Dielectric Displacement Research Articles

Suppression of viscous fingering during perfect dielectric fluid displacement using transverse electric fields

Suppression of viscous fingering during perfect dielectric fluid displacement using transverse electric fields

Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics

The variational implicit-solvent model (VISM) is an efficient approach to biomolecular interactions, where electrostatic interactions are crucial. The total VISM free energy of a dielectric boundary (i.e. solute–solvent interface) consists of the interfacial energy, solute–solvent interaction energy and dielectric electrostatic energy. The last part is the maximum value of the classical and concave Poisson–Boltzmann (PB) energy functional of electrostatic potentials, with the maximizer being the equilibrium electrostatic potential governed by the PB equation. For the consistency of energy minimization and computational stability, here we propose alternatively to minimize the convex Legendre-transformed Poisson–Boltzmann (LTPB) electrostatic energy functional of all dielectric displacements constrained by Gauss’ Law in the solute region. Both integrable and discrete solute charge densities are treated, and the duality of the LTPB and PB functionals is established. A penalty method is designed for the constrained minimization of the LTPB functional. In application to biomolecular interactions, we minimize the total VISM free energy iteratively, while in each step of such iteration, minimize the LTPB energy. Convergence of such a min–min algorithm is shown. Our numerical results on the solvation of a single ion indicate that the LTPB performs better than the PB formulation, providing possibilities for efficient biomolecular simulations.

High discharge energy density in rationally designed graphene oxide@zinc oxide/polymer blend-polyetherimide heterostructured bilayer nanocomposites

The advancement of new dielectric materials exhibiting greater discharge energy density is crucial for current power systems and electronic devices. In this work, various weight percentages of graphene oxide@zinc oxide (GO@ZO) nanofillers were incorporated inside a polymer blend of poly(vinylidene fluoride-hexafluoropropylene)/polyetherimide (P(VDF-HFP)/PEI; shortened as BP) and used as a high dielectric top layer. In contrast, linear-type PEI (L) was used as a bottom insulation layer to achieve a high breakdown strength (Eb) in bilayer nanocomposites. As a result, the 2BP-L composite demonstrated a high discharged energy density of 12.63 J/cm3 at an electric field of 527 MV/m with only 2 wt% GO@ZO nanofillers addition in the top layer. Such a high discharge energy density with minimal nanofiller loading is attributed to the utilization of novel surface-decorated GO@ZO nanofillers and new bilayer-heterostructured linear/ferroelectric-linear polymer. In comparison to its counterparts (i.e., PEI, P(VDF-HFP) and 0BP-L), the 2BP-L nanocomposite showed ∼426.3 %, 92.5 %, and 9.8 % enhancement in discharge energy density, respectively. The discharge rate and stability analysis revealed a significantly higher power density of 0.55 MW/cm3, indicating its high potential to be used as a pulsed power system. Finite element simulation revealed that the effective internal electric field distribution and higher dielectric displacement in 2BP-L resulted in such enhancement over its counterparts. This study presents a new model to maximize the energy storage capability of flexible energy storage devices and advances knowledge of the polarization mechanisms and breakdown of bilayer nanocomposite dielectric materials.

Tunable electromechanical properties of double-layer stacked anisotropic dielectric elastomer actuators

The current reported anisotropic dielectric elastomer (DE) actuators have some potential limitations for widespread application, such as the inability to adjust the anisotropic direction, and the related relatively complicated fabrication process. In this work, we propose a method to realize tunable direction and magnitude of electromechanical deformation of DE membranes. Two sheets of unequal-biaxial prestretched VHB 4905 membranes are attached at different rotation angles, forming an anisotropic DE actuator (DEA) with utilization of carbon grease electrodes. Experimental results demonstrate that, the direction and magnitude of the voltage-induced displacement of DEs is adjustable by tuning the unequal-biaxial prestretch ratio and rotation angle. In addition, the dielectric constant and maximum displacement at breakdown of the anisotropic DEA are also related to the rotation angle. The designed anisotropic DEA realizes the diversity of electromechanical actuation in both the planar 2D and the spatial 3D structures, which can be utilized to help design the practical soft actuators.

