Electric Field Gradient Effects Research Articles

The deflection platform phenomenon of functionally graded flexoelectric simply supported nanobeam

Direct flexoelectricity appears in dielectrics as a kind of coupling effect of electric field and elastic strain gradient. Its strong size dependence makes it effective in nanostructures. In this paper, based on the flexoelectric theory and mixed finite element method (FEM), the mechanical properties of the two-dimensional functionally graded (FG) flexoelectric nanobeam are studied, and the phenomenon of the deflection platform is found. By applying various types of loads to FG nanobeams, the influence of geometric parameters, length scale, and material distribution on the phenomenon of the deflection platform is discussed. According to the simulation results, it is found that the aspect ratio and the length scale of the beam will change the shape of the deflection platform, making it change regularly among various shapes. The geometric size will greatly increase the height of the platform, but it has little effect on the dimensionless deflection. Reasonable material distribution can enhance the internal coupling effect, increase the height of the platform and reduce the required load. Our results suggest that when studying nano-scale flexoelectric models, the deflection platforms or similar phenomena should be considered.

Electric field, strain and inertia gradient effects on anti-plane wave propagation in piezoelectric materials

In this study, we derive the dispersion relations for anti-plane waves in the second gradient electroelasticity theory considering the electric field, strain, and inertia gradient effects. Solutions are developed for bulk and surface shear horizontal (SH) waves including Bleustein–Gulyaev and Love waves. It is demonstrated that the presented model describes a normal dispersion of short waves in piezoelectric materials. The influence of additional model parameters (material characteristic length scales) on the phase velocity, coupled electromechanical factor, and attenuation of the SH waves is investigated. The non-classical upper bound for the Love wave velocity in the elastic layer/piezoelectric substrate system is given accounting for spatial dispersion. In the numerical examples, we use typical values of the length scale parameters of the order of the crystal lattice parameters such that all non-classical gradient effects are predicted for the electroelastic waves of the terahertz frequencies.

Refined Analysis of Piezoelectric Microcantilevers in Gradient Electroelasticity Theory

In this paper we present analytical solutions for the cantilever beam bending problems obtained in the non-classical electroelasticity theory with strain and electric field gradient effects. We show that considered model allows to provide the refined analysis for the electric field distribution around the supproted end of the cantilever taking into account the extended number of boundary conditions, which cannot be captured in classical models.

Space charge dynamics in double-layered insulation cable under polarity reversal voltage

To investigate space charge behavior in double-layered cable insulation, a one-dimensional axisymmetric model for bipolar charge transport is built in this work. Effects of temperature gradient and electric field gradient in the radial direction are considered. The transient distribution of space charge and electric field under polarity reversal voltage is simulated with the developed model, and then the influence of interface position is analyzed to guide the design of double-layered insulation. The results indicate that space charge and electric field distributions are affected by temperature gradient and voltage polarity. Under polarity reversal voltage, the electric field is intensified by the residual space charge generated before polarity reversal, which causes the severe electric field distortion. In addition, the comprehensive electric field distortion factor is the least when the interface is located at the middle of the insulation layer, which is more beneficial to the stable operation of cable.

Aqueous electrolytes’ transport through nanopores of polymeric membrane

Ion permeation and the selectivity of sodium and potassium ions through the nanopores of polyethylene terephthalate (PET) have been investigated at room temperature using the conductometric technique. The nanopores in PET with the high aspect ratio have been created using the ion track technology. The passive (due to the concentration gradient) and active transport (due to the applied potential) of aqueous electrolytes (i.e.; NaClO4 and KClO4 and their different combinations) has been studied. Along with the effect of concentration and electric field gradient, the effect of anion accumulation outside the nanopores on the transport of electrolytes has also been analysed using time series and current–voltage measurements. The transportation and selection of ions also depends on the hydration energy of the ions. A detailed study of transport of ions through the nanopores explains their I–V and I–t behaviour due to the inter- and intra- molecular interaction and their effective interaction with the walls of the nanopores.

Verification of the effect of electric field strength and gradient on the elongation of DNA molecules using the confinement effect

Verification of the effect of electric field strength and gradient on the elongation of DNA molecules using the confinement effect

Anti-plane fracture mechanics analysis of a piezoelectric material layer with strain and electric field gradient effects

The problem of an anti-plane crack in a polarized ceramic layer with both the strain and electric field gradient effects is studied. This model includes two characteristic length parameters l and m which describes the strain gradient and the electric field gradient effects, respectively. The analysis demonstrates that the near-tip asymptotic stress and electric displacement are governed by r−3/2 singularities. Due to stain gradient effect, stresses ahead of the crack tip are significantly higher than those in the classical linear piezoelectricity fracture mechanics. When the strain and electric field gradient parameters decrease to sufficiently small, the solutions reduce to the conventional linear elastic fracture mechanics results. The new contribution of this research is that it includes the effects of the strain gradient and electric field gradient simultaneously for a finite crack in a finite piezoelectric layer.

