Phenomenon Of Flexoelectricity Research Articles

Flexoelectricity Modulated Electron Transport of 2D Indium Oxide.

The phenomenon of flexoelectricity, wherein mechanical deformation induces alterations in the electron configuration of metal oxides, has emerged as a promising avenue for regulating electron transport. Leveraging this mechanism, stress sensing can be optimized through precise modulation of electron transport. In this study, the electron transport in 2D ultra-smooth In2O3 crystals is modulated via flexoelectricity. By subjecting cubic In2O3 (c-In2O3) crystals to significant strain gradients using an atomic force microscope (AFM) tip, the crystal symmetry is broken, resulting in the separation of positive and negative charge centers. Upon applying nano-scale stress up to 100nN, the output voltage and power values reach their maximum, e.g. 2.2mV and 0.2pW, respectively. The flexoelectric coefficient and flexocoupling coefficient of c-In2O3 are determined as ≈0.49nCm-1 and 0.4V, respectively. More importantly, the sensitivity of the nano-stress sensor upon c-In2O3 flexoelectric effect reaches 20nN, which is four to six orders smaller than that fabricated with other low dimensional materials based on the piezoresistive, capacitive, and piezoelectric effect. Such a deformation-induced polarization modulates the band structure of c-In2O3, significantly reducing the Schottky barrier height (SBH), thereby regulating its electron transport. This finding highlights the potential of flexoelectricity in enabling high-performance nano-stress sensing through precise control of electron transport.

The mechanical response of nanobeams considering the flexoelectric phenomenon in the temperature environment

The mechanical response of nanobeams considering the flexoelectric phenomenon in the temperature environment

Asperity shape in flexoelectric/triboelectric contacts

Triboelectric and flexoelectric phenomena have seen significant recent interest for energy harvesting. However, the underlying science responsible for triboelectricity has yet to be completely understood, both the fundamentals and an understanding of how the energy output depends upon the shape of the interacting surface. Here, we investigate the role of the contacting shapes (asperities) in triboelectricity. We demonstrate that their shape and size is very important, obtaining qualitative agreement with experimental results. Further, we discuss how the impact of the shape depends on material, geometric, gradient elasticity and electronic transport details. We provide scaling rules which can be exploited to better design energy harvesting devices based upon either triboelectricity or flexoelectricity.

An overview of the flexoelectric phenomenon, potential applications, and proposals for further research directions

An overview of the flexoelectric phenomenon, potential applications, and proposals for further research directions

Influence of flexoelectric effect on the bending rigidity of a Timoshenko graphene-reinforced nanorod

Abstract The focus of this work is to study the influence of flexoelectric phenomenon on the electromechanical response of graphene-reinforced nanocomposite (GNC) nanorods. An analytical model has been derived by utilizing the Timoshenko beam theory and the principle of variational work by incorporating flexoelectric effects. The GNC nanorod is subjected to a concentrated load acting downward for clamped-free and simply supported support types. The GNC is reinforced with a defective graphene sheet as it is known to show enhanced polarization. The elastic properties of defective graphene sheets have been evaluated using molecular dynamic simulations. The outcome of our model shows that the flexoelectric effect must be considered for accurate modeling of nanostructures. Irrespective of the support type, flexoelectric effect improves the stiffness of the nanorod. We also observed that the stiffness of the nanorod is significantly influenced by the support type. This work presents an opportunity for the development of high-performance graphene-based nanoactuators/sensors.

An analytical model for nanoscale flexoelectric doubly curved shells

The phenomenon of flexoelectricity, wherein the generation of electrical polarization results from strain gradients, has garnered significant attention in electromechanics. This phenomenon holds immense potential for diverse applications in nanoelectromechanical systems. Doubly curved shells present a particularly compelling structure for implementing flexoelectric devices, representing the most general scenario. To comprehensively understand the mechanical behavior of nanoscale flexoelectric doubly curved shells, we present a novel analytical model in this study. Our model incorporates a reformulated strain gradient elasticity theory, a modified expression of electric enthalpy density considering Maxwell’s self-field gradient, and a moderately thick shell configuration. To further elucidate this model, we establish complete formulations and analytical solutions of static bending and free vibration problems. This study reveals the crucial roles that various parameters such as principal curvature radii, length scale parameters, transverse structural sizes, and the Winkler–Pasternak foundation play in controlling the mechanical behavior of nanoscale flexoelectric doubly curved shells. These theoretical findings offer valuable insights into the design of nanodevices based on the direct flexoelectric effect.