Enhanced breakdown strength and electrostatic energy density of polymer nanocomposite films realized by heterostructure ZnO-ZnS nanoparticles

We demonstrate that introduction of heterostructure nanoparticles into a polymer matrix is an effective strategy to substantially enhance dielectric breakdown strength (Eb) and thus a high electrostatic energy storage density (Ue) can be obtained, which is highly desired in modern electronic and electrical systems for energy storage and conversion. This is realized through the special “electrical rectification” effect of heterostructure nanoparticles on the charge transport, which stems from capturing and confining charge carriers in the nanocomposites by potential well and potential barrier formed at the heterojunction of ZnO-ZnS nanoparticles. The leakage current of the ZnO-ZnS/polyetherimide nanocomposites (ZnO-ZnS/PEI) is suppressed by the introduced heterojunction, which is accompanied with the simultaneous increase of dielectric displacement and charge–discharge efficiency, resulting in significant enhancement of Ue. Notably, the 1 wt% ZnO-ZnS/PEI nanocomposite films possess high discharged energy density at room temperature, i.e. 6.9 J cm−3 at 650 MV m−1, and even at 150 °C, the Ue still remains 3.6 J cm−3 at 500 MV m−1. Outstanding fatigue resistance over 50,000 charge–discharge cycles at 200 MV m−1 and 150 °C demonstrates high temperature cyclic stability of the heterostructure in confining charge carriers. This work provides a novel and scalable strategy to obtain polymer-based dielectrics with superior energy storage performance.

Structure-preserving numerical method for Maxwell-Ampère Nernst-Planck model

Charge dynamics play essential role in many practical applications such as semiconductors, electrochemical devices and transmembrane ion channels. A Maxwell-Ampère Nernst-Planck (MANP) model that describes charge dynamics via concentrations and the electric displacement is able to take effects beyond mean-field approximations into account. To obtain physically faithful numerical solutions, we develop a structure-preserving numerical method for the MANP model whose solution has several physical properties of importance. By the Slotboom transform with entropic-mean approximations, a positivity preserving scheme with Scharfetter-Gummel fluxes is derived for the generalized Nernst-Planck equations. To deal with the curl-free constraint, the dielectric displacement from the Maxwell-Ampère equation is further updated with a local relaxation algorithm of linear computational complexity. We prove that the proposed numerical method unconditionally preserves the mass conservation and the solution positivity at the discrete level, and satisfies the discrete energy dissipation law with a time-step restriction. Numerical experiments verify that our numerical method has expected accuracy and structure-preserving properties. Applications to ion transport with large convection, arising from boundary-layer electric field and Born solvation interactions, further demonstrate that the MANP formulation with the proposed numerical scheme has attractive performance and can effectively describe charge dynamics with large convection of high numerical cell Péclet numbers.

An effective Fourier spectral phase-field approach for ferroelectric materials

In this article, we propose an efficient iterative numerical algorithm applying a Fourier spectral method to accurately compute the coupled elasto–electrostatic equilibrium equations in ferroelectric microstructures. The method is implemented for a phase-field model for domain pattern formation and domain kinetics evolution in tetragonal perovskite ferroelectrics, that uses spontaneous polarization as order parameter and includes the piezoelectric effect in the constitutive equation. The scheme is based on a two-scale homogenization approach, introducing local perturbations for stress and dielectric displacement. Green’s functions are derived in Fourier space for the coupled constitutive equations. Furthermore, using model parameters for BaTiO3 we investigate domain formation in 2D and 3D, and the polarization switching process starting from a critical nucleus subjected to an applied electric field and compressive stress. The simulation results based on the proposed method reveal that for polarization switching under external fields, intermediately appearing domains with 90° rotated polarization are formed, that reduce electrostatic or elastic strain energy.