Pure bending of a piezoelectric layer in second gradient electroelasticity theory

The semi-inverse analytical solution of a pure bending problem for a piezoelectric layer is developed in the framework of linear electroelasticity theory with strain gradient and electric field gradient effects. The simplified gradient theory of transversely isotropic material with a single additional length scale parameter is considered. A two-dimensional solution is derived assuming plane strain state of a layer (cylindrical bending of a plate) and low dielectric properties of the surrounding medium. The electromechanical response of a layer is found under conditions of prescribed bending moments at the end faces. Boundary conditions on the top and bottom surfaces of a layer are satisfied exactly. The analytical solution is validated based on numerical finite element modeling. It is shown that the obtained solutions can be used for the validation of size-dependent beam and plate models in the second gradient electroelasticity theory.

Effect of XLPE/EPDM Interface on Space Charge Behavior in Cable Accessory

Space charges accumulate easily at insulation interface of cable accessories, which cause different electric field distribution and aging characteristics compared to single-layered cable. To explore the space charge behavior in double-layered insulation of cable accessories, a one-dimensional (1D) axisymmetric model for bipolar charge transport is built in this work, in which the effects of temperature gradient and electric field gradient in the radial direction are considered. Then the influences of electric field/temperature gradient and interface position on transport behavior of space charges are investigated. The simulation results suggest that the charges accumulate easily at the interface, which severely reduce the electric field in the inner layer of insulation and further inhibit the injection and migration processes of charges. The charge density at the interface increases with temperature and voltage, which accelerates the decay of the charge injection, furthers the interface charges to reach the dynamic equilibrium state quickly. The charge density at the interface and the electric field distribution are closely related to the interface position, and the electric field is more uniform when XLPE occupies the 1/3 to 1/2 inner part of the whole insulation.

Gradient effects in a new class of electro-elastic bodies

Continuum theories for electro-elastic solids suggest the development of electric field or polarization-based models. Advanced versions of these models are the so-called gradient models, i.e., polarization gradient and electric field gradient models, which prove to be more than capable of explaining the behavior of a continuum in a wider range of length scales. In this work, implicit constitutive relations for electro-elastic bodies are considered with the introduction of polarization and electric field gradient effects. In this sense, the new class of electro-elastic bodies extends even further to account for nonlocality in constitutive equations, besides strain-limiting behavior and polarization saturation for large values of stresses and electric field, respectively. Nonlocality in constitutive equations is essential in modeling various phenomena.

Effects of electric field and strain gradients on cracks in piezoelectric solids

Abstract: The paper presents a general approach to analyze 2-D crack problems where the electric field and displacement gradients exhibit a size effect. The finite element method (FEM) is developed to analyze the general 2D boundary value problems in size-dependent piezoelectric solids with cracks if the electric field gradients are considered in the constitutive equations for the electric displacements. The size-effect phenomenon in micro/nano electronic structures is described by the strain- and electric field-gradient effects. The electric field-strain gradient coupling is considered in the constitutive equations of the material and the governing equations are derived with the corresponding boundary conditions using the variational principle. The FEM formulation is subsequently developed and implemented for strain- and electric field-gradient piezoelectricity. In the framework of this theory the path-independent J-integral is derived.

Effect of electric field and temperature gradient on orientational dynamics of nematics encapsulated in a hallow cylindrical cavity

We have considered a homogeneously oriented liquid crystal (HOLC) microvolume, confined between two infinitely long horizontal coaxial cylinders subjected to both a temperature gradient ∇T and a radially applied electric field E. We have investigated dynamic field pumping, i.e. studied the interactions between director, velocity, electric fields, as well as a radially applied temperature gradient, where the inner cylinder is kept at a lower temperature than the outer one. In order to elucidate the role of ∇T and E in producing hydrodynamic flow, we have carried out a numerical study of a system of hydrodynamic equations including director reorientation, fluid flow, and temperature redistribution across the HOLC cavity. Calculations show that, under the effect of the named perturbations and at high curvature of the inner cylinder, the HOLC microvolume settles down to a nonstandard pumping regime with maximum flow in the vicinity of the cooler inner cylinder.

A theory of thermopiezoelectricity with strain gradient and electric field gradient effects

This paper is concerned with a theory of thermopiezoelectricity in which the second gradient of displacement and the second gradient of electric potential are included in the set of independent constitutive variables. First, the basic equations of a linear theory are derived. The field equations for homogeneous and isotropic solids are established and the boundary-initial-value problems are formulated. Then, a uniqueness result for the mixed boundary-initial-value problem and a reciprocity relation are presented. This relation forms the basis of a reciprocal theorem and a new uniqueness result. Finally, the fundamental solutions in the stationary theory and representations of Somigliana type are derived.

First-Principles Framework to Compute Sum-Frequency Generation Vibrational Spectra of Semiconductors and Insulators.

