Local Electric Field Strength Research Articles

The effect of viscosity on the self-similar growth of conic cusps on the surface of a conducting liquid in an electric field: Limiting cone angle

The dynamics of the formation of conic cusps on an initially smooth surface of a perfectly conducting liquid (liquid metal) in an external electric field is analytically studied. When the singularity is formed, the apex curvature radius of the accelerating protrusion, local electric field strength, and fluid velocity become infinite in a finite time. It has been demonstrated that two scales with different types of fluid behavior can be distinguished in this process. At the nanoscale (the curvature radius of the conic apex is tens of nanometers or less; the electric field strength at the apex is about 108 V/cm and higher), viscous effects play a decisive role, and a cone with the limiting opening angle of 33.1° is formed. On the macroscopic scale (the local field strength is less than 108 V/cm for liquid metals), the ideal fluid approximation is applicable, and a cone of the opening angle 98.6° (Taylor's angle) develops. In both cases, self-similar fluid flow regimes are realized, for which the spatial scale decreases with time following the power law (t0 – t)2/3, where t0 is the blowup time. In this process, the Weber number remains practically unchanged and, according to our estimates, approximately equal to 102; at the same time, the Reynolds number decreases as (t0 – t)1/3.

Charge Shielding Effect of Sodium Ions in Improving The Hydrophobicity and Performance of Co/Na‐SSZ‐13 Zeolite for Passive NOx Adsorber

AbstractWith increasingly stringent regulations, the reduction of NOx emissions during vehicle cold start is a major challenge. Pd‐modified zeolites are considered as the most promising passive NOx adsorber (PNA) for cold start NOx control. Nevertheless, the scarcity and the high cost of Pd limit its practical application. Herein, a non‐precious metal modified Co/Na‐SSZ‐13 zeolite for low‐temperature NOx adsorption is reported. This one‐pot synthesized Co/Na‐SSZ‐13 exhibits an extraordinary NOx storage capacity (212 µmol gcat−1) under humid conditions (3% H2O v/v), which is more than double that of conventional Co or Pd‐modified SSZ‐13. This is attributed to the absence of the inert cobalt phyllosilicate commonly found in conventional Co‐SSZ‐13, as well as the highly dispersed Co and Na ions as the effective NOx adsorption sites in Co/Na‐SSZ‐13. Moreover, the presence of Na ions shields the negative charge generated by the Al center and weakens the local electric field strength of the Al and Co centers. This lowers the H2O adsorption energy and improves the zeolite hydrophobicity, which enhances the NO storage capacity of the Co/Na‐SSZ‐13 under humid conditions. This work highlights the Co/Na‐SSZ‐13, synthesize via a simple and high‐efficiency method, as a promising substitute for noble metal PNA materials.

Simulation analysis of synthetic electric field of UHV transmission line under mountain fire condition

Factors such as high temperature, charge density and charged particles have a major impact on the insulation strength of the transmission line gap. When the DC transmission line is in normal operation, the surface of the conductor is easy to adsorb dirt due to the environmental influences, so the local electric field strength is larger than the critical field strength of the corona discharge, and the gas molecules in the air are ionized to form space charges. The electric field of the space charge is superimposed with the electric field of the wire and the earth (nominal electric field) to form a synthetic electric field. In this work, the calculation model of the synthetic electric field is created and the influence of mountain fires on the synthetic electric field of the transmission line is simulated and analyzed. The influence of flame temperature, charge density, particle type and shape on the electric field is simulated and investigated. The law of variation of the electric field of the transmission line in mountain fire under different factors is obtained. The distorting effect of particles on the electric field under the UHV DC transmission line is simulated. The distorting effect of particle size and particle chain on the synthetic electric field is obtained and the simulation results are compared to the calculation results.