Flexo-Pyrophotronic Effect Modulated Giant Near Infrared Photoresponse from VO2 -Based Heterojunction for Optical Communication.

The flexoelectric phenomenon, which occurs when materials undergo mechanical deformation and cause strain gradients and a related spontaneous electric polarization field, can result in wide variety of energy- and cost-saving mechano-opto-electronics, such as night vision, communication, and security. However, accurate sensing of weak intensities under self-powered conditions with stable photocurrent and rapid temporal response remains essential despite the challenges related to having suitable band alignment and high junction quality. Taking use of the flexoelectric phenomena, it is shown that a centrosymmetric VO2 -based heterojunction exhibits a self-powered (i.e., 0V), infrared (λ = 940nm) photoresponse. Specifically, the device shows giant current modulation (103 %), good responsivity of >2.4mA W-1 , reasonable specific detectivity of ≈1010 Jones, and a fast response speed of 0.5ms, even at the nanoscale modulation. Through manipulation of the applied inhomogeneous force, the sensitivity of the infrared response is enhanced (> 640%). Ultrafast night optical communication like Morse code distress (SOS) signal sensing and high-performing obstacle sensors with potential impact alarms are created as proof-of-concept applications. These findings validate the potential of emerging mechanoelectrical coupling for a wide variety of novel applications, including mechanoptical switches, photovoltaics, sensors, and autonomous vehicles, which require tunable optoelectronic performance.

Flexoelectric aging effect in ferroelectric materials

In spite of the flexoelectric effect being a universal phenomenon in the ferroelectric perovskites, the current understanding of flexoelectric aging in ferroelectrics is, actually, rather incomplete. In this paper, we have fabricated a series of Mn-doped BaTiO3 perovskite ceramics (BaTi1–xMnxO3, x = 0.1% and 1%, BTMO) to systematically investigate the corresponding flexoelectric aging behavior by controlling the concentration of Mn. We found that the variation of Mn dopant significantly effects the Curie temperature, dielectric constant, flexoelectric aging, and flexoelectric coefficient of the BTMO ceramics. Especially for the BTMO (0.1%) ceramics, obvious ferroelectric aging and flexoelectric aging phenomenon are observed at room temperature. The main reason for aging of BTMO ceramics is that the doping of Mn introduces oxygen vacancies, which tend to be stable under the action of strain gradient and electric field. Therefore, the results presented in this paper verify that the flexoelectric aging in Mn-doped BTO ceramics is closely related to ferroelectric fatigue.

Intrinsic flexoelectricity of van der Waals epitaxial thin films

The direct measurement of flexoelectric coefficients in epitaxial thin films is an unresolved problem, due to the clamping effect of substrates which induces a net strain (and hence parasitic piezoelectricity) in addition to strain gradients and flexoelectricity. Herein, we propose and demonstrate the use of van der Waals epitaxy as a successful strategy for measuring the intrinsic (clamping-free = flexoelectric coefficients of epitaxial thin films. We have made, measured, and compared ${\mathrm{BaTiO}}_{3}$ and ${\mathrm{SrTiO}}_{3}$ thin film capacitor heterostructures grown both by conventional oxide-on-oxide epitaxy and by van der Waals oxide-on-mica epitaxy, and found that, whereas the former is dominated by parasitic piezoelectricity, the response of the latter is truly flexoelectric. The results are backed by theoretical calculations of the film-substrate mechanical interaction, as well as by direct measurements that confirm the strain-free state of the films. van der Waals epitaxy thus emerges as powerful new tool in the study of flexoelectricity and, in particular, they finally allow exploring flexoelectric phenomena at the nanoscale (where strain gradients are highest) with direct experimental knowledge of the actual flexoelectric coefficients of thin films.

On the flexoelectric effect on size-dependent static and free vibration responses of functionally graded piezo-flexoelectric cylindrical shells

The flexoelectric effect depends on the strain gradient, which naturally appears in intelligent structures at micro and nano scales. Therefore, the flexoelectric phenomenon significantly affects electro-mechanical behavior of structures in these scales. In this study, the first-order shear deformation theory and the reformulated flexoelectric theory are applied to derive coupling equations of motion for a size-dependent static and dynamic responses of multilayered composite shell with simply supported and clamped edges. Constitutive equations are defined based on assumption that the internal energy function depends not only on strains and polarization tensors but also on strains and polarization gradient tensors. The piezo-flexoelectric structure is made of an isotropic functionally graded core and two orthotropic layers. Reynolds transport theorem and variational Hamilton principle are used to derive equations of motion expressed by forces and displacements, and corresponding boundary conditions. In order to check the correctness of the formulation, and solution of the problem obtained by Galerkin method, static and free vibrations analyses of macro-/micro-/nanoshell are investigated. Diagrams of deflection and electrical potential variations of the structure under the load are obtained for the direct flexoelectric effect. Additionally, the influence of various parameters, e.g., geometric properties, size effect, power-law index, and flexoelectric layer thickness, on the deflection, potential function, and natural frequency of the microshell have been investigated. The numerical results and discussion present that above parameters significantly affect a mechanical behavior of the microshell under consideration.