We present a first-principles framework to compute sum-frequency generation (SFG) vibrational spectra of semiconductors and insulators. The method is based on density functional theory and the use of maximally localized Wannier functions to compute the response to electric fields, and it includes the effect of electric field gradients at surfaces. In addition, it includes quadrupole contributions to SFG spectra, thus enabling the verification of the dipole approximation, whose validity determines the surface specificity of SFG spectroscopy. We compute the SFG spectra of ice I_{h} basal surfaces and identify which spectra components are affected by bulk contributions. Our results are in good agreement with experiments at low temperature.

Effect of electric field gradient on sub-nanometer spatial resolution of tip-enhanced Raman spectroscopy.

Tip-enhanced Raman spectroscopy (TERS) with sub-nanometer spatial resolution has been recently demonstrated experimentally. However, the physical mechanism underlying is still under discussion. Here we theoretically investigate the electric field gradient of a coupled tip-substrate system. Our calculations suggest that the ultra-high spatial resolution of TERS can be partially attributed to the electric field gradient effect owning to its tighter spatial confinement and sensitivity to the infrared (IR)-active of molecules. Particularly, in the case of TERS of flat-lying H2TBPP molecules,we find the electric field gradient enhancement is the dominating factor for the high spatial resolution, which qualitatively coincides with previous experimental report. Our theoretical study offers a new paradigm for understanding the mechanisms of the ultra-high spatial resolution demonstrated in tip-enhanced spectroscopy which is of importance but neglected.

Effect of Non-Uniform Basic Temperature Gradient on the Onset of Rayleigh-Bénard-Marangoni Electro-Convectionin a Micropolar Fluid

The effects of electric field and non-uniform basic temperature gradient on the onset of Rayleigh-Benard-Marangoni convection in a micropolar fluid are studied using the Galerkin technique. The eigenvalues are obtained for an upper free/adiabatic and lower rigid/isothermal boundaries. The microrotation is assumed to vanish at the boundaries. A linear stability analysis is performed. The influence of various micropolar fluid parameters and electric Rayleigh number on the onset of convection has been analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed.

Calculation of Nuclear Contribution to the Zero-field Muon Spin Polarization Function of Single Crystal La2-XSrXCuO4

Abstract We calculate the zero-field muon spin polarization function P(t) of La2-xSrxCuO4 using a quantum mechanical model. The model includes the interaction between the positively charged muon and the nearby nuclei, and the effect of the crystal electric field gradient. We demonstrate that P(t) is strongly dependent on the muon site, and deviates substantially from a static Gaussian Kubo-Toyabe function.

Effect of Non-Uniform Temperature Gradient on the Onset of Rayleigh-Bénard Electro Convection in a Micropolar Fluid

The effects of electric field and non-uniform basic temperature gradient on the onset of Rayleigh-Benard convection in a micropolar fluid are studied using the Galerkin technique. The eigenvalues are obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations and for isothermal and/or adiabatic temperature boundaries. The microrotation is assumed to vanish at the boundaries. A linear stability analysis is performed. The influence of various micropolar fluid parameters and electric Rayleigh number on the onset of convection has been analyzed. One linear and five non-uniform temperature profiles are considered and their comparative influence on onset is discussed.

Improved constitutive equations of piezoelectric monomorphs: Application to the preliminary study of an original traveling-wave peristaltic pump

This article establishes the constitutive equations of a piezoelectric monomorph by separating the effects of the piezoelectric action from the effects of the external loads and by considering in both cases a static equilibrium of forces and moments. Unlike previous studies, our model explicitly incorporates the effects of transverse strains and electric field gradients in order to approach more faithfully the real strains and stresses in the monomorph. This model, which can be easily generalized to other types of benders and applied to complex study cases is used in this paper to analyse the impact of the characteristic parameters of an original traveling-wave peristaltic pump on its performance.

Effect of electric field and temperature gradient on the orientational dynamics of liquid crystals in a microvolume cylindrical cavity

We have considered a homogeneously aligned liquid crystal (HALC) microvolume confined between two infinitely long horizontal coaxial cylinders and investigated dynamic field pumping, i.e., studied the interactions between director, velocity, and electric E fields as well as a radially applied temperature gradient inverted Delta T, where the inner cylinder is kept at a lower temperature than the outer one. In order to elucidate the role of inverted Delta T in producing hydrodynamic flow u, we have carried out a numerical study of a system of hydrodynamic equations including director reorientation, fluid flow, and temperature redistribution across the HALC cavity. Calculations show that only under the influence of inverted Delta T does the initially quiescent HALC sample settle down to a stationary flow regime with horizontal component of velocity u(eq)(r). The effects of inverted Delta T and of the size of the HALC cavity on magnitude and direction of u(eq)(r) have been investigated for a number of hydrodynamic regimes. Calculations also showed that E influences only the director redistribution across the HALC but not the magnitude of the velocity u(eq)(r).