On the Development of Injection Cathode Electrodes for EHD Transducers

Purpose To study the possibility of changing cathode injection in a grid axisymmetric EHD transducer with planeparallel modified electrodes.Methods. An estimate of the influence of the edge effect of electrode grids on the surface conductivity in the periphery of the interelectrode gap was obtained by numerical simulation, and the optimal geometry of the electrode holders of the grid EHD transducer was determined. Using the method of numerical calculation in the software environment Agros 2D, as well as using the analysis of SEM scans and the method of estimating the form factor of structures, the parameters of local electric fields of the structures of the surfaces of wires of grid electrodes modified during laser scribing were obtained.Results. The results of the development of a grid system of electrodes for electrohydrodynamic converters with enhanced cathodic charge injection are presented. The influence of the edge effect on the operation of EHD transducers is analyzed. The possibility of improving the grid electrode system of a model EHD pump is described. The composition and shape of microand nanostructures after scribing on the FMark-20RL laser marking complex have been studied. A qualitative estimate of the local electric field strength on nanostructures obtained by laser scribing of brass grids with a characteristic radius of 50 nm is made, which indicates an increase in the cathode injection of negative charges in the EHD system. With a distance between the electrodes of 1.5 mm and a potential difference between the electrodes of 1.5 kV/cm, the magnitude of the local tension at the top of the nanostructure with a curvature radius of about 50 nm can reach 5.5⋅107 V/cm.Conclusion. Laser scribing in the form of concentric circles of brass grid electrodes makes it possible to intensify cathodic charge injection by amplifying local electric fields from microand nanostructures. The use of plexiglass dielectric holders can reduce surface leakage currents at the periphery of grid electrodes.

Creation of Nanotips on ITO Electrode by Nanoparticle Deposition: An Easy Way to Enhance the Performance of Electrically Responsive Photonic Crystal and Fabricate Electrically Triggered Anticounterfeiting Tags

AbstractElectrically responsive photonic crystals (ERPC) are promising materials for electrophoretic displays, smart windows, and tunable optical devices. However, the high working voltage limits the application of most polar ERPCs because it damages color saturation, response stability, and reversibility. Herein, an easy but general method based on the modification of electrodes with nanoparticles is developed to improve ERPC's performance. The deposition of Au, Cu, or Cu2O nanoparticles created nanotip structures on the electrode, which enhanced the charge injection and local electric field strength, lowered 43% of the working voltage, and increased the color saturation. Meanwhile, the lowered voltage inhibited the electrodeposition of colloidal particles and the electrochemical reaction, which also improved the stability and reversibility of the electrical response. Based on the region‐selective modification of the electrode and the resulting asymmetric electrical response, an electrically triggered tag with a “pattern showing/hiding” effect is fabricated for anticounterfeiting purposes.

High Sensitivity Surface Plasmon Resonance Magnetic Field Sensor Based on Au/Gold Nanoparticles/Magnetic Fluid in the Hollow Core Fiber

A type of surface plasmon resonance (SPR) magnetic field sensor based on Au/gold nanoparticles/magnetic fluid (MF)-processed hollow core fiber is proposed in this work, which fully utilizes SPR’s high sensitivity to RI and the magnetron refractive index characteristic of MF. The metal material Au excites SPR and gold nanoparticles excite the localized surface plasmon resonance (LSPR). The coupling of surface plasmon polariton (SPP) with localized surface plasmon (LSP) increases the local electric field strength, thus improving the sensor’s sensitivity. Both the theoretical analysis on the sensing mechanism and the experimental findings demonstrate that this novel SPR magnetic field sensor has a wide measurement range and high sensitivity. In the range of magnetic field strength from 0 to 603 Gs, the sensitivity can reach up to 156 pm/Gs, and the linearity is good (the coefficient of determination is 0.996). Compared with other optical fiber magnetic field sensors, the sensor proposed in this paper has the benefits of easy fabrication, excellent sensitivity, simple structure, strong anti-interference ability, and wide measurement range, exhibiting significant application potentials in the fields of military drills, aerospace, etc.

Surface-Enhanced Raman Scattering (SERS) Substrates Based on Ag-Nanoparticles and Ag-Nanoparticles/Poly (methyl methacrylate) Composites.