Modeling the flexoelectric effect via the reduced micromorphic model

This paper aims to demonstrate how the flexoelectric effect can be incorporated into the reduced micromorphic model, where materials can be designed and fabricated with complex structures that possess electric properties. These kinds of materials are known as composite metamaterials with properties that do not exist in nature such as the flexoelectric effect phenomena. These phenomena take place when both negative and positive charges move to occupy new positions inside the materials where the new positions of these charges depend on the applied external mechanical or electrical fields. The new arrangements of charges produce a spontaneous polarization inside the material that fades when removing the applied fields. According to the classical theory of elasticity, the spontaneous polarization is mathematically related to a macro-scale measure. In the present work, instead of the macro-scale, we use a micro-scale measure to formulate the polarization phenomena. This formulation is achieved by employing the variation technique for the internal energy functional and the virtual work done by the external fields. The field equations and the concomitant boundary conditions are also obtained. Moreover, the constitutive relations are presented in terms of internal state variables. Finally, an application is made in one-dimension and the results are presented in figures with physical explanation.

Boosting Self‐Powered Ultraviolet Photoresponse of TiO2‐Based Heterostructure by Flexo‐Phototronic Effects

AbstractUltraviolet photodetectors have long been used as key elements for various applications, including optical sensing and communication. However, accurate sensing of weak UV intensities under self‐powered conditions with stable photocurrent and rapid temporal response remains critical because of challenges related to having suitable band alignment and strong junction quality. Here, an enhancement in the self‐power ultraviolet (UV, λ = 365 nm) photoresponse of the silver nanowires/TiO2 Schottky photodetector is demonstrated by taking advantage of the flexoelectric phenomenon. The device does not show measurable photocurrent under self‐biased conditions with low‐intensity (200 µW cm–2) UV illumination, whereas a significant photocurrent of about 0.48 µA is measured by integrating the photovoltaic and flexo‐phototronic effects. Additionally, rise/fall times improved from 300/1068 to 43/165 µs by utilizing the flexo‐phototronic effects, depicting an enhancement of 597%. Further, remarkable responsivity of 124 mA W–1 and high detectivity of 6.5 × 1011 Jones under self‐biased conditions are recorded. Moreover, microscopic evidence of flexoelectric effect modulated photoresponse is provided by photoconductive atomic force microscopy measurements. High efficiency and self‐powered capability demonstrated in this study are likely to inspire the development of next‐generation ultrafast, energy‐efficient, and sophisticated photodetectors for communication, imaging, and sensing networks.

BEM evaluation of surface octahedral strains and internal strain gradients in 3D-printed scaffolds used for bone tissue regeneration

Most of the mechnoregulatory computational models appearing so far in tissue engineering for bone healing predictions, utilize as regulators for cell differentiation mainly the octahedral volume strains and the interstitial fluid velocity calculated at any point of the fractured bone area and controlled by empirical constants concerning these two parameters. Other stimuli like the electrical and chemical signaling of bone constituents are covered by those two regulatory fields. It is apparent that the application of the same mechnoregulatory computational models for bone healing predictions in scaffold-aided regeneration is questionable since the material of a scaffold disturbs the signaling pathways developed in the environment of bone fracture. Thus, the goal of the present work is to evaluate numerically two fields developed in the body of two different compressed scaffolds, which seem to be proper for facilitating cell sensing and improving cell viability and cell seeding efficiency. These two fields concern the surface octahedral strains that the cells attached to the scaffold can experience and the internal strain gradients that create electrical pathways due to flexoelectric phenomenon. Both fields are evaluated with the aid of the Boundary Element Method (BEM), which is ideal for evaluating with high accuracy surface strains and stresses as well as strain gradients appearing throughout the analyzed elastic domain.