Electrophoresis of Dielectric and Hydrophobic Spherical Fluid Droplets Possessing Uniform Surface Charge Density.

The present article deals with the theoretical study on electrophoresis of hydrophobic and dielectric spherical fluid droplets possessing uniform surface charge density. Unlike the ideally polarizable liquid droplet bearing constant surface ζ-potential, the tangential component of the Maxwell stress is nonzero for dielectric fluid droplets with uniform surface charge density. We consider the continuity of the tangential component of total stress (sum of the hydrodynamic and Maxwell stresses) and jump in dielectric displacement along the droplet-to-electrolyte interface. The typical situation is considered here for which the interfacial tension of the fluid droplet is sufficiently high so that the droplet retains its spherical shape during its motion. The present theory can be applied to nanoemulsions, hydrophobic oil droplets, gas bubbles, droplets of immiscible liquid suspended in aqueous medium, etc. Based on weak field and low charge assumptions and neglecting the Marangoni effect, the resultant electrokinetic equations are solved using linear perturbation analysis to derive the closed form expression for electrophoretic mobility applicable for the entire range of Debye-Hückel parameter. We further deduced an alternate approximate expression for electrophoretic mobility without involving exponential integrals. Besides, we have derived analytical results for mobility pertaining to various limiting cases. The results are further illustrated to show the impact of pertinent parameters on the overall electrophoretic mobility.

Extremal states and coupling properties in electroelasticity.

Electroelastic materials possess properties most attractive for the design of smart devices and systems such as actuators and sensors. Typical polymers show changes in shape under the action of an electric field, and vice versa, together with fast actuation times, high strain levels and low elastic moduli. This paper deals with an Ogden model inspired framework for large deformation electroelasticity which, as a special case, can also be reduced to the modelling of transversely isotropic elasticity. Extremal (local) states are elaborated based on a coaxiality analysis, i.e. extremal states of energy are considered at fixed deformation and changing direction of electric field, respectively, fixed electric field and changing principal directions of deformation. This analysis results in extremal states when stresses and strain commutate, respectively, dielectric displacements and electric field are aligned. In order to further elaborate electromechanical coupling properties, the sensitivity of stresses with respect to electric field is analysed. This sensitivity is represented by a third-order tensor which, in general, depends on deformation and electric field. To illustrate this third-order tensor, a decomposition into deviators is adopted. Related norms of these deviators, together with the electromechanical coupling contribution to the augmented energy, are investigated for different states under homogeneous deformation and changing electric field direction. The analysis is considered to contribute to a better understanding of electromechanical coupling properties and extremal states in large deformation electroelasticity and by that, as a long-term goal, may contribute to the improved design of related smart devices and systems.This article is part of the theme issue ‘The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity’.

Last developments in polymers for wearable energy storage devices

Last developments in polymers for wearable energy storage devices

Structure-Preserving Numerical Method for Ampere-Nernst-Planck Model

Charge dynamics play essential role in many practical applications such as semiconductors, electrochemical devices and transmembrane ion channels. An Amp\'{e}re-Nernst-Planck (ANP) model that describes charge dynamics via concentrations and the electric displacement is able to take effects beyond mean-field approximations into account. To obtain physically faithful numerical solutions, we develop a structure-preserving numerical method for the ANP model whose solution has several physical properties of importance. By the Slotboom transform with entropy-mean approximations, a positivity preserving scheme with Scharfetter-Gummel fluxes is derived for the generalized Nernst-Planck equations. To deal with the curl-free constraint, the dielectric displacement from the Amp\'{e}re equation is further updated with a local relaxation algorithm of linear computational complexity. We prove that the proposed numerical method unconditionally preserves the mass conservation and the solution positivity at the discrete level, and satisfies the discrete energy dissipation law with a mild time-step restriction. Numerical experiments verify that our numerical method has expected accuracy and structure-preserving properties. Applications to ion transport with large convection, arising from boundary-layer electric field and Born solvation interactions, further demonstrate that the ANP formulation with the proposed numerical scheme has attractive performance and can effectively describe charge dynamics with large convection of high numerical cell P\'{e}clet numbers.

