Nonlinear Electrical Response Research Articles

Numerical modelling of electro‐viscoelasticity for fibre reinforced electro‐active polymers

AbstractElectro‐active polymers (EAP) are smart materials that can deform dramatically and quasi‐instantaneously in response to an applied electric field. These properties make them suitable to be used as soft robotic actuators. As any passive rubber‐like material, those electro‐sensitive components are quasi‐incompressible and may show pronounced time‐dependent hysteresis behaviour. The direction of the electric field induced deformation can be tuned by incorporating stiff fibres in a relatively soft EAP, which renders an anisotropic mechanical response of the whole composite. The contribution at hand presents a constitutive model which is suitable for the simulation of an electro‐viscoelastic behaviour of transversely isotropic EAP. The material model is based on an additive split of the total energy function into purely mechanical, electrical and coupled electro‐mechanical contributions. The mechanical part of the energy is further decomposed into isotropic and anisotropic parts. For the electrical and the coupled contributions, formulations for both the perfectly linear dielectric and the nonlinear (deformation dependent) electrical response are presented. Regarding the numerical implementation, a mixed quasi‐incompressible and quasi‐inextensible electro‐mechanical finite element is developed. In addition to the displacement and electric potential, four additional field variables are introduced. The capabilities of the proposed theory and its numerical treatment are demonstrated through simulations of several electro‐mechanical actuator structures. The utilization of a quasi‐inextensible finite element is shown to improve the convergence behaviour of the numerical solution, allowing for the simulation of complex loading scenarios of fibre reinforced EAP in an efficient manner.

Investigation of Microstructural Evolution and Suitable Potential Barrier Model for Non-Linear Electrical Response of Sr and Nb Co-Doped CCTO Ceramics

Investigation of Microstructural Evolution and Suitable Potential Barrier Model for Non-Linear Electrical Response of Sr and Nb Co-Doped CCTO Ceramics

Calculation of Linear and Non-linear Electric Response Properties of Systems in Aqueous Solution: A Polarizable Quantum/Classical Approach with Quantum Repulsion Effects.

We present a computational study of polarizabilities and hyperpolarizabilities of organic molecules in aqueous solutions, focusing on solute–water interactions and the way they affect a molecule’s linear and non-linear electric response properties. We employ a polarizable quantum mechanics/molecular mechanics (QM/MM) computational model that treats the solute at the QM level while the solvent is treated classically using a force field that includes polarizable charges and dipoles, which dynamically respond to the solute’s quantum-mechanical electron density. Quantum confinement effects are also treated by means of a recently implemented method that endows solvent molecules with a parametric electron density, which exerts Pauli repulsion forces upon the solute. By applying the method to a set of aromatic molecules in solution we show that, for both polarizabilities and first hyperpolarizabilities, observed solution values are the result of a delicate balance between electrostatics, hydrogen-bonding, and non-electrostatic solute solvent interactions.

Investigation of the dielectric properties and nonlinear electrical response of CaCu3Ti4O12 ceramics prepared by a chemical combustion method

CaCu3Ti4O12 (CCTO) ceramic powders were successfully prepared by a wet-chemical combustion method. The phase formation, microstructure, giant dielectric response, and nonlinear electrical properties of the sintered ceramics were systematically investigated. The main phase in the CCTO powder is clearly indicated in the XRD pattern. A dense and fine-grained microstructure was obtained by sintering the compacted CCTO powders. Dielectric permittivity values are in the range of ~ 103–104 with a very low tan δ of ~ 0.03–0.11 at 1 kHz. Interestingly, a high breakdown electric field (9741.6 V/cm) and nonlinear coefficient (9.9) are observed in the CCTO ceramic sintered at 1030 °C for 1 h. Impedance spectroscopy analysis revealed that the electrical conductivity in the grains and grain boundaries is completely different. The electrically heterogeneous microstructure clearly indicates that the giant dielectric response and nonlinear electrical properties are correlated with the electrical response of the insulating grain boundaries. The origin of the n-type semiconducting grains is evident by considering the oxidation states of the Ti and Cu ions, which are quantitatively and qualitatively analyzed using X-ray absorption spectroscopy.