SERS substrates formed by spherical silver nanoparticles (Ag-NPs) with a 15 nm average diameter adsorbed on Si substrate at three different concentrations and Ag/PMMA composites formed by an opal of PMMA microspheres of 298 nm average diameter were synthesized. The Ag-NPs were varied at three different concentrations. We have observed from SEM micrographs, in the Ag/PMMA composites, the periodicity of the PMMA opals is slightly altered as the Ag-NP concentration is increased; as a consequence of this effect, the PBGs maxima shift toward longer wavelengths, decrease in intensity, and broaden as the Ag-NP concentration is increased in the composites. The performance of single Ag-NP and Ag/PMMA composites as SERS substrates was determined using methylene blue (MB) as a probe molecule with concentrations in the range of 0.5 µM to 2.5 µM. We found that in both single Ag-NP and Ag/PMMA composites as SERS substrates, the enhancement factor (EF) increases as the Ag-NP concentration is increased. We highlight that the SERS substrate with the highest concentration of Ag-NPs has the highest EF due to the formation of metallic clusters on the surface, which generates more "hot spots". The comparison of the EFs of the single Ag-NP with those of Ag/PMMA composite SERS substrates shows that the EFs of the former are nearly 10-fold higher than those of Ag/PMMA composites. This result is obtained probably due to the porosity of the PMMA microspheres that decreases the local electric field strength. Furthermore, PMMA exerts a shielding effect that affects the optical efficiency of Ag-NPs. Moreover, the metal-dielectric surface interaction contributes to the decrease in the EF. Other aspect to consider in our results is in relation to the difference in the EF of the Ag/PMMA composite and Ag-NP SERS substrates and is due to the existing mismatch between the frequency range of the PMMA opal stop band and the LSPR frequency range of the Ag metal nanoparticles adsorbed on the PMMA opal host matrix.

Self-Powered Sterilization System for Wearable Devices Based on Biocompatible Materials and Triboelectric Nanogenerator

Wearable electronics with multifunction and convenience are entering a period of rapid development. However, the longer people wear electronic devices, the easier it is for bacteria to infect the skin. Sterilization of wearables has received little research, partly because mature high-voltage sterilization systems require energy sources, which will greatly restrict the large-scale applications of wearable devices. Therefore, a self-powered sterilization system with high comfort and safety is strongly appealing. To solve the above problem, we design a wearable, self-powered sterilization system with a biocompatible nano/microporous fiber triboelectric nanogenerator (NMF-TENG) as the energy source and an interdigital electrode for better bactericidal performance. Ag nanowires (AgNWs) and carbon nanotube (CNT) are added to the indium tin oxide (ITO)-based interdigital electrode to improve the conductivity, bending performance, and local electric field strength. Due to the tip effect, the local electric field of the electrode can be improved as high as 1 MV m–1, which can kill the bacteria. The system can achieve a long-term sterilization rate of up to 90%, which has great application potential in the sterilization direction of wearable electronic devices.

Process optimization of nanosecond pulsed packed‐bed discharge plasma for SF6 degradation based on response surface methodology

AbstractIn this work, a nanosecond pulsed packed‐bed discharge (PBD) plasma was developed for SF6 degradation under different dilution gases. The discharge form transfers from filamentary discharge to the combination of surface discharge and microdischarge after introducing the packing material regardless of the dilution gas used, and the local electric field strength and SF6 degradation performance are promoted. The mean electron energy and rate coefficient for SF6 excitation in SF6/Ar system are significantly higher than those in SF6/N2 or SF6/air system, which results in higher SF6 degradation efficiency in SF6/Ar system. Moreover, the response surface methodology based on the Box–Behnken design model was constructed to optimize several key process parameters including pulsed voltage, gas flow rate, oxygen content, and relative humidity, as well as assess the contribution of each parameter to SF6 degradation. The proposed optimization model shows a satisfactory correlation between the predicted and the experimental results. The energy yield concerning SF6 degradation in nanosecond pulsed PBD plasma achieves approximately 75.3 g/kWh with nearly complete degradation. This work is expected to provide an efficient and energy‐saving plasma technique for SF6 degradation.

Observation of strong terahertz field-induced second harmonic generation in plasma filaments.

We report the observation of terahertz field-induced second harmonic (TFISH) generation produced by directly mixing an optical probe beam onto femtosecond plasma filaments. The produced TFISH signal is spatially separated from the laser-induced supercontinuum by impinging on the plasma at a noncollinear angle. The conversion efficiency of the fundamental probe beam to its second harmonic (SH) beam is greater than 0.02%, which represents a record in optical probe to TFISH conversion efficiency that is nearly five orders of magnitude larger than previous experiments. We also present the terahertz (THz) spectral buildup of the source along the plasma filament and retrieve coherent terahertz signal measurements. This method of analysis has the potential to provide local electric field strength measurements inside of the filament.

