Current Electrical Conductivity Research Articles

Explanation of the Compensation Law and the Isokinetic Point in the Electrical Conduction of Crosslinked Polyethylene

Thermally activated direct current (DC) electrical conductivity in low-density polyethylene (LDPE) is known to be subject to the compensation law. Accordingly, the preexponential factor follows a specific relation with activation energy, reducing overall changes in conductivity. This relationship is governed by the Meyer-Neldel temperature. However, there is no published evidence for a corresponding isokinetic point, a temperature where the conductivity of all LDPE samples is the same. Here, it is determined that the compensation law applies to both DC and alternating current (AC) conduction for LDPE and for crosslinked polyethylene (XLPE) without an observed isokinetic point. The potential origins of compensation in polyethylene are discussed as well as reasons for similarity between LDPE and XLPE. It is observed that prolonged water exposure removed the compensation behavior. Meanwhile, preheating samples in the oven prior to measurements modifies the compensation behavior and reduced the spread around the isokinetic point. It is thus deduced that an isokinetic point can be observed in polyethylene but is obscured by contributions from water and other impurities.

Comparative Study on the Direct Current Electrical Conduction in Monolayer and Bilayer Plasma Polymerized Thin Films

A comparative study on the nature of direct current electrical conduction in the monolayer and bilayer plasma polymerized thin films has been discussed in this article. The plasma polymerized pyrrole (PPPy) monolayer, plasma polymerized N,N,3,5-tetramethylaniline (PPTMA) monolayer and plasma polymerized pyrrole-N,N,3,5-tetramethylaniline (PPPy-PPTMA) bilayer thin films were deposited at room temperature onto glass substrates by using a parallel plate capacitively coupled glow discharge reactor. The current density-voltage (J-V) characteristics and the conductivity-voltage (σ-V) characteristics have been studied to analyze the direct current conduction mechanism in PPPy, PPTMA monolayer and PPPy-PPTMA bilayer thin films. The observed results have been presented in this paper. The J-V and σ-V characteristics of PPPy and PPTMA monolayer thin films of different thicknesses indicated an increase in electrical conduction and also an increase in conductivity in the films of lower thicknesses. It is also observed that PPTMA thin films are more conductive than that of PPPy thin films. As a result the PPPy-PPTMA bilayer thin films of different thicknesses and different deposition time ratios indicated an increase in conductivity as the proportion of PPTMA is increased in the films. In addition to that, from the J-V and σ-V characteristics of PPPy, PPTMA and PPPy-PPTMA thin films of same thickness, it is observed that the current conduction and the conductivity in the bilayer thin films is less compared to the monolayer thin films. This unusual result has been explained by studying ideal and real bilayer thin films. It is also seen that in the low voltage region, the current conduction obeys Ohm’s law while the charge transport phenomenon appears to be the space charge limited conduction (SCLC) in the higher voltage regions.

НЕРАЗРУШАЮЩИЙ КОНТРОЛЬ СОСТОЯНИЯ МАТЕРИАЛА ПАР ТРЕНИЯ НАСОСОВ УСТАНОВОК ВВЭР

The possibility of using non-destructive methods for monitoring the state of silicon carbide materials in friction pairs of pumps of WWER installations has been experimentally demonstrated which makes it possible to identify potential sites of future possible destruction on the working surface of bearings. The paper describes the methodology for studying the acoustic properties and electrical conductivity of products made of silicon carbide composite. The relationship between the electrical conductivity and acoustic parameters of the material of friction pairs of WWER installations with the characteristics of the microstructure of the material under study has been experimentally established. As the hardware part of the emission and reception of acoustic pulses Krautkramer USN 52 device certified by the State Standard of Russia with emitters and receivers of longitudinal and transverse waves was used. To assess the electrical conductivity a VT2 eddy current electrical conductivity meter with a 5 kHz clamp-on transducer was used which has a pointer transducer with a uniform scale not graduated in electrical conductivity units as an indicator device. Measurements of the electrical conductivity and velocity of longitudinal and transverse waves polarized along the radius at the same points of the working surface of the bearing showed the coincidence of the nature of the change in the measurement results. In this case, if the excess of the value of the velocity of longitudinal waves in the fracture zone over the average value for the entire working surface of the bearing is up to 30%, then for electrical conductivity it is 40%. By measuring the velocities of transverse waves with polarization parallel and perpendicular to the radius, the presence in the material of bearings that have not passed tests under conditions of high pressure and temperature of significant internal stresses provoking the appearance of destruction (chips) on the working surface has been established.