Phase-coherent THz-wave demodulation with a photomixer

The nonlinear electrical response from a low temperature grown GaAs photomixer driven with the optical beat of two continuous-wave lasers allows frequency mixing between radiofrequency and THz-waves. Phase-sensitive demodulation of the signal from a modulated THz-wave is theoretically and experimentally demonstrated using a photomixer electrically driven with an alternative voltage at the modulation frequency.

A computational approach to evaluate the nonlinear and noisy DC electrical response in carbon nanotube/polymer nanocomposites near the percolation threshold

This paper presents a percolating network model to determine the electrical behavior of carbon nanotube (CNT)/polymer nanocomposites, especially near the percolation threshold. In this extended model, we considered a voltage-dependent tunneling resistance at the CNT junctions, based on Simmons’ formulation. This assumption led to an electrical resistor network containing both linear and nonlinear resistance elements. We focused on extracting the continuous current-voltage (I-V) response of the nanocomposites through a recursive calculation to show the ability of the model to simulate the nonlinear and noisy behavior of the I-V curve in CNT/polymer systems. The effects of CNT diameter, length, concentration, and intrinsic conductance, as well as the tunneling gap at the junctions and matrix dielectric constant, were also investigated and discussed. Our results revealed that the nonlinearity in I-V curves near the percolation threshold is related to the voltage-dependent nature of the tunneling resistance. The number of junctions and equivalent CNT length in the percolation pathway are two effective parameters controlling the electrical behavior of CNT/polymer nanocomposites. The results obtained are also in good agreement with our previous experimental data on CNT/epoxy nanocomposite and confirmed that the proposed model can efficiently predict the I-V characteristic curves for CNT/polymer composites.

Dielectric properties, nonlinear electrical response and microstructural evolution of CaCu3Ti4-xSnxO12 ceramics prepared by a double ball-milling process

Recently, the dielectric properties and nonlinearity of the current-voltage (I–V) characteristics of CaCu3Ti4O12 (CCTO) ceramics, which can be controlled mainly by their microstructures, have been widely studied. The microstructure of CCTO ceramics has a great effect on both the dielectric properties and nonlinear current-voltage characteristics. In this work, the microstructure, dielectric response, and nonlinear I–V properties of CaCu3Ti4-xSnxO12 ceramics that were prepared by a double ball-milling process were studied. The crystal structures and microstructures were methodologically investigated. The dielectric permittivity of the CCTO ceramics at 1 kHz increased from ~3.90 × 104 to ~5.30 × 104-6.51 × 104 by doping with Sn4+ ions, while the dielectric loss decreased significantly. The nonlinear I–V properties of the CaCu3Ti4-xSnxO12 ceramics significantly improved as x increased. The improved dielectric and nonlinear I–V properties were mainly associated with the substantially enhanced grain boundary response.

Three-terminal ballistic junction based on phosphorene

We investigate nonlinear electric response of a phosphorene-based three-terminal ballistic junction (TBJ) where two terminals (‘ l’ and ‘ r’) are armchair nanoribbons and the other (‘ m’) is a zigzag ribbon. The transmission among leads is found to be strongly anisotropic. When the push–pull voltage is applied on the terminal ‘ l’ and ‘ m’ (), the output voltage exhibits a remarkable change of slope () from one side of its extremum point to the other. The heat flux in the input terminals is much smaller than that for the conventional symmetric-input configuration with . As one armchair terminal is grounded, the output voltage from the other armchair terminal exhibits a typical voltage diode feature. The voltage transistor function is demonstrated, whose response parameters depend on the choice of output terminals. We also examine the phosphorene TBJ with two zigzag terminals and one armchair terminal, whose voltage response in all cases is similar to conventional TBJs due to a weak transmission anisotropy. The heat flux in the TBJ transistor depends on the edge type and width of leads. Its amplitude under the symmetric-input configuration exceeds twice of that under the asymmetric-input configuration. These results reveal unique advantages of phosphorene-based TBJ for nanoelectronic applications.

