Electric Displacement Research Articles

Axisymmetric contact problem of piezoelectric coating-substrate system with functionally graded piezoelectric interfacial layer

In this paper, the electromechanical response of piezoelectric coating-functionally graded piezoelectric (FGP) interfacial layer–piezoelectric substrate system under the rigid spherical punch is considered. It is assumed that the piezoelectric coating and piezoelectric substrate are connected by the FGP interfacial layer which is simulated by a multi-layer model. The axisymmetric frictionless contact problem of piezoelectric coating–substrate system with FGP interfacial layer is formulated in terms of singular integral equation with the method of transfer matrix and Hankel integral transform technique. The effect of the gradient of material properties on the stress components and electric displacement components in piezoelectric coating–substrate system is gained by solving the equation numerically. The present results could serve as a useful reference for the design of piezoelectric coating–substrate system.

Students’ conceptual understanding of electric flux and magnetic circulation

Electricity and magnetism are closely related phenomena with a well-known symmetry found in Maxwell equations. An essential part of any electricity and magnetism course includes the analysis of different field source distributions through Gauss’s and Ampere’s laws to compute and interpret different physical quantities, such as electric flux, electric and magnetic field, or magnetic circulation. Still, some students have difficulties with these calculations or, in some cases, identifying the differences between those quantities. We present this article to explore and compare the challenges that students experience when asked to compute the electric flux (surface integral of the electric field) or the magnetic circulation (line integral of the magnetic field) in a nonsymmetric field-source distribution with two opposite field sources inside a Gaussian spherical surface or Amperian circular trajectory. The sample consisted of 322 engineering students finishing an electricity and magnetism course. They were presented with two parallel problems. Half answered one in the electricity context and the other in the magnetism context. After a phenomenographic analysis, our results showed that the students’ conceptual difficulties in both contexts can be grouped into the same categories but are not contextually parallel, as has happened when analyzing other electricity and magnetism concepts. Our results also suggest that the magnetic circulation concept is far more unfamiliar to students than the electric flux. We propose several factors that could explain this finding and suggest teaching to address the conceptual difficulties identified in our analysis.Received 6 December 2022Accepted 27 March 2023DOI:https://doi.org/10.1103/PhysRevPhysEducRes.19.013102Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasConcepts & principlesScientific reasoning & problem solvingPhysics Education Research

Saint-venant Torsion of Functional Graded Orthotropic Piezoelectric Hollow Circular Cylinder

This paper gives an analytical solution to the Saint-Venant torsion of the hollow and solid circular cylinder made of orthotropic functionally graded piezoelectric material. The elastic flexibility coefficients and piezoelectric constants and permittivities have only radial dependence. The considered material non-homogeneity is described by power function. The solution of the Saint-Venant torsion problem is presented for Prandtl’s stress function, shearing stresses, electric displacement potential function, torsion function and electric potential function. An example illustrates the application of the formulated analytical method.

Quasi-electrostatic three-dimensional charge model for contact-separation triboelectric nanogenerator

Triboelectric nanogenerators (TENGs) are at the forefront of energy harvesting and self-powered sensors, while further improvements in TENGs’ development and utilization essentially depend on the theoretical models. To understand the intrinsic mechanism of TENGs, a formal physical framework of TENGs was introduced based on Maxwell’s equations. Triboelectric charges would be produced on the dielectric layer surface after contact triboelectrification. As concerned about any transient, the electric field originating from the arbitrary fixed position over the finite charged plane would not change, constituting the electrostatic field. Since TENGs maintain low-frequency movement, they enter a quasi-electrostatic state. Under this state, the electric field would change along with the distance from the charged plane. Herein, a quasi-electrostatic three-dimensional (QETD) charge model was constructed to refine the theoretical modeling of TENGs. Finite element modeling (FEM) simulations were first provided to reveal the distribution of polarization vector (Pz), electric potential (φ), electric field (Ez) and electric displacement (Dz). Furthermore, an optimized theoretical framework for contact-separation TENGs was established, and it was validated by different driving and structural variables. Besides, the intrinsic displacement current of TENGs was linked with the conduction current to deduce the output capability. Compared with previous works, this QETD model shows the most consistent trend with experimental results, providing accurate predicts for distinct TENGs’ performance.

