Parallel Plate Capacitor Model Research Articles

2D heterostructures of graphene oxide and MoS2 to improve sensitivity performance of flexible pressure sensor with shell biological structure

Inspired by the multilayer structure of the shellfish, a novel two-dimensional (2D) composite structure consisting of graphene oxide, MoS2 and graphene oxide (G/M/G) was integrated to the flexible pressure sensing. The composite structure was prepared by the vacuum suction filtration in order to imitate the high toughness of shellfish. Based on the strategy of strain engineering, a comprehensive experimental bench capable of meeting different strain conditions was connected to a push–pull meter and an LCR digital bridge, and then a computer was used to record the changes in transducer capacitance when an external load was applied to the meter. Graphene oxide (GO) and G/M/G supercells were constructed, and density functional theory (DFT) simulations of the initial energy band structure under strain-free conditions were carried out to determine the relationship between the band gap, conductivity, capacitance, and sensitivity of the G/M/G structure based on band gap theory, and to easily understand the mechanism of the shellfish heterostructure leading to enhanced sensitivity of the sensors. Using two-point bending and axial tensile tests, a flexible pressure sensing device was designed to realize positive strains in the ranges of 0%–5 % and 5%–50 %. The results show that the sensitivity of both GO and G/M/G capacitive pressure sensors decreased with increased strain, and the sensitivity of the G/M/G sensors was significantly improved by 75%–102 % compared to the GO sensors at the same strain. The parallel-plate capacitor model and crack growth theory well explain the experimental results at small and large strains. Our results provide new concepts for the design of novel flexible sonar with high sensitivity and large strain operating range by a simple vacuum filtration method, which can be extended to the design of other high-performance 2D flexible electronic devices.

Mathematical modelling of the partial differential equations in microelectromechanical systems (MEMS) and its applications

This paper presents a model of a doubly clamped electrically actuated microbeam, which is a commonly used structure in microelectromechanical systems (MEMS). The model is based on Euler–Bernoulli beam theory and includes the effect of electrostatic forces on the beam’s deflection. The electric field is modeled using the parallel plate capacitor model, and the deflection of the beam is calculated using the Galerkin method. The behavior of a microbeam subjected to the van der Waals force, which is a weak intermolecular force that arises from the interaction between the beam and a nearby surface. The microbeam is modeled using the Euler–Bernoulli beam theory, and the van der Waals force is modeled using the Lennard–Jones potential. At the last we study the model of MEMS based on multi-walled carbon nanotubes (MWCNTs). MWCNTs have unique mechanical, thermal, and electrical properties, which make them ideal for use in MEMS applications. The approximate solution of the developed models is found by using homotopy perturbation based Aboodh transformation (HPATM). HPATM is a mathematical method used to solve nonlinear equations by converting them into linear forms. This approach involves introducing a small parameter and applying perturbation theory to obtain a solution in a series form. The method’s accuracy is defined based on the existing literature because its solution matched the variation iteration-based Laplace method. Also, we compared its results with the finite difference method. The validity of the stability analysis is further established by examining the stability in the vicinity of the fixed points. Sketches are made of the phase portraits close to the equilibrium points.

Solid–liquid interface disjoining pressure of frozen clay and its effect on water transport

To account for the influence mechanism of solid–liquid interface disjoining pressure on water migration during clay freezing, this study first provides a theoretical calculation model of solid–liquid interface disjoining pressure by combining the thermodynamic equilibrium relation of solid–liquid interface with the parallel plate capacitor model. This is done at the molecular level. An implicit equation for calculating the film thickness d of unfrozen water is also given and the accuracy of the model verified. Secondly, considering that unfrozen water film is anisotropic, the concept of tensor is introduced to show the distribution characteristics and functions of solid–liquid interface disjoining pressure in unfrozen water film. Finally, the effects of solution concentration and undercooling degree on film thickness d of unfrozen water are discussed. The results show that solid–liquid interface disjoining pressure can be expressed by the excess free energy on the surface of charged media, and it is a single-valued function of unfrozen water film thickness. Solid–liquid interface disjoining pressure not only provides an effective driving force for water migration, but also provides growth space for ice lenses; the thickness of unfrozen water film d is negatively correlated with solution concentration and undercooling degree. The research results can provide a theoretical reference for the study of frost heave mechanism in clay soils.