Nonlinear current-voltage and giant dielectric properties of Al3+ and Ta5+ co-doped TiO2 ceramics

The nonlinear current-voltage and dielectric properties of (Al3++Ta5+) co-doped TiO2 (ATTO) ceramics are represented. Microstructural analysis reveals that sintered ceramics are highly dense and nonporous. ATTO ceramics exhibit low loss tangent (tanδ<0.1) and large dielectric permittivity (ε′˜103-104). Furthermore, ATTO ceramics exhibited nonlinear current-voltage characteristics. The best dielectric properties are achieved in the (Al1/2Ta1/2)0.05Ti0.95O2 ceramic with a very low tanδ (˜0.012) and high ε′ (˜104) with excellent dielectric-temperature stability with a temperature coefficient at 150 °C as low as 2.69%. The resistivity of insulating phases decreases with increasing Al3+ and Ta5+ concentrations, which is correlated to decreased breakdown voltage. The nonlinear electrical properties and dielectric response are explained based on the electrical response of internal interfaces.

Nonlinear dynamic modeling of ultrathin conducting polymer actuators including inertial effects

Trilayer conducting polymer (CP) actuators are potential alternatives to piezoelectric and electrostatic actuators due to their large strain, and recently demonstrated operation at hundreds of Hertz. However, these actuators exhibit nonlinear electrical and mechanical properties as a function of their oxidation state, when operated over their full strain range, making it more challenging to accurately predict their mechanical behavior. In this paper, an analytical multi-physics model of the CP actuators is proposed to predict their nonlinear dynamic mechanical behavior. To demonstrate the accuracy of the model, a trilayer actuator composed of a solid polymer electrolyte sandwiched between two poly(3,4-ethylenedioxythiophene) (PEDOT) electrodes was fabricated and characterized. This system consists of an electrical subsystem represented by an RC equivalent circuit, an electro-mechanical coupling matrix, and a mechanical subsystem described by using a rigid finite element method. The electrical conductivity and the volumetric capacitance, an empirical strain-to-charge ratio, and Young’s modulus of the actuator as a function of the PEDOT electrode charge state were also implemented into the model, using measured values. The proposed model was represented using a bond graph formalism. The concordance between the simulations and the measurements confirmed the accuracy of the model in predicting the nonlinear dynamic electrical and mechanical response of the actuators. In addition, the information extracted from the model also provided an insight into the critical parameters of the actuators and how they affect the actuator efficiency, as well as the energy distribution including dissipated, stored, and transferred energy. These are the key parameters for designing, optimizing, and controlling the actuation behavior of a trilayer actuator.

A data-driven computational homogenization method based on neural networks for the nonlinear anisotropic electrical response of graphene/polymer nanocomposites

In this paper, a data-driven-based computational homogenization method based on neural networks is proposed to describe the nonlinear electric conduction in random graphene-polymer nanocomposites. In the proposed technique, the nonlinear effective electric constitutive law is provided by a neural network surrogate model constructed through a learning phase on a set of RVE nonlinear computations. In contrast to multilevel (FE $$^2$$ ) methods where each integration point is associated with a full nonlinear RVE calculation, the nonlinear macroscopic electric field-electric flux relationship is efficiently evaluated by the surrogate neural network model, reducing drastically (by several order of magnitudes) the computational times in multilevel calculations. Several examples are presented, where the RVE contains aligned graphene sheets embedded in a polymer matrix. The nonlinear behavior is due to the modeling of the tunelling effect at the scale of graphene sheets.