Electrical Transport and Current Conduction Mechanisms in ZnO/Si Heterojunction Diode

Abstract: The objective of this research is the relevant equations of electrical transport inside a junction device based on metallic oxides like zinc oxides retained on silicon substrate by spray pyrolysis process. Many characteristics, such as the heterojunction diode's non-ideal conduct, electronic conduction of electrons and gaps in the conduction and valence bands, charge carriers caught by trap centers, hopping conduction, and tunnel effect, are used in various conduction processes at electronic junctions. Poole-Frenkel (PF) emission, Schottky emissions, and trap aided tunneling are some of the other conduction mechanisms examined inside forward/reverse bias for ZnO/Si heterojunctions (TAT). This article also confirms, addresses, and elucidates the effect of temperature on the I-V properties of ZnO/Si.
 https://ecee.colorado.edu/~bart/book/book/chapter3/ch3_9.htm

Preparation, characterization and super electrocatalytic sensing study of polyaniline@yttrium phosphate (PANI@Y(III)PO4) nanocomposite

Synthesis of Y(III) phosphate-functionalized polyaniline nanocomposite (PANI@Y(III)PO4) was achieved through sol–gel method. The synthesized PANI@Y(III)PO4 was characterized by various techniques including Fourier-transform infrared spectroscopy (FTIR), Field emission scanning electron microscopy (FE-SEM), Energy dispersive X-ray spectroscopy (EDX), X-ray diffraction spectroscopy (XRD), X-ray photoelectron spectroscopy (XPS), Thermogravimetric analysis (TGA)-Differential thermal analysis (TGA-DTA) and direct current (DC) electrical conductivity. Efficient employment for the nanocomposite as modifier glassy carbon electrode was characterized by electrochemical impedance spectroscopy (EIS) and cyclicvoltametry (CV). The modified electrode showed a powerful enhancing effect and great stability in electrochemical sensing of the heavy metal ion Pb(II), giving an anodic peak current with a formal potential of - 0.195 V in acetic solution. The electrochemical parameters of the proposed sensor such as exchange current density (ⅉ0), active surface area of PANI@Y(III)PO4 modified GCE (A), surface coverage (Γ) of Pb (II) on the surface of PANI@Y(III)PO4, transfer coefficient (α) and number of electrons (n) involved in the electro-reduction, were found to be 92.21 μA cm-2, 0.27 cm2, 3.24×10-7 mol cm-2, 0.26 and 1.6 ≈ 2, respectively. Two voltametric techniques namely CV and linear sweep voltammetry (LSV) studies exhibited that the anodic peak current was linearly dependent on the concentration of Pb(II) with a broad dynamic range of 2.85–199.92 μM and 2.85–62.85 μM, respectively. However, the LSV method showed the highest sensitivity (5.58 μA μM-1 Cm-2) and the lowest detection limit (0.04 μM).

Synergistic Effect of Magnetite and Bioelectrochemical Systems on Anaerobic Digestion.