Numerical solution through finite elements for dielectric materials in space

The study of physical models is generally modeled by means of partial differential equations which is still an open field in current research, such is the case of Laplace’s differential equation which is surely one of the most important representations of the telecommunications industry. In the following article we will use techniques based on finite elements, through this technique we will find the behavior of the electrostatic potential in each part of the conductor: dielectric conductive material and armored material. The configuration of the coaxial cable allows to find the distribution of the dielectric displacement in the entire composition of the same in such a way that it guarantees the maximum data transfer as the signal transmission frequency increases and the attenuation of the external interference signals increases. In the first section we propose to obtain the linear terms that will calculate the weights of the values of a linear combination that numerically approximates the variable of interest through Galerkin’s residual theory applying the finite element method, which for the two-dimensional case with elements Triangular linear lines that discretize the cross section of the coaxial cable, in such a way that it is easier to find these constants including the initial conditions and contour, thus allowing to guarantee the existence of a numerical solution.

Dipolar Poisson models in a dual view

In this work, we study the continuum theories of dipolar-Poisson models. Both the standard dipolar-Poisson model and the dipolar-Poisson-Langevin model, which keeps the dipolar density fixed, are non-convex functionals of the scalar electrostatic potential ϕ. Applying the Legendre transform approach introduced by Maggs [Europhys. Lett. 98, 16012 (2012)], the dual functionals of these models are derived and are given by convex vector-field functionals of the dielectric displacement D and the polarization field P. We compare the convex functionals in P-space to the non-convex functionals in electric field E-space and apply them to the classic problem of the solvation of point-like ions. Since the dipolar-Poisson model does not properly describe polarization saturation, we argue that only the dipolar-Poisson-Langevin functional can be used to provide a nonlinear generalization of the harmonic polarization functional used in the theory of Marcus for the electron transfer rate to nonlinear regimes. We show that the model can be quantitatively parameterized by molecular dynamics simulations.

Influence of Different Solvents and High-Electric-Field Cycling on Morphology and Ferroelectric Behavior of Poly(Vinylidene Fluoride-Hexafluoropropylene) Films.

P(VdF-HFP) films are fabricated via a solution casting doctor blade method using high (HVS) and low (LVS) volatile solvents, respectively. The structural properties and the ferroelectric behavior are investigated. The surface structure and crystal phase composition are found to be strongly dependent on the type of solvent. LVS leads to a rougher copolymer surface structure with large spherulites and a lower crystallinity in contrast with HVS. The crystalline phase of copolymer films fabricated with HVS consists almost exclusively of α-phase domains, whereas films from LVS solution show a large proportion of γ-phase domains, as concluded from Raman and X-ray diffraction spectra. Virgin films show no ferroelectric (FE) switching polarization at electric field amplitudes below 180 MV/m, independent of the solvent type, observed in bipolar dielectric displacement—electric field measurements. After applying electric fields of above 180 MV/m, a FE behavior emerges, which is significantly stronger for LVS films. In a repeated measurement, FE polarization switching already occurs at lower fields. A shielding effect may be related to this observation. Additionally, Raman bands of polar γ-phase increase by high-electric-field cycling for the LVS sample. The solvent used and the resulting crystal phase composition of the virgin sample is crucial for the copolymer behavior during bipolar electrical cycling.