Three-dimensional nanoprinting with charged aerosol focusing via an electrified mask

Three-dimensional (3D) nanoprinting techniques attract significant research interest due to their capacity to manufacture diverse structures. The techniques enhance the performance of various applications by realizing unique functionalities from the size and geometrical effects of small-scale 3D structures. A recently reported 3D nanoprinting technique that utilizes charged aerosol jets generated by ion accumulation on the dielectric mask as a printing tool is promising for enabling parallel intricate 3D nanostructures in atmospheric conditions. In this technique, modulating the voxel size of the printed structure was difficult because the ion accumulation that was necessary for the generation of converged aerosol jets was not easy to be controlled. Here, we demonstrate a charged aerosol jet-based advanced 3D nanoprinting technique that enables the programming of the voxel size of 3D nanostructures by replacing the ion accumulated dielectric mask with the electrified mask. The electrified mask readily controls the local electric field strength between the mask and conducting substrate, which influences the diameter of charged aerosol jets and thus determines the voxel size of the 3D nanostructures. By additionally controlling the distance between the mask and substrate and changing the hole size of the mask, we show that the voxel size can be further altered. Moreover, moving the substrate in three-dimensions prints desired shapes of the 3D nanostructures, such as overhanging structures and helices with controlled voxel sizes. In addition, we present theoretical approaches to predict the geometries and voxel sizes of 3D nanostructures.

Action spectra and mechanisms of (in) efficiency of bipolar electric pulses at electroporation

The reversal of the electric field direction inhibits various biological effects of nanosecond electric pulses (nsEP). This feature, known as “bipolar cancellation,” enables interference targeting of nsEP bioeffects remotely from stimulating electrodes, for prospective applications such as precise cancer ablation and non-invasive deep brain stimulation. This study was undertaken to achieve the maximum cancellation of electroporation, by quantifying the impact of the pulse shape, duration, number, and repetition rate across a broad range of electric field strengths. Monolayers of endothelial cells (BPAE) were electroporated in a non-uniform electric field. Cell membrane permeabilization was quantified by YO-PRO-1 (YP) dye uptake and correlated to local electric field strength. For most conditions tested, adding an opposite polarity phase reduced YP uptake by 50–80 %. The strongest cancellation, which reduced YP uptake by 95–97 %, was accomplished by adding a 50 % second phase to 600-ns pulses delivered at a high repetition rate of 833 kHz. Strobe photography of nanosecond kinetics of membrane potential in single CHO cells revealed the temporal summation of polarization by individual unipolar nsEP applied at sub-MHz rate, leading to enhanced electroporation. In contrast, there was no summation for bipolar pulses, and increasing their repetition rate suppressed electroporation. These new findings are discussed in the context of bipolar cancellation mechanisms and remote focusing applications.

Unusual local electric field concentration in multilayer ceramic capacitors

Local electric-field around multitype pores (dielectric pore, interface pore, electrode pore) in multilayer ceramic capacitors (MLCCs) was investigated using Kelvin probe force microscopy combined with the finite element simulation to understand the effect of pores on the electric reliability of MLCCs. Electric-field is found to be concentrated significantly in the vicinity of these pores and the strength of the local electric-field is 1.5–5.0 times of the nominal strength. Unexpectedly, the concentration degree of the pores in the inner electrode is much higher than that in the dielectrics and dielectric-electrode interfaces. Meanwhile, geometry orientations are found to have a remarkable influence on the local electric field strength. The pores act as an insulation degradation precursor via local electric, thermal center, and oxygen vacancies accumulation center. Such unusual local electric field concentration of multitype pores can provide new insights into the understanding of insulation degradation evolution, processing tailoring and design optimization for MLCCs.

Regulation of Interfacial Polarization and Local Electric Field Strength Achieved Highly Energy Storage Performance in Polyetherimide Nanocomposites at Elevated Temperature via 2D Hybrid Structure

AbstractDielectric materials with excellent high‐temperature energy storage performances are urgently demanded in advanced electronic market. However, the sharply reduced energy storage capabilities caused by conduction loss impede the applications of polymer‐based nanocomposites at harsh environments. In this work, the 2D hybrid structure fillers of boron nitride nanosheets‐titanium dioxide (BNNSs‐TiO2), where TiO2 nanoparticles tightly wrap around the 2D BNNSs, are fused with polyetherimide (PEI) forming polymer nanocomposite films. The finite element simulation and experiment results indicate that the hybrid structure 2D BNNSs‐TiO2 can effectively regulate local electric field strength and interfacial polarization, facilitating the enhancement in energy storage properties. Accordingly, the composite film delivers a superior discharged energy density (≈4 J cm−3) and charging/discharging efficiency (≈90%) at 150 °C, better than recently discussed high‐temperature pristine polymer and their composite films. This contribution offers a feasible idea to explore reliable dielectric capacitors at high temperature.