Quantitative capacitance measurements in frequency modulation electrostatic force microscopy

We have proposed a method for quantitative capacitance measurements using frequency modulation electrostatic force microscopy (EFM) with a dual bias modulation method and demonstrated it on n- and p-type Si samples. First, we theoretically derived a conversion formula from a frequency shift of cantilever resonance in EFM into a capacitance value based on the parallel plate capacitor model, by which a pair of an EFM tip and a semiconductor sample is expected to be equivalently represented. Then the capacitance measurements were experimentally conducted on the n- and p-type Si substrates, and the acquired capacitance–voltage curves indicated that the obtained capacitance values were consistent with the expected ones and that the carrier densities evaluated from the depletion capacitances were also in good agreement with those evaluated by the conventional Hall effect measurements. From those results, the validity of our quantitative evaluation method has been well confirmed.

Energy alignment manipulation at the C60/TiO2(110) interface using a blanket molecular dipole approach

Modifying the energy alignment between the frontier levels of a chromophore and the band edges of a semiconductor substrate using a “blanket layer” of molecular dipoles is explored. The electronic structure, measured with ultraviolet and x-ray photoemission spectroscopy, of C60 deposited directly onto the TiO2(110) surface is compared with that of C60 deposited onto the surface covered by a blanket layer of the custom-designed helical peptide Z-(Aib)6-Ipa, which has a large dipole moment of 18.6 D oriented along its molecular axis and pointing toward the substrate. The C60 HOMO level is shifted 600 meV to deeper binding energy in the presence of the blanket layer, in good agreement with what is expected from a simple parallel plate capacitor model. These results demonstrate a simple and versatile strategy for controlling energy level alignment at organic/inorganic interfaces.

Modeling the Electrical Energy Discharged by Lightning Flashes Using Capacitors for Application with Lightning Datasets

AbstractThis study employed a parallel-plate capacitor model by which the electrostatic energy of lightning flashes could be estimated by considering only their physical dimensions and breakdown electric fields in two simulated storms. The capacitor model has previously been used to approximate total storm electrostatic energy but is modified here to use the geometry of individual lightning flashes to mimic the local charge configuration where flashes were initiated. The energy discharged may then be diagnosed without context of a storm’s entire charge structure. The capacitor model was evaluated using simulated flashes from two storms modeled by the National Severe Storms Laboratory’s Collaborative Model for Multiscale Atmospheric Simulation (COMMAS). Initial capacitor model estimates followed the temporal evolution of the flash discharge energy of COMMAS for each storm but demonstrated the need to account for an adjustment factor μc to represent the fraction of energy a flash dissipates, as this model assumes the entire preflash energy is discharged by a flash. Individual values of μc were obtained simply by using the ratio of the COMMAS flash to capacitor energy. Median values were selected to represent the flash populations for each storm, and were in range of . Application of aligned the magnitudes of the capacitor model discharge energy estimates to those of COMMAS and to those estimated in previous studies. Therefore, by considering a μc within range of , application of the capacitor model for observed lightning datasets is suggested.

Analytical Modeling, Design, and Performance Analysis of a Micromirror for Space-Based Multiobject Spectroscopy

This article presents the analytical modeling, design, and performance analysis of an electrostatic micromirror for space-based Multiobject Spectroscopy (MOS). The micromirror under investigation is a double-bridge design with hidden cantilevers architecture in which the deflection is achieved by a combination of bending and twisting cantilevers. A simple closed-form solution of pull-in voltage and deflection is obtained using the parallel-plate capacitor model that assumes micromirror deflection dominated by bending cantilevers due to electrostatic actuation. The design optimization is done to achieve a micromirror of size $200\,\,\mu \text{m}\,\,\times 200\,\,\mu \text{m}$ , deflection $2.5~\mu \text{m}$ , pull-in voltage smaller than 25 V, and a shock survival capacity of at least 10 000 g. The static and dynamic behavior of the optimized design is obtained using the analytical model and compared with the finite-element method (FEM) and characterization results and found to be in close agreement. The micromirror exhibits an analytical pull-in voltage near the FEM and measured pull-in voltage with a deviation of 5% and 0.9%, respectively. The analytical resonance frequency is also closer to simulation and measurement results with a deviation of 4.66% and 2.58%, respectively. The analytical switching time is also very close to the FEM results, with a deviation of 28%. The analytical model and the simple approach of design optimization using tuning parameters presented in the article can be used to design the micromirror according to desired specifications.