Analysis of the Distributions of Displacement and Eddy Currents in the Ferrite Core of an Electromagnetic Transducer Using the 2D Approach of the Edge Element Method and the Harmonic Balance Method

The negative impact of the displacement currents on the operation of electromagnetic converters results in additional losses and faster insulation degradation, as well as the self-resonance phenomenon. Effective measurement of the dielectric displacement currents in converters is quite complex; thus, advanced simulation programs should be used. However, currently, they do not enable the analysis of the systems in terms of the displacement currents distribution. In order to elaborate an effective tool for analyzing the distribution of the displacement currents by means of the Finite Element Method, we have decided to supplement the well-known reluctance-conductance network model with an additional capacitance model. In the paper, equations for the linked reluctance-conductance-capacitance network model have been presented and discussed in detail. Moreover, we introduce in the algorithm the Harmonic Balance Finite Element Method (HBFEM) and the Fixed-Point Method. This approach enables us to create a field model of electromagnetic converters, which includes the electromagnetic core’s saturation effect. The application of these methods for the reluctance-conductance-capacitance model of the finite element has allowed us to develop a practical tool ensuring complex analysis of the magnetic flux, eddy, and the displacement currents’ distribution in electromagnetic converters with an axial symmetrical structure.

Three dimensional numerical solution for the bending study of magneto-piezo-elastic spherical and cylindrical shells

This paper presents an exact solution for the static analysis of magneto-electro-elastic simply supported shallow shells panels. The mechanical equations are derived via equilibrium elasticity relations. The electrical and magnetic governing equations are obtained by electrostatic and magnetostatic equilibrium relations. The shell displacements, electrical and magnetic potential functions are solved analytically by the Navier closed form solutions. The governing equations formulated in terms of thickness coordinate are solved semi-analytically by using the differential quadrature method. The Lagrange polynomials are employed as basis functions. The equations are discretized per each layer by the Chebyshev-Gauss-Lobatto grid distribution. The continuity conditions in the adjacent layers for mechanical displacement, transverse dielectric displacement, electric and magnetic scalar function and transverse magnetic induction are complied. The correct load traction condition is considered at the top and bottom of the shell. Numerical results for spherical, cylindrical and rectangular panels are reported. The results are in excellent agreement with other 3D elasticity solutions reported in the literature so a new benchmark problem for shell is proposed.

Electric-field-based Poisson-Boltzmann theory: Treating mobile charge as polarization.

Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of an electrolyte can then be treated as a composite nonuniform dielectric body. Writing the electrostatic interactions as an integral over electric-field energy density we show that the Poisson-Boltzmann functional in this formulation is convex and can be used to derive the equilibrium equations for electric potential and ion concentration by a variational procedure developed by Ericksen for dielectric continua [J.L. Ericksen, Arch. Rational Mech. Anal. 183, 299 (2007)AVRMAW0003-952710.1007/s00205-006-0042-4]. The Maxwell field equations are enforced by extending the set of variational parameters by a vector potential representing the dielectric displacement which is fully transverse in a dielectric system without embedded external charge. The electric-field energy density in this representation is a function of the vector potential and the sum of ionic and solvent polarization making the mutual screening explicit. Transverse polarization is accounted for by construction, lifting the restriction to longitudinal polarization inherent in the electrostatic potential based formulation of Poisson-Boltzmann mean field theory.

Semiconductor-based dynamic heterojunctions as an emerging strategy for high direct-current mechanical energy harvesting