Conventionally, the anaerobic digestion of industrial effluent to biogas constitutes less than 65% methane, which warrants its potential methanation to mitigate carbon dioxide and other anthropogenic gas emissions. The performance of the anaerobic digestion process can be enhanced by improving biochemical activities. The aim of this study was to examine the synergistic effect of the magnetite and bioelectrochemical systems (BES) on anaerobic digestion by comparing four digesters, namely a microbial fuel cell (MFC), microbial electrolysis cell (MEC), MEC with 1 g of magnetite nanoparticles (MECM), and a control digester with only sewage sludge (500 mL) and inoculum (300 mL). The MFC digester was equipped with zinc and copper electrodes including a 100 Ω resistor, whereas the MEC was supplied with 0.4 V on the electrodes. The MECM digester performed better as it improved microbial activity, increased the content of methane (by 43% compared to 41% of the control), and reduced contaminants (carbon oxygen demand, phosphates, colour, turbidity, total suspended solids, and total organic carbon) by more than 81.9%. Current density ( = 25.0 mA/m2) and electrical conductivity (275 µS/cm) were also high. The prospects of combining magnetite and bioelectrochemical systems seem very promising as they showed a great possibility for use in bioelectrochemical methane generation and wastewater treatment.

Influence of tin oxide (SnO2) interlayer on the electrical and reverse current conduction mechanism of Au/n-InP Schottky junction and its microstructural properties

The microstructural and current-voltage (I-V) characteristics of the prepared Au/SnO2/n-InP heterojunction (HJ) with an e-beam evaporated tin oxide (SnO2) film as an interlayer between the Au and InP substrate have been explored. The X-Ray diffraction and transmission electron microscopy results confirm the formation of the SnO2 thin film on InP surface. Then, the Au/SnO2/n-InP HJ diode is prepared and explored its electrical properties by the I-V approach. Low reverse leakage current is noted for HJ diode than the Au/n-InP Schottky junction (SJ). Higher barrier height (BH) is attained for the HJ compared to the SJ, which indicates that the insertion of SnO2 interlayer leads to an increase in the BH of SJ. Further, the BH is evaluated for the SJ and HJ diodes by Hernandez and Cheung's methods and matched with one another. Results exhibit that the interface state density (NSS) of HJ is less than the SJ, suggesting that the use of the SnO2 layer plays a key role in reducing NSS. Analysis of the reverse leakage current transport suggested the dominance of Poole-Frenkel emission in the lower bias region while the Schottky emission mechanism governs at upper bias region in both the SJ and HJ diodes. These results could provide expedient information of SnO2 interlayer for the design of metal/interlayer/semiconductor or heterojunction devices.

Comparative study of the effect of different interlayer thicknesses on frequency dependent electric modulus and conductivity in Au/n-Si structures

Frequency dependent capacitance (C) and conductance (G/ω) data for Au/n-Si structures fabricated at room temperature without interlayers and with 5 nm and 10 nm aluminium-oxide (Al2O3) interlayer thicknesses are investigated. The Al2O3 interlayers were deposited by atomic layer deposition. Data on the complex electric modulus (M*) and alternating current electrical conductivity (σac) values are acquired for the three structures in the 3 kHz-3 MHz frequency range between (-3 V) – (+5 V) bias interval and compared. It was observed that the C and G/ω values decreased with the increase in frequency and interlayer thickness and that the frequency increases as a result of polarization which also increases M*, especially in 5 nm and 10 nm interlayered structures. Frequency and interlayer thickness increment have a positive impact by increasing σac, while conductivity has been shown to be highly sensitive to the presence of an interlayer and to its thickness.