Artificial neural network (ANN) based investigation on the static behaviour of piezo-magneto-thermo-elastic nanocomposite sandwich plate with CNT agglomeration and porosity

In this article, a novel finite element method (FEM) – artificial neural network (ANN) approach is adopted to investigate the coupled static parameters (stresses and potentials) of a smart sandwich plate with agglomerated Carbon Nanotubes (CNTs) porous nanocomposite core and piezo-magneto-thermo-electric (PMTE) facings. The main focus of this work is to study the synergistic effects of agglomeration of CNTs, porosity and pyro-coupling of the PMTE materials. Nearly 5184 data points collected from the in-house developed house finite element (FE) computational tool are used to train the ANN model using Levenberg–Marquardt algorithm. The FE formulation is derived using the principle of virtual work in association with higher-order shear deformation theory (HSDT) and von-Karman’s nonlinearity. The externally applied thermal loads are assumed to vary uniformly and linearly across the thickness of the plate. Two states of agglomeration, such as partial and complete; three forms of porosity, such as uniformly distributed, and two variants of functionally graded porosity, have been considered for investigation. Numerical examples are solved to understand the interrelated effects of these material properties on the direct (potentials) and derived (stresses, electric displacement, and magnetic flux densities) static parameters.

Analytical assessment of modulated electric flux triggered degradation of chlorfenapyr and deltamethrin pesticides in guava fruits

The purpose of this study was to explore the new effective method and investigate the dissipation of chlorfenapyr and deltamethrin (DM) pesticides used in the treatment of guava fruit from tropical and sub-tropical areas of Pakistan. Five different solutions of varying concentrations of pesticides were prepared. This study involved the in-vitro and in-vivo analysis of modulated electric flux-triggered degradation as an efficient method for the safer degradation of selected pesticides. The Taser gun was used as a tool for providing different numbers of electrical shocks of million voltages to the pesticides present in guava fruit at different temperatures. The degraded pesticides were extracted and analyzed by High-performance liquid chromatography (HPLC). The HPLC chromatograms verified that significant dissipation of pesticides took place when these were exposed to 9 shocks at 37 °C, which proved the efficiency of this degradation method. More than 50% of the total spray of both pesticides was dissipated. Thus, modulated electrical flux-triggered degradation is one of the effective methods for pesticide degradation.

On Nanobubble Dynamics under an Oscillating Pressure Field during Salting-out Effects and Its DLVO Potential

We have investigated the origin, stability, and nanobubble dynamics under an oscillating pressure field followed by the salting-out effects. The higher solubility ratio (salting-out parameter) of the dissolved gases and pure solvent nucleates nanobubbles during the salting-out effect, and the oscillating pressure field enhances the nanobubble density further as solubility varies linearly with gas pressure by Henry's law. A novel method for refractive index estimation is developed to differentiate nanobubbles and nanoparticles based on the scattering intensity of light. The electromagnetic wave equations have been numerically solved and compared with the Mie scattering theory. The scattering cross-section of the nanobubbles was estimated to be smaller than the nanoparticles. The DLVO potentials of the nanobubbles predict the stable colloidal system. The zeta potential of nanobubbles varied by generating nanobubbles in different salt solutions, and it is characterized by particle tracking, dynamic light scattering, and cryo-TEM. The size of nanobubbles in salt solutions was reported to be higher than that in pure water. The novel mechanical stability model is proposed by considering both ionic cloud and electrostatic pressure at the charged interface. The ionic cloud pressure is derived by electric flux balance, and it is found to be twice the electrostatic pressure. The mechanical stability model for a single nanobubble predicts the existence of stable nanobubbles in the stability map.