Electrically tuneable nonlinear anomalous Hall effect in two-dimensional transition-metal dichalcogenides WTe2 and MoTe2

We studied the nonlinear electric response in WTe2 and MoTe2 monolayers. When the inversion symmetry is breaking but the the time-reversal symmetry is preserved, a second-order Hall effect called the nonlinear anomalous Hall effect (NLAHE) emerges owing to the nonzero Berry curvature on the nonequilibrium Fermi surface. We reveal a strong NLAHE with a Hall-voltage that is quadratic with respect to the longitudinal current. The optimal current direction is normal to the mirror plane in these two-dimensional (2D) materials. The NLAHE can be sensitively tuned by an out-of-plane electric field, which induces a transition from a topological insulator to a normal insulator. Crossing the critical transition point, the magnitude of the NLAHE increases, and its sign is reversed. Our work paves the way to discover exotic nonlinear phenomena in inversion-symmetry-breaking 2D materials.

Nonlinear anisotropic electrical response of carbon fiber-reinforced polymer composites

Composites materials are often subjected to multi-physics conditions in different applications where, in addition to mechanical loads, they also need to sustain other types of loads such as electrical currents. Composite materials have heterogeneous electrical properties at the local level that can be different at the global level. In this study, electrical response was measured to explore how different lamina orientation and electrical current density affect anisotropic electrical properties of composite. For in-plane study, current was applied up to 80 kA/m2 for both unidirectional and quasi-isotropic composite. In thickness direction, maximum current density was 6 kA/m2. As expected, electrical properties are indeed dependent on fiber architecture which acts as conduction path in the laminate, and also depends on progressive increase in current density. Anisotropic electrical behavior was measured experimentally and the threshold of nonlinear behavior due to high current was identified. Threshold current density for unidirectional composite in fiber direction and for quasi isotropic are, respectively, 48.14 ± 4.3% kA/m2, 56.06 ± 4.4% kA/m2. For off-axis fiber laminates, this threshold limit shifts from 34.36 ± 5.9% kA/m2 to a lower value of 17.95 ± 7.9% kA/m2 as the fibers are oriented away from the x axis. In thickness direction, this threshold limit is in between 2.56 and 3.80 kA/m2. The electrical-thermal responses were also studied experimentally with thermography tests and the results were compared to indicate damage. A 3D X-ray microscope has been used to visualize and quantify (down to 1 micron) such local material state changes due to electrical current.

Particles with nonlinear electric response: Suppressing van der Waals forces by an external field.

We study the classical thermal component of Casimir, or van der Waals, forces between point particles with highly anharmonic dipole Hamiltonians when they are subjected to an external electric field. Using a model for which the individual dipole moments saturate in a strong field (a model that mimics the charges in a neutral, perfectly conducting sphere), we find that the resulting Casimir force depends strongly on the strength of the field, as demonstrated by analytical results. For a certain angle between the external field and center-to-center axis, the fluctuation force can be tuned and suppressed to arbitrarily small values. We compare the forces between these particles with those between particles with harmonic Hamiltonians and also provide a simple formula for asymptotically large external fields, which we expect to be generally valid for the case of saturating dipole moments.

On effective holographic Mott insulators

We present a class of holographic models that behave effectively as prototypes of Mott insulators, materials where electron-electron interactions dominate transport phenomena. The main ingredient in the gravity dual is that the gauge-field dynamics contains self-interactions by way of a particular type of non-linear electrodynamics. The electrical response in these models exhibits typical features of Mott-like states: i) the low-temperature DC conductivity is unboundedly low; ii) metal-insulator transitions appear by varying various parameters; iii) for large enough self-interaction strength, the conductivity can even decrease with increasing doping (density of carriers), which appears as a sharp manifestation of `traffic-jam'-like behaviour; iv) the insulating state becomes very unstable towards superconductivity at large enough doping. We exhibit some of the properties of the resulting insulator-superconductor transition, which is sensitive to the amount of disorder in a specific way. These models imply a clear and generic correlation between Mott behaviour and significant effects in the nonlinear electrical response. We compute the nonlinear current-voltage curve in our model and find that indeed at large voltage the conductivity is largely reduced.