Thermally improved crystalline phase and intercalated PEO/OMMT nanocomposites for high to ultrahigh radio frequency range low‐permittivity nanodielectrics

AbstractPoly(ethylene oxide) (PEO)/organomodified‐montmorillonite (OMMT) nanoclay based nanocomposites having 1, 3, 5, 10, and 20 wt% OMMT nanofiller were prepared by homogeneous mixing and the melt‐compounding method. These hybrid materials were characterized by employing X‐ray diffractometer, differential scanning calorimeter, and radio frequency impedance analyzer. The experimental results confirmed the formation of OMMT intercalated structures with reduced crystallinity and increased melting temperature of PEO crystallites which are predominantly ruled by the nanofiller amounts in the PEO/OMMT nanocomposites. Dielectric permittivity of these nanocomposites measured at 20°C exhibited a gradual decrease with increasing frequencies of the applied harmonic electric field of high to ultrahigh range (i.e., 1 MHz–1 GHz), but it changed anomalously in the range of 2.6–3.6 with the increase of OMMT amounts in the PEO matrix. The dielectric losses in these composites were found low and their loss spectra exhibited a hydrogen bond dipolar reorientation relaxation process around 1 GHz. The alternating current electrical conductivity of these nanocomposites increased with frequency and also changed with the OMMT concentrations. These PEO/OMMT nanocomposites are classified as low permittivity nanodielectrics which could be potential candidates for advances in flexible and biodegradable radio‐electronic devices.

Impedance, FTIR and transport properties of plasticized proton conducting biopolymer electrolyte based on chitosan for electrochemical device application

Biodegradable polymer-based electrolyteswere synthesized through a solution casting technique. Chitosan (CS) as host polymer was plasticized with varying quantities of glycerol after being integrated with 40% ammonium thiocyanate (NH4SCN). The electrochemical behavior of the prepared sampleswas investigated throughelectrochemicalimpedance spectroscopy (EIS). Each of linear sweep voltammetry (LSV) and transference number measurement (TNM) technique were employed to determine the polymer electrolyte’s potential stability and main charger carrier transport. The performance of the fabricated electrical double layer capacitor (EDLC) was analyzed using cyclic voltammetry (CV). Essential parameters, such as specific capacitance (Cs), equivalent series resistance (ESR), efficiency, energy density (Ed), and power (Pd) density, were determined.It has been discovered that adding glycerol as a plasticizer can improve ionic conductivity and its capacitance behavior. Electrical impedance spectroscopy (EIS) was used to evaluate the direct current electrical conductivity of the films, and the electrolyte with the highest glycerol inclusion had the highest ionic conductivity of (8.57 × 10-4 S/cm). Fourier transformed infrared (FTIR) spectroscopy has been used to investigate the compatibility of CS with the electrolyte components. The degree of interactions was demonstrated by the shift and change in the intensity of the FTIR peaks. The breakdown voltage of the polymer electrolyte was identified to be 2.09 V. It was computed and discovered that the ionic transference number (tion) is 0.956, verifying the dominancy of ionic conduction in the electrolyte system. To examine theassembled EDLC, the specific capacitance (Cs) was evaluated and determined as 41.11F/g at the scan rates of 50 mV/swithits initial (Ed) and (Pd) values of 15.56 Whkg−1 and 750 Wkg−1, respectively.

Impedance, structural and thermal analyses of polyvinyl alcohol/polyvinyl pyrrolidone blend incorporated with Li+ ions for lithium-ion batteries

As an attempt to pave the way for developing the lithium polymer batteries, (PVA/PVP) blend filled with different weight percentages of lithium perchlorate (LiClO4) was prepared using solution casting technique. Morphological and microstructural properties of the SPE were studied via SEM, XRD and FT-IR spectroscopy, where its semicrystalline nature was confirmed. Thermal stability, dielectric properties, the relaxation dynamics inside the current system and electrical conduction behavior of the synthesized films were prudently studied. The electrical conduction mechanism inside the samples was interpreted using the Jonscher's double power law. Activation energy was calculated using Coats-Redfern and Broido models. The oblate semicircular arc observed in Nyquist curves indicated the non-Debye behavior of ions relaxation in the present SPE samples. This behavior was assured by the evident decrease in intensity of the M'' relaxation peak. The complex impedance analysis not only verified the dominance of the resistive nature over the capacitance but also demonstrated that the conduction in the SPE was only produced by the induced ions. Mixing LiClO4 filler at 8 wt.% with the PVA/PVP host matrix had a fruitful effect on amelioration in the structural, thermal and dielectric properties of the prepared composite sample. This beneficial enhancement recommends the (PVA/PVP)/LiClO4 composite to be used in fabricating lithium polymer batteries and energy storage devices with high performance.