Electro-thermo-mechanical instability study of fiber-reinforced bimorph convex dielectric elastomer

ABSTRACT Intelligent electroactive polymer-based dielectric elastomer actuators (DEAs) are capable of geometrical disorientation. These actuators are susceptible to electro-thermo-mechanical instability due to their ability to be electrically powered at various stresses and temperatures. This proposed work provides mathematical derivations for the study of instability in coupled electro-thermo-mechanical anisotropic bimorph convex DEAs. The equilibrium equations are formulated assuming the taper ratio because of the convex structure and the ply angles due to anisotropy. MATLAB is employed to numerically solve the complicated equations for critical stretch, nominal electric field, and entropy under a variety of mechanical, electrical, and thermal loads. The observations indicate that under conditions of , and , an increase in nominal stress from to leads to a corresponding increase in the peak point of the nominal electric field, specifically from to for axial stretch values of 2.107 and 2.159, respectively. When the nominal electric field is reported against nominal electric displacement, it enhances with the rise in temperature and reduces with the hike in nominal stress and taper ratio. When the fibers are arranged parallel to the axial stretch direction then the failure point of stretch is least, compared to that oriented in a perpendicular direction. The present study demonstrates that elevated temperature and nominal stress result in an increase in entropy, leading to a corresponding increase in system disorder. Furthermore, the perpendicular alignment of fibers with respect to axial stretch is found to decrease the degree of system randomness.

Coupled Solution of Volume Integral and Hydrodynamic Equations to Analyze Electromagnetic Scattering From Composite Nanostructures

A coupled system of volume integral and hydrodynamic equations is solved to analyze electromagnetic scattering from nanostructures consisting of metallic and dielectric parts. In the metallic part, the hydrodynamic equation relates the free electron polarization current to the electric flux and effectively “updates” the constitutive relationship to enable the modeling of nonlocality. In the metallic and dielectric parts, the volume integral equation relates the electric flux and the free electron polarization current to the scattered electric field. Unknown electric flux and free electron polarization current are expanded using Schaubert–Wilton–Glisson (SWG) basis functions. Inserting these expansions into the coupled system of the volume integral and hydrodynamic equations and using Galerkin testing yield a matrix system in unknown expansion coefficients. An efficient two-level iterative solver is proposed to solve this matrix system. This approach “inverts” the discretized hydrodynamic equation for the coefficients of the free electron polarization current and substitutes the result in the discretized volume integral equation. Outer iterations solve this reduced matrix system while the inner iterations invert the discretized hydrodynamic equation at every iteration of the outer iterations. Numerical experiments are carried out to demonstrate the accuracy, the efficiency, and the applicability of the proposed method.

Effects of Schottky junction on surface waves in a piezoelectric semiconducting film over a metal substrate

Shear horizontal (SH) waves propagating in a metal substrate covered with a transversely isotropic piezoelectric semiconductor thin film is analyzed in the present paper. The Schottky junction, which is created by the metal and the n-type piezoelectric semiconductor with a higher Fermi level, can be seen as an electrically gradient layer between the substrate and the thin film. The transfer matrix of the Schottky junction is derived by using Magnus series expansion and approximate laminated medium methods, respectively. The influences of the Schottky junction, semiconductor coupling, doping density, and electric boundary conditions on the dispersion and attenuation and the first three wave modes are discussed via numerical example. It reveals that numerical results obtained by these two methods are well matched and the existence of Schottky junction has less influence on the dispersion of SH surface wave although, but evidently influences on the attenuation. In particular, the mode shapes of electric potential, electric displacement, carrier perturbation density, and the electric current density are affected evidently by the existence of Schottky junction.