Direct Demonstration of Unified Brønsted−Evans−Polanyi Relationships for Proton-Coupled Electron Transfer Reactions on Transition Metal Surfaces

Brønsted-Evans-Polanyi (BEP) relationships, which relate elementary reaction barriers to reaction thermodynamics, have long been discussed in electrochemical science, but demonstration of their existence in heterogeneous electrocatalysis, across many different catalyst surfaces and voltages, is lacking. In this contribution, the BEP model is demonstrated to describe both multiple catalyst surfaces and variable voltages in electrochemical environments. For proton-coupled electron transfer (PCET) to surface nitrogen (N*) and nitric oxide (NO*), reaction energies and activation barriers are calculated using Density Functional Theory (DFT) on a parallel plate capacitor model at three different potentials and for nine different transition metal surfaces. Linear BEP relations that describe all potentials and catalyst surfaces are obtained for these elementary reactions, and the slopes of the correlations are shown to be directly related to the fractional coordinate of the transition states (FCTS) of the reactions. The results, which are explained in terms of Marcus Theory, prove a direct equivalence between unified BEP coefficients, describing both variable catalyst surfaces and voltages, and electrochemical symmetry factors and provide a straightforward means of estimating this quantify for PCET reactions on transition metal surfaces. The resulting relationships, in turn, could lead to predictions of electrocatalytic reactivity trends of enhanced accuracy and efficiency.

Triboelectric and Piezoelectric Nanogenerators for Future Soft Robots and Machines.

SummaryThe triboelectric nanogenerator (TENG) and piezoelectric nanogenerator (PENG) are two recently developed technologies for effective harvesting of ambient mechanical energy for the creation of self-powered systems. The advantages of TENGs and PENGs which include large open-circuit output voltage, low cost, ease of fabrication, and high conversion efficiency enable their application as new flexible sensors, wearable devices, soft robotics, and machines. This perspective provides an overview of the current state of the art in triboelectric and piezoelectric devices that are used as self-powered sensors and energy harvesters for soft robots and machines; hybrid approaches that combine the advantages of both mechanisms are also discussed. To improve system performance and efficiency, the potential of providing self-powered soft systems with a degree of multifunctionality is investigated. This includes optical sensing, transparency, self-healing, water resistance, photo-luminescence, or an ability to operate in hostile environments such as low temperature, high humidity, or high strain/stretch. Finally, areas for future research directions are identified.

Radiation detection using fully depleted 50 μm thick Ni/n-4H-SiC epitaxial layer Schottky diodes with ultra-low concentration of Z1/2 and EH6/7 deep defects

Recent advances in the development of thick 4H-SiC epitaxial layers for the fabrication of surface barrier radiation detectors have been paving the way for their use in highly penetrating radiation detection. Challenges still exist to achieve full depletion all the way to the epilayer width, while maintaining a low leakage current at high reverse bias conditions. We report the fabrication of high-resolution and low leakage current Schottky barrier alpha particle detectors with a large active area of 11 mm2 on 50 μm thick n-type 4H-SiC epitaxial layers, which can be fully depleted. The detectors were cut out of large substrates of 100 mm diameter with a micropipe density <1 cm−2 in the epilayers. Mott–Schottky plots obtained from the capacitance–voltage measurements revealed an effective doping concentration of 1.9×1014cm−3. A parallel plate capacitor model implied that a reverse bias of ∼440 V was needed to achieve a full-depletion width (50 μm). The current–voltage characteristics demonstrated a very low leakage current of 0.45 nA at a reverse bias of −450 V, which is low enough for the detector to be operated at full-depletion bias. In fact, pulse height spectroscopy using a 241Am alpha source, with the detector biased at −120 V, exhibited a well-resolved alpha spectrum with an energy resolution of 0.8% for the alpha peak corresponding to 5486 keV. This energy resolution was maintained consistently up to a full-depletion bias of −440 V. The ultra-stable performance of the detector has been attributed to the remarkably low concentration of carrier lifetime affecting deep-level defects like Z1/2 and EH6/7, which were found to be of the order of 1012cm−3 or less using capacitance mode deep-level transient spectroscopy measurements.