Flexoelectricity in soft elastomers and the molecular mechanisms underpinning the design and emergence of giant flexoelectricity

Soft robotics requires materials that are capable of large deformation and amenable to actuation with external stimuli such as electric fields. Energy harvesting, biomedical devices, flexible electronics, and sensors are some other applications enabled by electroactive soft materials. The phenomenon of flexoelectricity is an enticing alternative that refers to the development of electric polarization in dielectrics when subjected to strain gradients. In particular, flexoelectricity offers a direct linear coupling between a highly desirable deformation mode (flexure) and electric stimulus. Unfortunately, barring some exceptions, the flexoelectric effect is quite weak and rather substantial bending curvatures are required for an appreciable electromechanical response. Most experiments in the literature appear to confirm modest flexoelectricity in polymers although perplexingly, a singular work has measured a "giant" effect in elastomers under some specific conditions. Due to the lack of an understanding of the microscopic underpinnings of flexoelectricity in elastomers and a commensurate theory, it is not currently possible to either explain the contradictory experimental results on elastomers or pursue avenues for possible design of large flexoelectricity. In this work, we present a statistical-mechanics theory for the emergent flexoelectricity of elastomers consisting of polar monomers. The theory is shown to be valid in broad generality and leads to key insights regarding both giant flexoelectricity and material design. In particular, the theory shows that, in standard elastomer networks, combining stretching and bending is a mechanism for obtaining giant flexoelectricity, which also explains the aforementioned, surprising experimental discovery.

Flexoelectricity and the entropic force between fluctuating fluid membranes

Biological membranes undergo noticeable thermal fluctuations at physiological temperatures. When two membranes approach each other, they hinder the out-of-plane fluctuations of the other. This hindrance leads to an entropic repulsive force between membranes which, in an interplay with attractive and repulsive forces owing to other sources, affects a range of biological functions: cell adhesion, membrane fusion, self-assembly, binding–unbinding transition among others. In this work, we take cognizance of the fact that biological membranes are not purely mechanical entities and, owing to the phenomenon of flexoelectricity, exhibit a coupling between deformation and electric polarization. The ensuing coupled mechanics–electrostatics–statistical mechanics problem is analytically intractable. We use a variational perturbation method to analyze, in closed form, the contribution of flexoelectricity to the entropic force between two fluctuating membranes and discuss its possible physical implications. We find that flexoelectricity leads to a correction that switches from an enhanced attraction at close membrane separations and an enhanced repulsion when the membranes are further apart.

Porosity distribution effect on stress, electric field and nonlinear vibration of functionally graded nanostructures with direct and inverse flexoelectric phenomenon

In the present paper, the effect of the diverse distribution of porosity on the static and nonlinear dynamic responses of a sandwich functionally graded nanostructure with thermo-electro-elastic coupling is presented based on the modified flexoelectric theory. The rectangular nanoplate satisfying the classical Kirchhoff’s assumptions is taken into consideration as example of a nanostructure. It is assumed that sandwich functionally graded porous nanoplate is embedded on an elastic foundation and subjected to a thermo-electro-mechanical load. The Winkler-Pasternak model was considered to present the effect of elastic foundation. Components of the Green-Lagrange strain tensor are taken as linear and infinitesimal. The appeared source of nonlinearity in nanostructure is caused by using the properties of the flexoelectric effect. Therefore, change a volume element due to the elastic deformation cannot be negligible. The constitutive relations for functionally graded porous material are expressed by a power-law variation of material parameters in conjunction with cosine functions to create a possibility to investigate the effect of distribution of diverse types of porosity on mechanics of structures. The equilibrium and governing equations of the sandwich nanoplate resting on the Winkler-Pasternak foundation are derived based on Hamilton’s principle. The obtained differential equations for the static and dynamic problems of nanoplate were solved by Galerkin’s and multiple scale methods. The influence of some important material and geometrical parameters as well as diverse boundary conditions on mechanical responses of the nanostructure were comprehensively investigated and discussed.

On wave dispersion characteristics of fluid-conveying smart nanotubes considering surface elasticity and flexoelectricity approach

Wave dispersion response of a fluid-carrying piezoelectric nanotube is studied in this paper utilizing an improved model for piezoelectric materials which capture a new effect known as flexoelectricity in conjunction with the surface elasticity. For this aim, a higher order shear deformation theory is employed to model the problem. Furthermore, strain gradient effect as well as nonlocal effect is taken into consideration throughout using the nonlocal strain gradient theory (NSGT). Surface elasticity is also considered to make an accurate size-dependent formulation. Additionally, a non-compressible and non-viscous fluid is taken into consideration to model the flow effect. The wave propagation solution is then implemented to the governing equations obtained by Hamiltonian’s approach. The phase velocity and group velocity of the nanotube is determined for three wave modes (i.e. shear, longitudinal and bending waves) to study the influence of various involved factors including strain gradient, nonlocality, flexoelectricity and surface elasticity and flow velocity on the wave dispersion curves. Results reveal a considerable effect of the flexoelectric phenomenon on the wave propagation properties especially at a specific domain of the wave number. The size-dependency of this effect is disclosed. Overall, it is found that the flexoelectricity exhibits a substantial influence on wave dispersion properties of the smart fluid-conveying systems. Hence, such size-dependent effect should be considered to achieve exact and accurate knowledge on wave propagation characteristics of the system.