Direct-current (DC) power generation through mechanically modulated semiconductor-based heterojunctions is a newly found physical phenomenon, where mechanical-to-electric power conversion can take place in various material systems, including e.g., metal/semiconductor sliding Schottky contact, p-n junction sliding/impact contact, metal/conducting polymer compressive contact, and liquid/semiconductor moving interface. Such systems are capable of generating a continuous DC with a current density up to 10–100 A/m2, which is 3–4 orders of magnitude higher than the pulsed alternating current (AC) density in traditional piezoelectric and triboelectric nanogenerators. Unlike the dielectric displacement current generation mechanism in traditional methods, the DC generation is associated with a multi-scale and multi-physics interaction at the dynamic interfaces with semiconductor junctions involved. The resulting electronic excitation, which is referred to the tribovoltaic effect, and the subsequent direct electron conduction are considered to play a key role in the DC power output. In an effort to provide an overview of the novel concepts and inspiration for their applications, the fundamental aspects of the dynamic interfaces, nanoscale observation of the phenomenon, and recent progress in material and device development are summarized and discussed in this review. The dynamic DC generator concept shows great promise for scaled-up as well as miniaturized self-powering applications. Moreover, the new photo/thermal-electro-mechanical coupling effects discovered in the dynamic semiconductor heterojunctions may be exploited for hybrid energy harvesting and advanced sensing.

Non-linearity in engineered lead magnesium niobate (PbMg1/3Nb2/3O3) thin films

The local compositional heterogeneity associated with the lack of long-range ordering of Mg2+ and Nb5+ in PbMg1/3Nb2/3O3 (PMN) is correlated with its characteristic “relaxor” ferroelectric behavior. Earlier work [Shetty et al., Adv. Funct. Mater. 29, 1804258 (2019)] examined the relaxor behavior in PMN thin films grown at temperatures below 1073 K by artificially reducing the degree of disorder via synthesis of heterostructures with alternate layers of Pb(Mg2/3Nb1/3)O3 and PbNbO3, as suggested by the “random-site model.” This work confirmed the development of ferroelectric domains below 150 K in long-range-ordered films, epitaxially grown on (111) SrTiO3 substrates using alternate target timed pulsed-laser deposition of Pb(Mg2/3Nb1/3)O3 and PbNbO3 targets with 20% excess Pb. In this work, the first through third-harmonic dielectric charge displacement densities and complex dielectric susceptibilities were analyzed as a function of temperature and frequency in zero-field-cooled PMN films with short- and long-range ordering. The long-range ordering decreased the dispersion in the first- and third-harmonic dielectric charge displacement densities relative to short-range-ordered films. It was found that the one-dimensional ordering achieved in the long-range-ordered film is insufficient to achieve a fully normal ferroelectric state. In the presence of quenched random electric fields, these films require a small ac field to facilitate percolation of the polar nano-regions, enabling normal ferroelectric-like behavior at lower temperature (T < 240 K). The films behave like a typical relaxor near room temperature. With reduced ordering, the short-range films exhibit greater dispersion in linear and higher order harmonic dielectric charge displacement density.

The modification of contribution: electric conductivity, dielectric displacement and domain switching in ferroelectric hysteresis loops

The actual ferroelectric polarization can be misjudged due to the existence of the leakage current. How to distinguish the impact of each part is of great significance to evaluate the actual domain switching polarization and liner polarization. The current (I)–electric field (E) curves are suggested to distinguish the electric displacement contribution of electric conductivity D1, dielectric displacement D2 and domain switching polarization P. However, the previous model cannot accurately estimate the contribution of each part due to the inaccurate assumption. Thus, an alternative model had been constructed to demonstrate respective contributions of D1, D2 and P. Through the I–E curves, one baseline was made from the vertex (I > 0) at negative maximum electric field to another vertex (I > 0) at the positive and maximum electric field. The area above the baseline represents the domain switching P by high-order even power. The areas enclosed by I–E curve, baseline, and I = 0 line represent the contribution of electric conductivity. Besides, the parallelogram area represents the contribution of dielectric displacement D2. The accuracy of the present model had been verified by the simulation mean and fabrication in traditional BaTiO3 ferroelectric films. It shows that the contribution of electric conductivity D1 is two times than actual contribution by previous model, and dielectric displacement D2 is of great error than the actual one. And the present model is in more accordance with the actual contribution by constructing more accurate conductance form, and there is only small error in present model. It is revealed that the present model is more suitable to distinguish the contribution of each part than the previous one.