Theories for triboelectric nanogenerators: A comprehensive review

Abstract Triboelectric nanogenerators (TENGs) have attracted much attention as energy harvesting and sensor devices. Compared with experimental means, theoretical analysis is of low cost and time-saving for behavior prediction and structural optimization and is more powerful for understanding the working mechanism of TENGs. In this article, the theoretical system for performance simulation of TENGs has been reviewed systematically. The parallel-plate capacitor model, the distance-dependent electric field (DDEF) model, figures of merit (FOMs), and multi-parameter analysis are introduced. The parallel-plate capacitor model is the most fundamental model of TENGs, which is used to simulate the output of TENGs with planar configurations. For non-planar TENGs, the DDEF model is proposed, according to which the electric field is assumed to be distance-dependent rather than being uniform throughout the space. Further, to realize the standardization of TENGs, a series of FOMs are proposed as the standardized evaluation tools for TENGs’ output performance, which are used to reflect the influence of device parameters on the output from different aspects. Lastly, the multi-parameter analysis is introduced to consider the impact of multiple parameters on the output of TENGs simultaneously. These theories constitute the theoretical simulation system of TENGs, which could be used to guide the experimental work on TENGs and boost device optimization in commercial manufacturing.

Multi-Scale Model for Describing the Effect of Pore Structure on Carbon-Based Electric Double Layer

On the basis of the characteristics of wide pore size distribution of biomass activated carbon, this study reports a multiscale model to describe the effect of pore structure on electric double layer capacitor. The capacitance of micropores, mesopores, and macropores in H2SO4 and KOH aqueous solutions are simulated by sandwich-type capacitor model, spherical capacitor model, and parallel plate capacitor model, respectively. Chestnut shell is selected as precursor in this experiment. According to the different chemical properties and activation mechanisms, five types of carbon are synthesized by chemical activation using H3PO4, ZnCl2, K2CO3, and KOH as activators including the one without activation. The influence of carbonization and activation processes on pore structure is studied by the apparent morphology characterization collected by scanning electron microscopy. Detailed pore structure information is obtained by both N2 adsorption–desorption isotherms and nonlocal density functional theory. By analyzing the effects of pore curvature and densification degree of solvent molecules on the relative dielectric constant εr and the thickness of the electric double layer d at the electrode–electrolyte interface, it is revealed that carbon materials have a sieving effect on electrolyte ions. The capacitance measured by galvanostatic charge–discharge is in good agreement with the simulated value, which indicates that the parameters in the model can reasonably predict the capacitance behavior of hierarchical porous carbon. This work provides a feasible scheme for estimating the electric double layer capacitance produced by hierarchical porous carbon, which can help in electrode materials selection in supercapacitors with different electrolytes.

Helical Peptides Design for Molecular Dipoles Functionalization of Wide Band Gap Oxides.

The use of helical hexapeptides to establish a surface dipole layer on a TiO2 substrate, with the goal of influencing the energy levels of a coadsorbed chromophore, is explored. Two helical hexapeptides, synthesized from 2-amino isobutyric acid (Aib) residues, were protected at the N-terminus with a carboxybenzyl group (Z) and at the C-terminus carried either a carboxylic acid or an isophthalic acid (Ipa) anchor group to form Z-(Aib)6-COOH or Z-(Aib)6-Ipa, respectively. Using a combination of vibrational and photoemission spectroscopies, bonding of the two peptides to TiO2 surfaces (either nanostructured or single-crystal TiO2(110)) was found to be highly dependent on the anchor group, with Ipa establishing a monolayer much more efficiently than COOH. Furthermore, a monolayer of Z-(Aib)6-Ipa on TiO2(110) was exposed for different binding times to a solution of a zinc tetraphenylporphyrin (ZnTPP) derivative terminated with an Ipa anchor group (ZnTPP-P-Ipa). Photoemission spectroscopy revealed that ZnTPP-P-Ipa partly displaced Z-(Aib)6-Ipa, forming a coadsorbed monolayer on the oxide surface. The presence of the peptide molecular dipole shifted the HOMO levels of the ZnTPP group to lower energy by ∼300 meV, in accordance with a simple parallel plate capacitor model. These results suggest that a mixed-layer approach, involving coadsorption of a strong molecular dipole compound with a chromophore, is a versatile method to shift the energy levels of such chromophores with respect to the band edges of the substrate.