Apparent Flexoelectricity Due to Heterogeneous Piezoelectricity

Abstract Recent work has highlighted how the phenomenon of flexoelectricity can masquerade as piezoelectricity. This notion can not only be exploited to create artificial piezoelectric-like materials without using piezoelectric materials but may also explain measurement artifacts in dielectrics. In this article, we show that the reverse is also possible and potentially advantageous in certain situations (such as energy harvesting). By constructing a computational homogenization approach predicated on the finite element method, we argue that composites made of piezoelectric phases can conspire to endow the material with a distinct overall flexoelectric-like response even though the native flexoelectricity of the constituent materials is negligible. Full finite element procedures for numerical evaluation of the different effective tensors, including the flexoelectric tensor, are provided. Numerical investigations are conducted, showing variation of the effective flexoelectric properties with respect to local geometry and properties of the composite in piezoelectric–piezoelectric and polymer–piezoelectric composites. We find that the flexoelectric response can be tuned to nearly five times higher than the constituents.

Size dependent electro-elastic enhancement in geometrically anisotropic lead-free piezocomposites

Improving the performance of lead-free piezocomposites to the levels of state-of-the-art lead-based composites has been an important challenge in composite research. Consequently, an important agenda of piezocomposite research has been to identify new coupled mechanisms that can enhance the piezoelectric response. One such method is to tap into the size-dependent flexoelectric phenomenon in geometrically anisotropic structures. Numerical models which can account for flexoelectricity and nonlinear effects such as electrostriction are not well-developed for piezocomposite design, and current designs are based on linear piezoelectric models. Here, we develop an advanced model with flexoelectric and electrostrictive contributions in geometrically tailored piezocomposites to obtain insights on aspects of enhanced response due to small-size effects. Here, based on design considerations, we numerically demonstrate that in epoxy-matrix-based piezocomposites which are structured as truncated pyramids, flexoelectricity can lead to significant enhancements in both the electric field and the electric flux generation at small length scales. Particularly, we show that at dilute inclusion concentrations, dramatic improvements nearing 150% in the piezoelectric response are possible. Further, the flexoelectric enhancement is sensitive to the packing of the inclusions within the composite structure with the best enhancements occurring when the inclusions are closer to the inclined edges of the pyramids. We also show that in composite structures with CNT-modified matrices, flexoelectricity produces similar enhancements as in the case of unmodified matrices, demonstrating that the effect operates almost independent of nanoscale elastic and dielectric modifications by the nanotubes. Finally, we also establish that for a large range of applied stresses, the nonlinear deviations in the response due to electrostriction are negligible and flexoelectricity is the predominant size-dependent enhancement mechanism in structured lead-free piezocomposites.

Flexoelectric effects on wave propagation responses of piezoelectric nanobeams via nonlocal strain gradient higher order beam model

This paper is devoted to investigate the effects of the flexoelectric phenomenon on wave dispersion characteristics of piezoelectric nanobeams. Modified constitutive relations containing the flexoelectric effects are taken into account. The problem is formulated utilizing Reddy’s higher order shear deformation beam theory in conjunction with the nonlocal strain gradient theory (NSGT). Additionally, Hamilton’s principle is employed to derive the governing equations of the problem. Thereafter, considering harmonic wave dispersion, the solution of equations of motion is expressed as complex form. Applying this solution to the governing equations gives rise to the eigenvalue problem. Afterwards, the eigenvalue problem is solved analytically to achieve the wave frequencies and phase velocities of the system. Totally, the role of various involved parameters namely the flexoelectric effects and applied electric voltage on the wave dispersion curves is studied in detail. In addition, the size-dependency of the flexoelectric phenomenon on wave dispersion behavior of the nanobeam is explored. Due to the fact that adequate knowledge about wave dispersion characteristics of structures is of great value especially in nanotechnology field, it is hoped that the results presented here may be helpful for exact behavior determination of piezoelectric nano-structures.