The Electrical Performances and Leakage Current Conduction Mechanism of Al2O3/ZrO2/SiO2/ZrO2/Al2O3 MIM Capacitors

In this paper, we prepared the Al2O3/ZrO2/SiO2/ZrO2/Al2O3 (AZSZA) metal-insulator-metal (MIM) capacitors by atomic-layer-deposition technique. By increasing the thickness of SiO2 from 0 nm to 3 nm, the quadratic capacitance voltage coefficients improved significantly from 2130 ppm/V2 to −121 ppm/V2 because of the offsetting effects of ZrO2 and SiO2 dielectric. Meanwhile, for our interested SiO2=3nm sample, the capacitance density is 7.40 fF/µm2 and the leakage current density is 3.08 × 10−8 A/cm2 at 5 V. We also studied the leakage current conduction mechanism of AZSZA dielectric MIM capacitors and found that at high field the conduction mechanism was dominated by Poole Frenkel emission.

Enhanced thermoelectric properties of single phase Na doped NaXCoO2 thermoelectric material

Single-phase thermoelectric materials Sodium (Na) doped Cobalt Oxide NaxCoO2 (x = 1, 0.98, 0.96 and 0.94) were synthesized by the sol–gel method. Structural and morphological analysis of the prepared samples revealed excellent phase purity and high crystallinity. We found out that the direct current (DC) electrical conductivity was enhanced with the decrease in Na content, whereas, the thermal conductivity of the prepared samples increased slightly by decreasing the Na concentration. Seebeck coefficient was also increased and consequently, a figure of merit (zT) value of 1.24 was obtained at 1010 K which is about 28% improvement compared to the un-doped sample.

The lithium-ion battery: Study of alternative current conduction mechanisms on the Li3PO4 - based solid electrolyte

Lithium-ion batteries have been dominating as a power source in digital cameras, laptop computers, mobile phones and electric/hybrid electric vehicles. This can be explained by their high life cycle and power density which differentiate them from other battery types. Lithium phosphate is considered among the favored solid electrolyte materials for the lithium-ion battery because of its high ionic conductivity. In this study, Lithium phosphate (Li3PO4) compound was obtained by the classic ceramic method. The X-ray powder diffraction pattern indicates that at room temperature, Li3PO4 crystallized in the orthorhombic system with Pnma space group. The morphology and composition of Li3PO4 were performed by scanning transmission electron microscope coupled with energy dispersive X-ray spectroscopy (STEM-EDS). Infrared spectroscopy was confirmed the presence of (PO4)3− anion and its vibrations. The measurements of the electrical properties were performed in the 100 Hz to 1 MHz frequency range and 528–713 K temperature intervals. The interpretation of Nyquist curves revealed the presence of three electrically active areas equivalent to the electrode processes, distribution of grain boundaries and bulk mechanism. The alternative current electrical conduction in Li3PO4 was interpreted through several processes, which can be associated to two different models: the non-overlapping small polaron tunneling (NSPT) model in the region I and the overlapping large polaron tunneling (OLPT) model in the region II. Elliot's theory was used to interpret the conduction mechanism, and all Elliot's parameters were determined.