Neuronal activity under transcranial radio-frequency stimulation in metal-free rodent brains in-vivo

As the use of Radio Frequency (RF) technologies increases, the impact of RF radiation on neurological function continues to receive attention. Whether RF radiation can modulate ongoing neuronal activity by non-thermal mechanisms has been debated for decades. However, the interactions between radiated energy and metal-based neural probes during experimentation could impact neural activity, making interpretation of the results difficult. To address this problem, we modified a miniature 1-photon Ca2+ imaging device to record interference-free neural activity and compared the results to those acquired using metal-containing silicon probes. We monitored the neuronal activity of awake rodent-brains under RF energy exposure (at 950 MHz) and in sham control paradigms. Spiking activity was reliably affected by RF energy in metal containing systems. However, we did not observe neuronal responses using metal-free optical recordings at induced local electric field strengths up to 230 V/m. Our results suggest that RF exposure higher than levels that are allowed by regulatory limits in real-life scenarios do not affect neuronal activity.

The performance of Al plasmon enhanced β-Ga<sub>2</sub>O<sub>3</sub> solar-blind photodetector

<p indent="0mm">The surface plasmon effect based on metal nanoparticles can enhance the local electric field strength and exhibit excellent light trapping capabilities, which can effectively improve the performance of optoelectronic devices. In this study, combined with the Finite Difference Time Domain (FDTD) method and magnetron sputtering technology, the effects of metallic Al nanoparticles on the photoelectric characteristics of β-Ga₂O₃ solar-blind photodetectors are studied theoretically and experimentally. The results show that Al nanoparticles with a radius of <sc>30 nm</sc> can produce an LSPR effect under <sc>254 nm</sc> solar-blind ultraviolet light. Due to the LSPR effect of Al NPs, the spectral responsivity and detectivity of the β-Ga₂O₃ solar-blind photodetector have been increased by 4.7 times and 6 times, respectively, and the dark current of the device has been reduced to 62.5% of the original value. This study provides a theoretical and experimental basis for the application of Al NPs in the solar-blind band, and provides a new method for further improving the performance of solar-blind photodetectors.

Interface engineering to optimize polarization and electric breakdown strength of Ba2Bi3.97Pr0.03Ti5O18/BiFeO3 ferroelectric thin-film for high-performance capacitors

Electrostatic capacitors based on dielectrics are ubiquitous components for applications in modern electronics and electric power systems. However, the relatively low energy density of electrostatic capacitors, which is one or two orders of magnitude lower than that of the batteries, has greatly hindered the implementation of its in energy storage devices. Here, we propose a strategy to overcome the tradeoff between high polarizability and breakdown electric field, and attain great enhancement energy storage density in the lead-free (Ba2Bi3.97Pr0.03Ti5O18/BiFeO3)N (BBPT/BFO)N multilayer ferroelectric thin films with different BFO layers through interface engineering. The interface engineering could be utilized to concurrently modify both polarization and local electric field strength caused by the synergistic effect of multiple polar structures and electric field amplifying effect. Accordingly, the discharged energy density of the optimized (BBPT/BFO)1 ferroelectric thin-film capacitors as high as ∼ 79.3 J/cm3 with discharged efficiency exceeding ∼ 75 % are achieved. Combined with its fatigue-free, favorable temperature and frequency stabilities, the multilayer ferroelectric thin films of BBPT/BFO could be a promising dielectric material for practical energy storage applications.

Local Charge Distributions, Electric Dipole Moments, and Local Electric Fields Influence Reactivity Patterns and Guide Regioselectivities in α-Ketoglutarate-Dependent Non-heme Iron Dioxygenases.

