysis predicts that grain boundary transitions in solute absorption are coupled to localized structural order-disorder transitions. An example calculation of a planar grain boundary using a symmetric binary alloy shows that first-order boundary transitions can be predicted as a function of the crystallographic grain boundary misorientation and empirical gradient coefficients. The predictions are compared to published experimental observations.