Design of potassium ion conducting PVA based polymer electrolyte with improved ion transport properties for EDLC device application

This work presents a report on the preparation of plasticized polyvinyl alcohol PVA-based polymer electrolytes using solution cast technique and their characteristics using a number of electrochemical techniques. Electrical impedance spectroscopy (EIS), linear sweep voltammetry (LSV), and transfer number measurement (TNM) techniques were examined on the prepared films to determine the conductivity, decomposition voltage and ion transference number, respectively. The cyclic voltammetry (CV) and charge-discharging measurements were implemented on an assembled EDLC device to estimate the charge storage process and evaluate the device performance, respectively. The EIS was employed for measuring the direct current (DC) electrical conductivity of the films and calculating the ion transport parameters. The CV and charge-discharging responses were used to estimate the capacitance and stability, respectively. The influence of plasticization on the polymer electrolytes was investigated in terms of electrochemical properties. The TNM measurements were used to determine te and tion respectively. The obtained ionic transference number, tion for the electrolytes incorporated with 40 wt.% and 50 wt.% of glycerol content were found to be 0.969 and 0.944, respectively. The LSV study was used to identify the decomposition voltage of the sample. The absence of redox peaks was proved via CV technique, indicating the mechanism of the charge storing process that comprised ion accumulation at the interfacial region. The initial specific capacitance (Cs) of the fabricated EDLC displayed the value of 152.4 F/g.

High‐performance and cost‐effective melt blended poly(ether ether ketone)/expanded graphite composites for mass production of antistatic materials

AbstractIn this study unfunctionalized expanded graphite (EG) was incorporated into poly(ether ether ketone) (PEEK) using twin‐screw extrusion and injection moulding to manufacture cost‐effective PEEK/EG composites for mass production of high‐performance antistatic materials. Direct current electrical conductivity, morphology, rheological and thermal properties of the composites were investigated. At an EG loading of 5 vol%, the electrical conductivity exhibited an abrupt increase to 1.45 × 10−5 S m−1 which was in the required range of electrical conductivity of antistatic materials. The frequency dependence of the storage modulus of the melt containing 2 vol% EG decreased significantly at low frequencies. Viscosity did not increase much with the addition of EG in comparison with other nanofillers such as carbon nanotubes. The crystallinity of PEEK increased to 41.11% from 35.87% upon addition of 3 vol% EG. EG improved the thermal stability of PEEK by an increase in the initiation temperature of its decomposition steps. © 2021 The Authors. Polymer International published by John Wiley & Sons Ltd on behalf of Society of Industrial Chemistry.

Hibrit olarak alüminyum ve demir elektrotlar kullanarak elektrokoagulasyon prosesleri ile sulu çözeltilerden salisilik asit gideriminin araştırılması

In this study, salicylic acid, an important and widely used micropollutant in the pharmacy sector, removal by electrocoagulation process was investigated. Electrocoagulation and electroflotation processes are commonly used techniques in electrochemical treatment. The type of electrode material employing in electrochemical processes is one of the basic variables which determining the process performance. In the experiments, iron and aluminum plates were employed as a hybrid electrode combination in the electrocoagulation process. The effect of current density, initial pH, electrolysis time, and electrical conductivity were investigated. For this purpose, the current density was 20 A/m2 and 100 A/m2, initial pH 5-8, electrolysis time 2-50 min electrical conductivity 250-1000 µs/cm range and electrode connection type monopolar parallel (MP-P) salicylic acid removal efficiencies from aqueous solutions were investigated during the experimental studies. The best removal results were obtained at pH 6 with a current density of 80 A/m2, solution conductivity of 750 µs/cm, and 40 min of electrolysis time. In these operation conditions, operation cost, amount of sludge, and removal efficiency of salicylic acid were determined as 1.34 $/m3, 0.8 kg/m3, and 91.4%, respectively.