Non-heme iron dioxygenases catalyze vital processes for human health related to the biosynthesis of essential products and the biodegradation of toxic metabolites. Often the natural product biosyntheses by these non-heme iron dioxygenases is highly regio- and chemoselective, which are commonly assigned to tight substrate-binding and positioning. However, recent high-level computational modeling has shown that substrate-binding and positioning is only part of the story and long-range electrostatic interactions can play a major additional role.In this Account, we review and summarize computational viewpoints on the high regio- and chemoselectivity of α-ketoglutarate-dependent non-heme iron dioxygenases and how external perturbations affect the catalysis. In particular, studies from our groups have shown that often a regioselectivity in enzymes can be accomplished by stabilization of the rate-determining transition state for the reaction through external charges, electric dipole moments, or local electric field effects. Furthermore, bond dissociation energies in molecules are shown to be influenced by an electric field effect, and through targeting a specific bond in an electric field, this can lead to an unusually specific reaction. For instance, in the carbon-induced starvation protein, we studied two substrate-bound conformations and showed that regardless of what C-H bond of the substrate is closest to the iron(IV)-oxo oxidant, the lowest hydrogen atom abstraction barrier is always for the pro-S C2-H abstraction due to an induced dipole moment of the protein that weakens this bond. In another example of the hygromycin biosynthesis enzyme, an oxidative ring-closure reaction in the substrate forms an ortho-δ-ester ring. Calculations on this enzyme show that the selectivity is guided by a protonated lysine residue in the active site that, through its positive charge, triggers a low energy hydrogen atom abstraction barrier. A final set of examples in this Account discuss the viomycin biosynthesis enzyme and the 2-(trimethylammonio)ethylphosphonate dioxygenase (TmpA) enzyme. Both of these enzymes are shown to possess a significant local dipole moment and local electric field effect due to charged residues surrounding the substrate and oxidant binding pockets. The protein dipole moment and local electric field strength changes the C-H bond strengths of the substrate as compared to the gas-phase triggers the regioselectivity of substrate activation. In particular, we show that in the gas phase and in a protein environment C-H bond strengths are different due to local electric dipole moments and electric field strengths. These examples show that enzymes have an intricately designed structure that enables a chemical reaction under ambient conditions through the positioning of positively and negatively charged residues that influence and enhance reaction mechanisms. These computational insights create huge possibilities in bioengineering to apply local electric field and dipole moments in proteins to achieve an unusual selectivity and specificity and trigger a fit-for-purpose biocatalyst for unique biotransformations.

Using a Digital Twin of an Electrical Stimulation Device to Monitor and Control the Electrical Stimulation of Cells in vitro.

Electrical stimulation for application in tissue engineering and regenerative medicine has received increasing attention in recent years. A variety of stimulation methods, waveforms and amplitudes have been studied. However, a clear choice of optimal stimulation parameters is still not available and is complicated by ambiguous reporting standards. In order to understand underlying cellular mechanisms affected by the electrical stimulation, the knowledge of the actual prevailing field strength or current density is required. Here, we present a comprehensive digital representation, a digital twin, of a basic electrical stimulation device for the electrical stimulation of cells in vitro. The effect of electrochemical processes at the electrode surface was experimentally characterised and integrated into a numerical model of the electrical stimulation. Uncertainty quantification techniques were used to identify the influence of model uncertainties on relevant observables. Different stimulation protocols were compared and it was assessed if the information contained in the monitored stimulation pulses could be related to the stimulation model. We found that our approach permits to model and simulate the recorded rectangular waveforms such that local electric field strengths become accessible. Moreover, we could predict stimulation voltages and currents reliably. This enabled us to define a controlled stimulation setting and to identify significant temperature changes of the cell culture in the monitored voltage data. Eventually, we give an outlook on how the presented methods can be applied in more complex situations such as the stimulation of hydrogels or tissue in vivo.

Front Cover: Investigation of entrance effects on particle electrophoretic behavior near a nanopore for resistive pulse sensing

DOI: 10.1002/elps.202100162 The cover picture illustrates entrance effects of a solid-state nanopore immersed in an electrolyte solution on the electrophoretic behavior of a charged biomolecule. The intense electric field in the high electrical resistance nanopore generated by an external electric potential bias across the membrane gives rise to a significant electroosmotic flow opposing the molecule migration. Whether or not the molecule can translocate through the nanopore for resistive pulse sensing is subject to both the zeta potential difference between the molecule and nanopore and the variation of the local electric field strength from the nanopore-reservoir junction into the nanopore.