Construction of 2-2 Type Cement-Based Piezoelectric Composites’ Mechanic–Electric Relationship Based on Strain Rate Dependence

It has been found that the mechanic-electric response of cement-based piezoelectric composites under impact loading is nonlinear. Herein, we prepared a 2-2 cement-based piezoelectric composite material using cutting, pouring, and re-cutting. Then, we obtained the stress-strain and stress-electric displacement curves for this piezoelectric composite under impact loading using a modified split Hopkinson pressure bar (SHPB) experimental apparatus and an additional electrical output measurement system. Based on the micromechanics of the composite materials, we assumed that damage occurred only in the cement paste. The mechanical response relationship of the piezoelectric composite was calculated as the product of the viscoelastic constitutive relationship of the cement paste and a constant, where the constant was determined based on the reinforcement properties of the mechanical response of the piezoelectric composite. Using a modified nonlinear viscoelastic Zhu-Wang-Tang (ZWT) model, we characterized the stress-strain curves of the piezoelectric composite with different strain rates. The dynamic sensitivity and stress threshold of the linear response of the samples were calibrated and fitted. Thus, a mechanic-electric response equation was established for the 2-2 type cement-based piezoelectric composite considering the strain rate effects.

Fracture analysis of a curved crack in a piezoelectric plane under general thermal loading

The mixed-mode problem of a cracked piezoelectric plane subjected to a general in-plane thermal load is considered. The crack is modeled as distributed thermo-mechanical dislocations with unknown density which are determined by using the Fourier transform method. Furthermore, stress, electric displacement, and heat flux in the intact plane, under thermal load are obtained. These solutions are used to construct singular integral equations in the piezoelectric plane with an arc-shaped crack under thermo-mechanical loading. The integral equations are solved numerically to obtain dislocation density functions on a crack surface. These functions are used to determine field intensity factors for the crack. Finally, the effect of the crack length, the radius of the crack, and distance from the temperature disturbance is investigated under different loading conditions.

A Maxwell–Ampère Nernst–Planck Framework for Modeling Charge Dynamics

Understanding the properties of charge dynamics is crucial to many practical applications, such as electrochemical energy devices and transmembrane ion channels. This work proposes a Maxwell–Ampère Nernst–Planck (MANP) framework for the description of charge dynamics. The MANP model with a curl-free condition on the electric displacement is shown to be energy dissipative with respect to a convex free-energy functional, and demonstrated to be equivalent to the Poisson–Nernst–Planck model. By the energy dissipation law, the steady state of the MANP model reproduces the charge conserving Poisson–Boltzmann (PB) theory, providing an alternative energy stable approach to study the PB theory. In order to achieve the curl-free condition, a companion local curl-free relaxation algorithm, which is shown to naturally preserve the discrete Gauss’s law and converge robustly with linear computational complexity, is developed for the MANP model. One of the main advantages of our development is that it can efficiently deal with space-dependent permittivity instead of solving the variable-coefficient Poisson’s equation. Many-body effects such as ionic steric effects and Coulomb correlations can be incorporated within the MANP framework to derive modified MANP models for problems in which the mean-field approximation fails. Numerical results on the charge dynamics with such beyond mean-field effects in inhomogeneous dielectric environments are presented to demonstrate the performance of the MANP models in the description of charge dynamics, illustrating that the proposed MANP model provides a general framework for modeling charge dynamics.

Effect of Inorganic Nanoparticles on Energy‐Storage Properties of P(VDF–HFP)‐Based Nanocomposites

Polyvinylidene fluoride (PVDF) and its copolymers have been widely used in polymer‐based film capacitors due to their relatively high permittivity and electrical displacement compared with other polymers. Herein, poly(vinylidene fluoride‐hexafluoropropylene) (P(VDF–HFP)) is selected as the polymer matrix, and 0.5 (Bi0.5Na0.5)TiO3–0.5(Sr0.85Sm0.1)TiO3 (BNT–SST) nanoparticles are added as the filler into the polymer to prepare BNT–SST/P(VDF–HFP) nanocomposites. The microstructure, electrical properties, mechanical properties, and energy‐storage properties of the nanocomposites are investigated. The addition of BNT–SST nanoparticles improves the dielectric characteristics and breakdown strength of the nanocomposites. Particularly, when the BNT–SST filler content is 0.7 vol%, the highest breakdown strength reaches 545 MV m−1, which is 1.3 times higher than pure P(VDF–HFP). In addition, the insulation and mechanical properties of BNT–SST/P(VDF–HFP) composite films are improved. The highest direct current resistivity and Young's modulus obtained by 0.7 vol% BNT–SST/P(VDF–HFP) nanocomposites are 6.8 × 1013 Ω cm and 1.94 GPa, respectively. More importantly, at 545 MV m−1, the energy‐storage density and efficiency of 0.7 vol% BNT–SST/P(VDF–HFP) composites are 19.07 J cm−2 and 67.01%, respectively, which are better than other polymer matrix composites. These findings suggest that the addition of inorganic nanoparticles has important research implications for improving the energy‐storage performance of polymer‐based film capacitors.