Conductive, adaptive, multifunctional hydrogel combined with electrical stimulation for deep wound repair

• By adjusting crosslinking density of dynamic network obtaining well-adaptive hydrogels. • Adaptive hydrogels with both fluid and solid behavior that filled deep wounds. • The hydrogel exhibited good electroactive that promotes cell proliferation and signaling. • The hydrogel exhibited hemostatic, antibacterial, anti-inflammatory. • The hydrogel-electrostimulation resulted in an efficacy to the all phases of wound healing. To promote wound healing and solve the limitations of current hydrogel wound dressings—that is, they can only cover the surface of deep wounds, leaving a cavity underneath that blocks endogenous and external electrical current conduction—we designed an adaptive conductive hydrogel that spontaneously adapted to the shape of wounds. We prepared this hydrogel by including tannic acid (TA) and human-like collagen (HLC) into polyvinyl alcohol (PVA) and borax hydrogel dynamic crosslinking networks, in which borax functioned as a crosslinker and an ionic conductor. Dynamic crosslinking via borate bonds gave the hydrogel adaptive and self-healing properties. Adding HLC and TA changed both the crosslink density and pH of the hydrogel—and thus adjusted the adaptability of the PVA–borax matrix—and imparted functionalities such as hemostasis, antibacterial, anti-inflammation, cell proliferation, and collagen deposition. We also investigated the potential of this adaptive conductive hydrogel in electrical stimulation (ES) therapy. The adaptive conductive hydrogel perfectly fit the cavity of deep wounds, permitted endogenous and external current conduction, facilitated intercellular signaling as well as current transmission from external electrical stimuli, which promoted cell migration and angiogenesis. The hydrogel dressing / ES treatment strategy facilitated wound healing throughout healing. By day 10, a wound was completely closed, and the subcutaneous tissue (blood vessels and pores) was reconstructed. Hence, the combination of an adaptive conductive hydrogel and ES is a promising strategy for treating deep wounds.

Porosity Evaluation of Additive Manufactured Parts: Ultrasonic Testing and Eddy Current Testing

This study was conducted to investigate the effectiveness of ultrasonic testing (UT) and eddy current testing (ECT) for the porosity evaluation of additive manufactured (AM) parts. AM samples containing different levels of porosity were fabricated at varying laser scanning speeds. The porosity of each sample was evaluated through scanning acoustic microscopy, which was adopted as reference. For UT, the ultrasonic velocity and ultrasonic attenuation coefficient were measured with an ultrasonic contact transducer using the traditional pulse-echo method. For ECT, the electrical conductivity was measured using an eddy current electrical conductivity meter. The relationship between the measured parameters and the porosity content showed that an increase in the porosity content decreased the ultrasonic velocity, increased the ultrasonic attenuation coefficient, and decreased the electrical conductivity. UT was preferred in terms of measurement sensitivity, whereas ECT facilitated a simple setup and high inspection speeds.

Relativistic electric potential near a resting straight carbon nanotube of a finite-length with stationary current

Based on the Lienard – Wiechert potentials for a uniformly and rectilinearly moving electron, a relativistic electric field is studied near a densely filled with potassium atoms single-walled carbon nanotube (K@CNT) with a stationary electric current inside it. The relativistic electric field in the laboratory coordinate system arises (due to the Lorentz transformations) only for a nanotube of a finite length. This field is a result of summation of the Coulomb fields of stationary positively charged ionic cores of potassium and an equal number of ballistically moving valence electrons of potassium that create a current. It is shown that the magnitude of the negative relativistic electric potential of K@CNT in the direction perpendicular to the nanotube does not depend on the direction of the current density. The relationship is obtained between the K@CNT radius and the number of open channels of ballistic electron transfer over potassium atoms. The Landauer formula is used, which relates the number of open quasi-one-dimensional channels and the direct current electrical conduction. For the first time, analytical formulas are obtained for the dependence of the relativistic potential near K@CNT on the electric voltage between the ends of the nanotube and on its radius in the limit of zero absolute temperature. The case is considered when the distance from the point of registration of the relativistic potential above the center of the nanotube is much less than its length. For nanotube with diameter of 2 nm and length of 100 mm, under an external electric field strength of 5 mV/mm, the magnitude of the potential of the relativistic electric field is of about 2 mV. Modern measurement techniques make it possible to register the predicted relativistic potential.