Quantitative electrostatic force measurement and characterization based on oscillation amplitude using atomic force microscopy

Measurement of electrostatic force at the micro-/nanoscale has a great scientific value and engineering significance. This paper develops a new determination method of electrostatic forces based on Kelvin probe force mode in atomic force microscopy (AFM). Applying DC voltage and AC voltage simultaneously, we measured the oscillation amplitudes of the probe at two specific frequencies. By the equivalent parallel-plate capacitor model and the vibration theory, we established quantitative relationship between electrostatic force and AFM raw data, and derived a complete and practical formula for calculating electrostatic force. Then, the fundamental characteristics of electrostatic force with time were revealed, and the changes of all components of electrostatic force with tip–sample distance and applied AC peak voltage were discussed in detail. The regulation effects of the distance and the voltage on the total electrostatic force were also compared. Furthermore, we pointed out the main advantages and disadvantages of this method and stated the applicable conditions of the conclusions according to the experimental results and theoretical analysis.

Direct Demonstration of Unified Brønsted−Evans−Polanyi Relationships for Proton-Coupled Electron Transfer Reactions on Transition Metal Surfaces

The existence of Brønsted-Evans-Polanyi (BEP) relationships, which relate elementary reaction barriers to reaction thermodynamics across a space of different catalysts, has been extensively investigated for reactions on traditional heterogeneous catalysts, and BEP’s are known to provide the central physical paradigm underlying the existence of volcano plots and other trends-based descriptions of catalytic reactivity. However, the extension of such relationships to elementary electrochemical reactions, simultaneously spanning a space of both different applied voltages and different catalyst surfaces, has been widely discussed but never verified. In this contribution, the BEP model is explicitly shown to describe both multiple catalyst surfaces and variable voltages in electrochemical environments. For proton-coupled electron transfer to surface nitrogen (N*) and nitric oxide (NO*), reaction energies and activation barriers are calculated using density functional theory on a parallel plate capacitor model at three different potentials and for nine different transition metal surfaces. Linear BEP relations that describe all potentials and catalyst surfaces are obtained for these elementary reactions, and the slopes of the correlations are shown to be directly related to the fractional coordinate of the transition states (FCTS) of the reactions. The results, which are explained in terms of Marcus Theory, prove a direct equivalence between unified BEP coefficients, describing both variable catalyst surfaces and voltages, and electrochemical symmetry factors and provide a straightforward means of estimating this quantify for proton-coupled electron transfer reactions on transition metal surfaces. The resulting relationships, in turn, could lead to predictions of electrocatalytic reactivity trends of enhanced accuracy and efficiency.

Substitution‐induced near phase transition with Maxwell–Wagner polarization in SrBi2(Nb1−xAx)2O9 ceramics [A = W, Mo and x = 0, 0.025

AbstractThe synthesis, micro‐structure, spectroscopic, and dielectric properties of [with AW, Mo and , 0.025] ceramics were systematically studied. A relative density of 98% was obtained for all the samples using a two‐step solid state sintering process. XRD images showed that a single phase layered perovskite structure of (SBN) was formed. The orthorhombic structure with phase group was found up to ∼2.5 at.% substitution of W and Mo into the SBN matrix. SEM revealed the rod‐like grain structure similar to the Maxwell–Wagner (MW) parallel plate capacitor model in SBN ceramic, whereas smaller heterogeneous grain structure was observed in W and Mo donor doped ceramics. The initial high value of real and imaginary part of relative permittivity also indicated the presence of interfacial MW relaxation in the SBN ceramics. The experimental data fit well to the theoretical data obtained from MW polarization model in SBN ceramics. The possible origin of the difference of the properties present in the doped sample has been explained based on grain size, orientation, and modification done in the ceramic matrices.