Couple stress-based flexoelectricity of frictionless contact in dielectrics

The presence of flexoelectricity in dielectric materials can affect the mechanics of contact between solid bodies, especially when viewed at the micro/nano-scale. Such an effect can also contribute significantly to contact electrification ─ a charge transfer event that takes place at the contact interface. In particular, the state of deformation and stresses in the vicinity of the contacting area can differ markedly from that anticipated from classical elastic Hertzian contact theory. In the present work, we investigate the flexoelectric effect near the contacting area of an isotropic dielectric material pressed by a frictionless rigid insulator probe, serving as a model problem to reveal the potential role of flexoelectricity in contact mechanics and electrification. The investigation is based on consistent couple stress flexoelectric theory, in which electric polarization may appear due to two-way coupling between the electric field and mean curvature vectors, even for centrosymmetric dielectric materials. To this end, we develop a new boundary element formulation to calculate the displacement, stress, electric potential, and electric displacement for two-dimensional isotropic flexoelectric contact problems. The subsequent computational mechanics investigation highlights several important characteristics of triboelectric phenomena and shows that the state of stress and polarization in contacting isotropic dielectrics is dependent on the effective length scale parameter l of couple stress elasticity and the coupling flexoelectric coefficient f.

Large interfacial polarization in metal–organic framework hollow ZIF-8/polyimide low-k nanocomposite films

Polymer films with tailored dielectric properties and large electrical displacement are required for applications in microelectronics due to the need for ultrahigh speed and low transmission delays. In this study, we developed a low-k polyimide (PI) nanocomposite incorporated with metal–organic framework hollow ZIF-8 (HZIF-8) nanocrystals to achieve a high energy storage capacity. The PI nanocomposite film was prepared by solution casting a mixture of HZIF-8/polyamide acid with thermal imidization. A dielectric constant of 2.26 was obtained at 100 Hz for the 5 wt% nanocomposite with a multi-stage pore architecture. Due to improved interfacial polarization, the 1 wt% nanocomposite had a high energy density of 12.2 J/cm3 and a charge–discharge efficiency of 70% at 600 MV/m. The PI nanocomposite film exhibited dielectric reliability with inherent flexible performance, and it is expected to be a primary candidate for polymer dielectric applications in microelectronics.

Highly enhanced energy storage performance of trilayered gradient polymer-based nanocomposite via 2D SNO@Ag nanosheets

Simultaneous enhancement in dielectric constant and electric breakdown strength is the desired way for polymer-based dielectric materials to achieve a high discharge energy density. Herein, an artificial gradient trilayered polymer nanocomposite with remarkable energy storage performance is proposed. Two-dimensional Sr2Nb2O7 nanosheets (SNO NSs) functionalized with polydopamine and Ag-quantum-dots (D-SNO@Ag NSs) are introduced into a poly(vinylidene fluoride)/polymethyl methacrylate (PVDF/PMMA) blend polymer matrix (BPM). Attributed to the incorporation of Ag-quantum-dots (Ag QDs) on the surface of SNO NSs, the local capacitance around SNO NSs is improved and the electron migration near the Ag QDs is inhibited. As a result, a large Weibull breakdown strength (585.13 MV m−1) and an enhanced dielectric constant (13.98) was obtained to achieve a high difference between electric displacement and remnant electric displacement (12.98 μC cm−2 at 580 MV m−1) from the gradient trilayered nanocomposite, which contributes a remarkable discharge energy density of 31.0 J cm−3 with a charge–discharge efficiency of 66%.