Estimation of Joule heating and its role in nonlinear electrical response of Tb 0.5 Sr 0.5 MnO 3 single crystal

Abstract Highly non-linear I–V characteristics and apparent colossal electro-resistance were observed in non-charge ordered manganite Tb 0.5 Sr 0.5 MnO 3 single crystal in low temperature transport measurements. Significant changes were noticed in top surface temperature of the sample as compared to its base while passing current at low temperature. By analyzing these variations, we realize that the change in surface temperature ( Δ T sur ) is too small to have caused by the strong negative differential resistance. A more accurate estimation of change in the sample temperature was made by back-calculating the sample temperature from the temperature variation of resistance (R–T) data ( Δ T cal ) , which was found to be higher than Δ T sur . This result indicates that there are large thermal gradients across the sample. The experimentally derived Δ T cal is validated with the help of a simple theoretical model and estimation of Joule heating. Pulse measurements realize substantial reduction in Joule heating. With decrease in sample thickness, Joule heating effect is found to be reduced. Our studies reveal that Joule heating plays a major role in the nonlinear electrical response of Tb0.5Sr0.5MnO3. By careful management of the duty cycle and pulse current I–V measurements, Joule heating can be mitigated to a large extent.

Piezoresistive natural rubber-multiwall carbon nanotube nanocomposite for sensor applications

We explore, both experimentally and theoretically, the possibility to use a composite of natural rubber (NR) and multiwall carbon nanotubes (MWCNT) as a piezoresistive tensile sensor. As an essentially new feature relative to the previous work, we have performed a systematic study of the mechanism of the piezoresistance at large deformations in a wide range of MWCNT concentrations and crosslinking degrees of the host rubber material. In qualitative agreement with the previous work, the conductivity of the unstrained NR/MWCNT nanocomposite is shown to be adequately described by the percolation theory with the critical exponent evaluated to ∼2.31. Varying tensile stress-induced strains in the composite has been shown to results in a non-linear electrical response that cannot be described by simple modifications of the percolation theory. In order to explain the observed non-linear dependence of the resistance R of the composite on the strain ε, we have developed a scaling theory that relates this resistance to the structural changes in the conducting MWCNT network caused by deforming the host NR. Based on the obtained results, we discuss the ways of using the highly stretchable conductive elastomer composites as an efficient piezoresistive tensile sensor.

The influence of the parasitic current on the nonlinear electrical response of capacitively sensed cantilever resonators

The influence of the parasitic feedthrough current on the nonlinear electrical response of capacitively sensed cantilever resonators is analyzed theoretically and experimentally. We show that the parasitic current strongly affects the shape of the nonlinear electrical frequency response of such devices. Specifically, we demonstrate that in the electrical measurement, the directions of the jumps from the different transitions between branches of stable solutions depend on the parasitic current and are independent of the jumps directions in the mechanical domain. As a consequence, the nonlinear electrical frequency response of cantilevers with capacitive readout presents three different hysteretic cycle topologies: counterclockwise, bow tie, and clockwise. This is in contrast with the only one topology (counterclockwise) that appears in the nonlinear mechanical frequency response.

What are Memristor, Memcapacitor, and Meminductor?

Memristor, memcapacitor, and meminductor are new fundamental circuit elements, whose properties depend on the history of devices. This paper presents the physical analysis of these memory devices. Three simple examples are given for the memristor, memcapacitor, and meminductor, and are then generalized to reveal their general physical origin. It is found that the memristance, memcapacitance, and meminductance are caused by different combinations of nonlinear electric responses. The mathematical expressions for the currents through any voltage-driven memristor, memcapacitor, and meminductor are given, and the corresponding expressions for the memristance, memcapacitance, and meminductance are derived. Moreover, a method to determine the charge-flux relationship of a memristor is proposed.

Electrically tunable resonant terahertz transmission in subwavelength hole arrays

An actively enhanced resonant transmission in a plasmonic array of subwavelength holes is demonstrated by use of terahertz time-domain spectroscopy. By connecting this two-dimensional element into an electrical circuit, tunable resonance enhancement is observed in arrays made from good and relatively poor metals. The tunable feature is attributed to the nonlinear electric response of the periodic hole array film, which is confirmed by its voltage—current behavior. This finding could lead to a unique route to active plasmonic devices, such as tunable filters, spatial modulators, and integrated terahertz optoelectronic components.