Multi-physics modelling and experimental validation of electrovibration based haptic devices

Electrovibration tactile displays exploit the polarisation of the finger pad, caused by an insulated high voltage supplied plate. This results in electrostatic attraction, which can be used to modulate the users' perception of an essentially flat surface and induce texture sensation. Two analytical models of electrovibration, based on parallel plate capacitor assumption, are demonstrably taken and assessed by comparisons with experimental results published in literature. In addition, an experimental setup was developed to measure the electrostatic force between the finger pad and a high voltage supplied plate in a static and out-of-contact state in order to support the use of parallel plate capacitor model. Development, validation, and application of a computational framework for modelling tactile scenarios on real and virtual surfaces rendered by electrovibration technique is presented. The framework incorporates fully parametric model in terms of materials and geometry of the finger pad, virtual and real surfaces, and can serve as a tool for virtual prototyping and haptic rendering in electrovibration tactile displays. This is achieved by controlling the applied voltage signal in order to guarantee similar lateral force cues in real and simulated surfaces.

High and rapid alkali cation storage in ultramicroporous carbonaceous materials

To achieve better supercapacitor performance, efforts have focused on increasing the specific surface area of electrode materials to obtain higher energy and power density. The control of pores in these materials is one of the most effective ways to increase the surface area. However, when the size of pores decreases to a sub-nanometer regime, it becomes difficult to apply the conventional parallel-plate capacitor model because the charge separation distance (d-value) of the electrical double layer has a similar length scale. In this study, ultramicroporous carbonaceous materials (UCMs) containing sub-nanometer-scale pores are fabricated using a simple in situ carbonization/activation of cellulose-based compounds containing potassium. The results show that alkali cations act as charge carriers in the ultramicropores (<0.7 nm), and these materials can deliver high capacitances of ∼300 F g−1 at 0.5 A g−1 and 130 F g−1, even at a high current rate of 65 A g−1 in an aqueous medium. In addition, the UCM-based symmetric supercapacitors are stable over 10,000 cycles and have a high energy and power densities of 8.4 Wh kg−1 and 15,000 W kg−1, respectively. This study provides a better understanding of the effects of ultramicropores in alkali cation storage.

Charge transfer of single laser crystallized intrinsic and phosphorus-doped Si-nanocrystals visualized by Kelvin probe force microscopy

Isolated intrinsic and phosphorus doped (P-doped) Si-nanocrystals (Si-NCs) on n- and p-Si substrates are fabricated by excimer laser crystallization techniques. The formation of Si-NCs is confirmed by atomic force microscopy (AFM) and conductive AFM measurements. Kelvin probe force microscopy (KPFM) is then carried out to visualize the trapped charges in a single Si-NC dot which derives from the charge transfer between Si-NCs and Si substrates due to their different Fermi levels. The laser crystallized P-doped Si-NCs have a similar Fermi level around the mid-gap to the intrinsic counterparts, which might be caused by the inactivated impurity atoms or the surface states-related Fermi level pinning. A clear rise of the Fermi level in P-doped Si-NCs is observed after a short time thermal annealing treatment, indicating the activation of dopants in Si-NCs. Moreover, the surface charge quantity can be estimated using a simple parallel plate capacitor model for a quantitative understanding of the KPFM results at the nanoscale.

Tuning Energy Level Alignment At Organic/Semiconductor Interfaces Using a Built-In Dipole in Chromophore–Bridge–Anchor Compounds

A chromophore–bridge–anchor molecular architecture is used to manipulate the molecular level energy position, with respect to the band edges of the substrate, of a chromophore bound to a surface via an anchor group. An energy shift of the chromophore’s frontier orbitals is induced by the addition of an oriented molecular dipole into the bridge part of the compound. This principle has been tested using three Zinc Tetraphenylporphyrin derivatives of comparable structure: two of which possess a dipole, but pointing in opposite directions and, for comparison, a compound without a dipole. UV–vis absorption and emission spectroscopies have been used to probe the electronic structure of the compounds in solution, while UV photoemission spectroscopy has been used to measure the relative position of the molecular levels of the chromophore with respect to the band edges of a ZnO(11–20) single crystal substrate. It is shown that the introduction of a molecular dipole does not alter the chromophore’s HOMO–LUMO gap, and that the molecular level alignment of the compounds bound to the ZnO surface follows the behavior predicted by a simple parallel-plate capacitor model.