Non-polynomial hybrid models for the bending of magneto-electro-elastic shells

This paper presents different non-polynomial hybrid models in the framework of Carrera’s Unified Formulation for the bending of a magneto-electric shell with variable radii of curvature. The shell’s middle surface is graphed by a parametric surface. Differential Geometry is employed for evaluating the Lamé Parameters and Radius of Curvature. The mechanical displacements are modeled in the context of an equivalent single layer by sinusoidal, hyperbolic, and tangential models. The electrical and magnetic scalar potential functions are written by a polynomial thickness function in the framework of Layerwise theory. The shell panels are subjected to mechanical, electrical, and magnetic loads. The governing equations are obtained by the Principle of Virtual Displacement. The correspondent partial differential equations are discretized by Chebyshev-Gauss-Lobatto grid distribution and solved by the so-called Differential Quadrature Method. The classical Lagrange polynomial is employed as the basis function for the method. The stresses, electrical displacement, and magnetic induction are recovered by the three-dimensional (3D) equilibrium equations. A comparative analysis with 3D solutions provided in the literature is performed for a square plate and a doubly curved shallow shell panel and remarkable results are obtained. So, the validated models are further used to study shells with variable radii of curvature; specifically, for helicoid, ellipsoid, and catenoid panels.

Achieving high comprehensive energy storage properties of BNT-based ceramics via multiscale regulation

It is difficult to obtain high polarization strength and high breakdown strength synchronously, resulting in the drawback of lower energy storage density, which inhibits commercial application of energy storage materials. We have successfully prepared (1-x)(0.93Bi0.5Na0.5TiO3-0.07CaSnO3)-xSrTiO3 (BNT–CS–xST) ceramics by solid-state method. The presence of polymorphic nanodomains and the large electric displacement generated by the high charge Sr2+-Sr2+ ion pairs help to delay saturation polarization (Pm ∼ 48.64 μC/cm2 at 315 kV/cm). In addition, the breakdown field strength (Eb) is increased by grain refinement and increasing the band gap. It is noteworthy that a high recoverable energy storage density (Wrec = 4.2 J/cm3) and a great efficiency (η = 88%) were achieved simultaneously in BNT–CS–0.5ST ceramic. Moreover, excellent charge-discharge performance was also achieved, with a discharge energy density Wd of 2.2 J/cm3, a current density CD of 1724 A/cm2 and a power density PD of 250 MW/cm3. The study demonstrates that the great potential of BNT–CS–xST ceramics in power storage devices and provides an effective strategy for designing ceramics dielectric capacitors with excellent performance.

Enhanced energy density at low operating field strength of laminated multicomponent polymer-based composites via regulation of electrical displacement

Dielectric polymer-based composites have demonstrated enormous promise in the applications of electrostatic film capacitors due to their exceptional insulating characteristics. However, the achievement of great energy-storage density (U e) is always difficult in linear dielectric polymer-based composites for operation at weak field strength due to the low permittivity (ϵ r) and electric displacement difference (D max − D rem) values. Here, a tri-layered configuration of multicomponent polymeric films is proposed. The outer layers of the tri-layered composite are linear dielectric polymethyl methacrylate (PMMA), and the inner layer is a nonlinear polymer incorporating a low number of polydopamine-modified barium titanate particles (BT@PDA). An increased ϵ r of 8.9@1 kHz is achieved in the designed composite featuring only 2 wt% BT@PDA fillers, equivalent to 234% of the PMMA (∼3.8@1 kHz) matrix. An improved U e of 9.3 J cm−3 at 340 MV m−1 is endowed in the designed film, implying an enormous ∼343% increment of the energy storage compared to the benchmark biaxially oriented polypropylene (∼2.1 J cm−3 at 300 MV m−1). All these advantages present a practical strategy for supplying linear dielectric polymer-based composites with anticipative capacitive energy-storage properties for operation at weak field strengths.